Applied Econometrics ECN 201
Popular in Course
Popular in Economcs
This 49 page Class Notes was uploaded by Sydni D'Amore on Wednesday October 28, 2015. The Class Notes belongs to ECN 201 at Wake Forest University taught by Allin Cottrell in Fall. Since its upload, it has received 12 views. For similar materials see /class/230744/ecn-201-wake-forest-university in Economcs at Wake Forest University.
Reviews for Applied Econometrics
Report this Material
What is Karma?
Karma is the currency of StudySoup.
Date Created: 10/28/15
Economics 201 CottrellLawlor Macroeconomic Time Series The Consumption Function This unit has two prerequisites You should install gretl on your computer You should read the two extracts from Keynes s General Theory available from the class home page 1 Installing gretl 1 Go to the course website httpr39i cardoecnwfueduecn201 Under Basic resourcesquot click on the here of Local Windows download herequot When prompted save the le gretl39i nstall exe to your desktop 2 Go to the desktop and doubleclick on gretl39i nstall exe You ll be asked various questions about the installation It is safe to accept the default choices by pressing OK or hitting the Enter key When the installer has nished running you may delete gretl39i nstall exe you have no more use for it W There should now be a gretl icon on your desktop which you can use to start the program We ll use it shortly 2 Reading Keynes The extracts are from two chapters of Keynes s General Theory Chapter 4 Choice of Unitsquot and Chapter 8 The Propensity to Consumequot Keynes was the most in uential economist of the 20th century and the founder of the branch of the subject now known as macroeconomics Here are some brief notes on what to look for in your reading Choice of Units What s of interest here is Keynes s posing of a sort of data question that should probably be asked more often That is are suchandsuch data really meaningful Do they in fact measure what they are supposed to measure When we see numbers presented to say 6 signi cant digits is the implied precision appropriate or does it go beyond what can reasonably be claimed given how the data were constructed In modern macroeconomic discussions two key variables that are bandied around a lot are real GDPquot and the price levelquot We quite often see long timeseries given for these variables But in this chapter Keynes argues that neither of these measures are wellde ned outside of the short run Apparently most macroeconomists these days think that Keynes was overly scrupulous yet his argu ments deserve attention Think back to introductory macro How do we de ne real output of the US economyquot when the mix of products is changing year by year and changing quite radically decade by decade Keynes comes down in favor of two macroeconomic measures that he claims are less fuzzy than real output and the price level namely sums of money and sums of labortime Question How might one criticize Keynes s idea that hours of laborquot constitute a unit of measure that is truly homogeneous over time Propensity to Consume The part of this discussion that we re most interested in is section 111 pages 12 14 Here Keynes sets out what he claims is a fundamental psychological law namely the people are disposed to increase their consumption as their income increases but not by as much as the increase in their income or in other words that the marginal propensity to consume is positive and less than unity He also suggests that when real income increases an increased proportion of income will be saved not just an increased amount You should also look into section 11 although Keynes emphasizes income as the primary objective factor governing the level of consumption in section II he spells out various additional factors which may play a role Among these he seems to give most weight to factor 3 windfall changes in capital values 3 Keynes and the Data OK now it s time to try to match Keynes s theory up with the data Note however that we will not follow Keynes in working in terms of wageunits Rather we will work in terms of the nowstandard real values of consumption and incomeibut bearing in mind Keynes s comments on the limitations of such data i Start gretl Under the File menu select Browse databases on database server 2 You ll now see a window displaying the various databases on the Economics department server Take a look at what s available for future reference W Select the fedstl database St Louis Federal Reserve Bank Click the Install button below to place a copy of this database on your computer 9 Open the fedstl database From now on you ll be able to nd this database under File Browse databases gretl native iyou don t have to go back to the server each time 5 There are several hundred series in this database We re looking for suitable measures of dis posable income and consumption Hint for our purposes here a good keyword to search on is personal Start a search by clicking the Find menu item continue by clicking Find next 0 Once you ve found suitable series for consumption and income the next step is to import them into gretl s workspace You can do this in any of three ways drag the series from the database window to the main gretl window highlight the series and select Import from the Series menu in the database window or rightclick and select Import from the popup menu 7 The names of the imported series are a bit cryptic For graphing it would be nice to have more comprehensible labels Select the income variable in the gretl main window and rightclick Select Edit attributes from the popup menu Give the variable a display name of income Do the same for the consumption variable giving it a display name of consumption Now select both variables you can do this with a mouse drag rightclick and select Time series plot Think about what you see Does it look to be compatible with what Keynes said It there anything else noteworthy about the graph Note that you can click on the graph window for a menu that lets you do various things including zooming and copying the graph to the clipboard from where you can put it into Word 9 Now let s take a different view At the foot of the main gretl window there s a toolbar Click on the little graph icon to de ne an X Y scatter plot Which variable should go on the X axis and which on the Y Once you ve gured that create the plot You ll notice that when gretl draws the scatter it automatically adds a line of best t actually it does this only if the straight line of best t provides a reasonably good t to the scatter Comment on the degree of t in this case 10 In this plot we can t see if the line of best t has a positive zero or negative Y intercept1 Click on the graph for the popup menu and select Edit Click on the Xaxisquot tab and set the minimum to 0 Click Apply and get the dialog box out of the way Any comments At this point it might be nice to put some numbers to the line of best t that was shown on the consumption income scatter plot Here s how I From gretl s Model menu select Ordinary Least Squares Select the consumption variable as dependent doubleclicking on the variable name is a shortcut for this action Select the income variable as the independent rightclicking on the variable name is a shortcut Click OK 2 Whoa There s a bunch of statistics in the window that appears We ll concentrate on just a few of them The COEFFICIENT column in effect shows the equation of the line The coefficient for const is the Y intercept and the coefficient for the income variable is the slope in this example the marginal propensity to consume Think about these numbers and comment At the righthand end of the rows in the coefficient table are some stars These indicate statistical signi cancequot Roughly if a variable has two or three stars at the end of its row that s saying you d be very unlikely to get a measured coefficient like the one shown if the true effect were zero In other words we can be con dent the true coefficient is not zero In this case we can be con dent it seems a that the true intercept is not zero and b that there really is an upwardsloping relationship between income and consumption reallyquot that is as opposed to this just being a luck of the drawquot effect in the sample we re looking at 4 The average propensity to consume What s the deal with the intercept of the consumption function Take literally it seems to mean the level of consumption that would take place if disposable income were zeroquot Viewed in this way it doesn t seem to make sense that the intercept should be anything other than zero For each individual household if income is zero they can t keep on consuming for very long they could for a short while by running down past saving so a positive intercept seems to be out But a negative intercept seems even worse Negative consumption would have to mean selling off not buying consumer goods This could not go on for long either Then consider the fact that the macroeconomic consumption function is an aggregate relationship Particular households might have an income of zero from time to time but could aggregate disposable income ever be zero That would mean that the economy had completely imploded in which case all bets would be off regarding consumer behavior To make sense of the intercept don t think of it as predicted consumption when income is zero Its mathematical role is to allow for the possibility that the fraction of income that people consume is not constant but varies with the level of income In general the consumption function can be written as C a hY where a is the intercept and h the slope The slope is also known as the marginal propensity to consume MPC for short and it represents the fraction that consumers will spend out of any increment to their income The average propensity to consume APC for short on the other hand is the ratio CY L E b Y Suppose a is positive That means that the APC is greater than the MPC As Y increases aY falls so the APC also falls Now consider a negative a That would mean that the APC is less than the MPC but it increases as income rises The tables below illustrate this idea The two functions are calibrated to give the same level of consumption and an APC of 91 percent out of an income of 5000 Notice how the function with a gt 0 on the left shows a decline in the APC as income rises while the one on the right with a lt 0 shows the APC rising with income 1Note that the x axis does not start at zero C30085Y C730097Y Y C CYAPC Y C CYAPC 2000 2000 1000 2000 1640 0820 3000 2850 0950 3000 2610 0870 4000 3700 0925 4000 3580 0895 5000 4550 0910 5000 4550 0910 6000 5400 0900 6000 5520 0920 7000 6250 0893 7000 6490 0927 8000 7100 0888 8000 7460 0933 Keynes was concerned with the possibility that the APC would fall with rising income This would imply an increasing gap by which consumption falls short of income as the economy grows If the economy is not to fall into underemployment this gap must be plugged by investment spending Keynes was worried that it would become progressively harder to nd enough pro table investment opportunities to plug the increasing gap Investment would have to increase as a percentage of GDP but would there be suf cient incentive for this to occur If not a rich economy would have a perennial tendency towards unemployment On the other hand if the intercept of the consumption function is negative and hence the APC rises with increasing income the problem that Keynes perceived seems less worrisome Is it really the case that the US consumption function has a negative intercept so that the APC in creases with income contrary to Keynes s fears If one doubts this what alternative hypothesis might one propose Recall that Keynes did not say income was the only factor governing consumptionihe speci cally mentioned changes in wealth as another factor In the assignment to follow we will explore this possibility DEFINITIONS OF VARIABLES IN OECD HEALTH DATASET Expenditure on health Total expenditure on health is de ned as the sum of expenditure on ac tivities thatithrough application of medical paramedical and nursing knowledge and technologyi has the goals of 0 Promoting health and preventing disease 0 Curing illness and reducing premature mortality 0 Caring for persons affected by chronic illness Who require nursing care 0 Caring for persons With healthrelated impairments disability and handicaps Who require nursing care 0 Assisting patients to die With dignity 0 Providing and administering public health Providing and administering health programmes health insurance and other funding arrange ments With this boundary general public safety measures such as technical standards monitoring and road safety are not considered as part of expenditure on healt I Activities such as food and hygiene control and health research and development are considered healthrelated but are not included in total health expenditure Expenditures on those items are reported separately in the chapter on healthrelated functions Health can be divided into the following functional components of health care HC and health carerelated HCIR items according to the International Classi cation for Health Accounts ICHA Which is presented in the OECD manual A System of Health Accounts77 SHA www0ecd org ENdocument O ENdocument684 5no27245080 00htm1 HCIl Services of curative care HCIQ Services of rehabilitative care HCIS Services of longterm nursing care HCI4 Ancillary services to health care HCI5 Medical goods dispensed to outpatients HCIliHCIS Total expenditure on personal health HCI6 Services of prevention and public health HCI7 Health administration and health insurance HCI6 HCI7 Total expenditure on collective health HCIliHCI7 Total current expenditure HCIRIl Investment gross capital formation in health HCIliHCJ HCIRIl TOTAL EXPENDITURE ON HEALTH Further health carerelated items1 HCIRIZ Education and training of health personnel WECDSHA de nition of Total expenditure on health HCR3 Research and development in health HCR4 Food hygiene and drinking water control HCR5 Environmental health HCR6 Administration and provision of social services in kind to assist living with disease and impairment HCR7 Administration and provision of healthrelated cashbene ts Gross domestic product Gross domestic product is an aggregate measure of production equal to the sum of the gross values added of all resident institutional units engaged in production plus any taxes and minus any subsidies on products not included in the value of their outputs The sum of the nal uses of goods and services all uses except intermediate consumption measured in purchasers7 prices less the value of imports of goods and services or the sum of primary incomes distributed by resident producer units Sources 8 Methods OECD National Accounts Paris published annually Extracted 22 April Life expectancy at birth Life expectancy at birth also given for ages 40 60 65 and 80 is the average number of years that a person at that age can be expected to live assuming that agespeci c mortality levels remain constant Sources 8 Methods For the 22 European countries the Eurostat NewCronos database is the main data source for 1985 onwards Note Life expectancy at birth for the total population is estimated by the OECD Secretariat for all countries using the unweighted average of life expectancy of men and women Australia Australian Bureau of Statistics Deaths Australia Cat No 33020 Canberra ABS Infant mortality The number of deaths of children aged under one year of age that occurred in a given year expressed per 1000 live births Sources and Methods For the 22 European countries the main data source is the Eurostat New Cronos database Compensated absence from work due to illness The number of compensated work days lost per year due to illness per employed person Sources 8 Methods A 39 39 39 sources A quot f r quot absence from work due to illness eg social security public or private insurance agencies Please note that differences in the coverage of the working population and in reporting systems limits the comparability of data across countries Practising physicians The number of physicians general practitioners and specialists including selfemployed who are actively practicing medicine in public and private institutions The data should exclude dentists stomatologists quali ed physicians who are working abroad working in administration research and industry positions Data should include foreign physicians licensed to practice and actively practicing medicine in the country Practising nurses Total number of nurses certi edregistered and actively practicing in public and private hospitals clinics and other health facilities including selfemployed Nursing assistants and midwives should be included Data should exclude nurses who are working abroad working in administrative research and industry positions Computed tomography scanners Number of computed tomography CT scanners also known as CAT7 scans for Computed Axial Tomography CT scanners image anatomical information from a cross sectional plane of the body Each image is generated by a computer synthesis of xray transmission data obtained in many different directions in a given planer Sources 8 Methods The de nition is based on Stedmanls Concise Medical Dictionary for the Health Professions 1997 Number of magnetic resonance imaging MRI units Note that MRI refer to a diagnostic modality in which the magnetic nuclei especially protons of a patient are aligned in a strong uniform magnetic eld absorb energy from tuned radio frequency pulses and emit radio frequency signals as their excitation decaysi These signals which vary in intensity according to nuclear abun dance and molecular chemical environment are converted into sets of tomographic images by using eld gradients in the magnetic eld which permit 3D localization of the point sources of the signals Unlike conventional radiography or CT MRI does not expose patients to ionizing radiation Sources 8 Methods The de nition is based on Stedmanls Concise Medical Dictionary for the Health Professions 1997i Mammographs Number of dedicated mammography machines those designed exclusively for taking mammograms Health care coverage Share of population eligible for health care bene ts inkind under public programmesi This series gives the share of the population which is eligible to health care goods and services that are included in total public health expenditure Coverage in the sense of this index is therefore independent of the scope of costsharing For the USA these estimates are the results of a household survey that collects information on health care coverage The de nition of this series is persons covered by Medicaid Medicare and military health care for active military and their families including care for retired military and veterans Total sulphur oxide emissions Manmade emissions of sulphur oxides SOx expressed in tonnes 000 and kilograms per capita Sulphur oxides SOx exert pressure on human health they also contribute to acid deposition and thus have negative effects on aquatic ecosystems and buildings and may have negative effects on crops and forests Data are given as quantities of S02 Alcohol consumption Alcohol consumption in liters per capita age 15 Annual consumption of pure alcohol in liters per person aged 15 years and over Economics 201 Economic Data Analysis CottrellLawlor A Reader s Guide to the Keynes on the Consumption Function Keynes proposed a theory of the output level of the economy as a whole in his General Theory of Employment Interest and Money 1936 It is no exaggeration to say that this book transformed the world of economics Today we take the macroeconomics that he created for granted and do not notice that many of its characteristic ways of thinking were originally quite controversial One such tool of macroeconomics today is the data convention of dividing total output of the economy into spending on consumption and investment To Keynes his insights into what caused consumption to change was of such fundamental importance to him that he enshrined it in a formulaic relationship that he dubbed the consumption function And because this consumption function s behavior determined how unstable output would be under changing investment levels he called this characteristic a Fundamental Psychological Law In our short excursion into the data analysis of this relationship we are most interested in how to formulate and express both consumption data and its determinants As you will see below Keynes was intensely interested in the same issues In his day though national data on the economy s output such as we also take for granted with the wide availability of the National Income and Product Accounts were still in their infancy Our excerpts from the General Theory see Keynes exploring two issues 1 What units are appropriate to a macroeconomic level of analysis 2 What variables that are causally related to aggregate consumption Chapter 4 The Choice of Units What s of interest here is Keynes s posing of a sort of data question that should probably be asked more often That is are suchandsuch data really meaningful Do they in fact measure what they are supposed to measure When we see numbers presented to say 6 signi cant digits is the implied precision appropriate or does it go beyond what can reasonably be claimed given how the data were constructed In modern macroeconomic discussions two key variables that are bandied around a lot are real GDP and the price level We quite often see long timeseries given for these variables But in this chapter Keynes argues that neither of these measures are well defined outside of the short run Apparently most macroeconomists these days think that Keynes was overly scrupulous yet his arguments deserve attention Think back to introductory macro How do we de ne real output of the US economy when the mix of products is changing year by year and changing quite radically decade by decade Keynes comes down in favor of two macroeconomic measures that he claims are less fuzzy than real output and the price level namely sums of money and sums of labortime Question How might one criticize Keynes s idea that hours of labor constitute a unit of measure that is truly homogeneous over time Chapter 8 The Propensity to Consume I The Objective Factors Returning to the main theme of his book after the Book II excursions into units and expectations Keynes is again taking up the question of what determines the volume of employment So far he has characterized it in general as determined by the aggregate supply and demand functions He emphasizes he is mainly interested in aggregate demand since supply can be assumed familiar to economists particularly those brought up on the classical teachings In Book I he de ned aggregate demand as made up of the proceeds expected from sums spent on consumption and investment Since the factors which govern these quantities are largely distinct they will be treated separately starting in this section Book III with the factors governing consumption followed by a discussion of investment Book IV The proper units in which the aggregate demand for consumption should be considered are the sum spent on consumption C in money and the level of employment N For us as modern readers of Keynes it is more intuitively natural to think of C in real terms as a function of real income All of the casting of his argument in wage unit terms is Keynes peculiar method of converting nominal values into real values by deflating them by an index of the cost of a unit of labor Cataloguing the argument to come then Keynes claims that an inclusive list of all the possible in uences on C are i the amount of aggregate income ii other objective factors and iii the subjective needs and psychology of the public and the distribution of income Although in fact these are all tied up together we can for purposes of analysis divide them up for separate analysis This is the rationale for the division of this chapter and the next In general the assumption is that matters of social custom taste and historical circumstance will figure largely into the amount that a country consumes out of a given income but that these subjective factors can be considered the product of past social evolution and can for the short period be considered given and stable This leaves the determination of the level of investment open to the objective factors 11 This section is Keynes catalogue of objective factors capable of affecting the level of consumption spending 1 A change in the wage unit This essentially refers to the issue of nominal versus real wages If the wage unit changes and so the real value of a given money wage change then consumption will be effected As long as the consumption function is defined for real income and real consumption this matter is taken care of 2 The difference between income and net income This is a matter of accounting for depreciation in the definition of national income recall GNP versus NNP in our review of the NIPA categories It is a trivial point don t waste your time on it 3 Windfall changes in capital values This relates to the idea of changes in wealth affecting the propensity to consume out of a given income An example would be for instance the effect of the recent stock market crash on consumption spending Does the fact that financial balance sheets are dramatically altered a windfall with no change in current income alter the amount of spending out of income Keynes thinks it is quite possible that this may be important But recent experience tends to show a prominent example of this The spending of wealthy US income earners was recently greatly extended by the late nineties runup of stock prices So far during this recession the downward effect on consumption of the collapse of stock prices since 2000 has been a worry of the Federal Reserve It s dramatic lowering of short term interest rates may have offset this depressing effect for the last two year particularly by fueling a vast amount of home mortgage refinancing Thus even though the recovery has yet to show itself and will not do so until private investment spending resumes the cheeriest macro news of the last two year has been the American consumer spending levels The worry about this trend is that it is coming at the cost of increasing consumer indebtedness Unless growth returns to levels consistent with lower unemployment this could come back to haunt us 4 Changes in time preference Here Keynes is taking on the classical theory of consumption and saving By that account all such intertemporal decisions were just a matter of the preferred rate of trading current consumption for future consumption Elsewhere in the book Keynes rails against this doctrine particularly its unthinking presumption that total output is constant while such changes in savings and consumption are worked out He felt this led to a disastrous neglect of the fact that output did indeed change and that such changes were not the result of changes in time preference mainly but of changes in current levels of activity of real output and employment changing Keynes s final assessment The in uence of this factor on the rate of spending out of a given income is open to a good deal of doubt 5 Changes in fiscal policy This essentially refers to the idea of taxation and government spending In general Keynes view is that income taxation will increase the propensity to consume in two ways If the return from saving is to be taxed away there is less inducement to save And if the proceeds of taxation constitute a redistribution scheme from low income high propensity to consume groups to high income low propensity to consume groups this will increase aggregate consumption out of any given level of income 6 Changes in expectations of the relation between present and future income This falls under the heading of lifecycle plans for consuming and saving Some age groups will save more than others Generally it is considered by Keynes to cancel out at the aggregate level But thinking of the current disparity in age groups associated with the baby boom phenomena this may be more relevant today Considering all of these taken together We are left therefore with the conclusion that in a given situation the propensity to consume may be considered a fairly stable function provided we have eliminated changes in the wage unit in terms of money The fact that given the general economic situation the expenditure on consumption in terms of the wage unit depends in the main on the volume of output and employment is the justification for summing up the other factors in the portmanteau function the propensity to consume pp 1112 111 Given that the propensity to consume can be a fairly stable function C CY etc the next question is what is the shape of this function Keynes takes it on intuition and casual observation that it will exhibit a characteristic which turns out to be so important for this theory that he dubs it his Fundamental Psychological Law The fundamental psychological law upon which we are entitle to depend with great confidence both a priori from our knowledge of human nature and from the detailed facts of experience is that men are disposed as a rule and on the average to increase their consumption as their income increases but not by as much as the increase in their income As we have seen from our own development of the consumption function Keynes insight here was quite sound In literally thousands of empirical studies the slope of the consumption function the marginal propensity to consume is found to be positive and less than one Keynes also feels that this slope may taper off at high income levels both across income classes but more importantly for the community as a whole Thus a more wealthy community will save a greater proportion of its income than a less wealthy one This is interesting but not essential All that the rest of this theory will require is the range of the marginal propensity to stay within the bounds set by the fundamental psychological law IV This section is a diatribe based on the consumption function against the notion prevalent in the 30s that the only way to fight the depression was by a policy of sound finance This need not concern us at this stage so just skim this section What is perhaps most interesting is the data tables on the collapse of investment in the 30s Looking at this it is easy to see how Keynes came to regard uctuations in business investment spending as the major source of cyclical macroeconomics performance Do read pages 104 to 106 though as they are a very nicelydone summary of the issues raised in this chapter Particularly at the end there is a strong sense in this chapter of the ever present in uence of time on the economic problem Discontinuous capitalistic production requires future provision from production today of capital goods to capture the enormous productivity of the division of labor Thus we get Keynes twist on the great theme of economics from Adam Smith onwards the important role of saving and accumulating for productivity and growth The provision for the future is only beneficial today Keynes is telling us if it can generate enough employment to keep past provisioned capital and labor at work The greater the productivity of the vast economic machine in potential the greater the risk of partial idleness of that machine in actuality This paradoxical potential for idleness is Keynes explanation of poverty in the midst of plenty Further this potential for idleness is exacerbated if the financial forms of saving for the future have no definite counterpart in the real provision for the future Hence thrift in and of itself is no good What is needed is production and consumption Extracts from Tbs General Tyeary ofEmpZoymem Im erm and Money by John Maynard Keynes London Macmillan 1936 Chapter 4 pp 37744 and Chapter 8 pp 89798 footr notes omitted CHAPTER4 THE CHOICE OF UNITS I IN this and the next three chapters we shall be occupied with an attempt to clear up certain perplexities which have no peculiar or exclusive relevance to the problems which it is our special purpose to examine Thus these chapters are in the nature of a digression which will prevent us for a time from pursuing our main theme Their subjectrmatter is only discussed here because it does not happen to have been already treated elsewhere in a way which I nd adequate to the needs of my own particular enquiry The three perplexities which most impeded my progress in writing this book so that I could not express myselfconver niently until I had found some solution for them are rstly the choice of the units of quantity appropriate to the probe lems of the economic system as a whole secondly the part played by expectation in economic analysis and thirdly the de nition of income 11 That the units in terms of which economists commonly work are unsatisfactory can be illustrated by the concepts of the National Dividend the stock of real capital and the general pricerlevel 7 i The National Dividend as de ned by Marshall and Professor Pigou measures the volume of current output or real income and not the value of output or moneyrincome Furthermore it depends in some sense on net output 7 on the net addition that is to say to the resources of the community available for consumption or for retention as capital stock due to the economic activities and sacri ces of the current period after allowing for the wastage of the stock of real capital existing at the commencement of the period On this basis an attempt is made to erect a quantitative science But it is a grave objection to this de nition for such a purpose that the community s output of goods and services is a nonrhomogeneous complex which cannot be measured strictly speaking except in certain special cases as for example when all the items of one output are included in the same proportions in another output ii The dif culty is even greaterwhen in order to calculate net output we try to measure the net addition to capital equipment for we have to nd some basis for a quantitative comparison between the new items of equipment produced during the period and the old items which have perished by wastage In order to arrive at the net national dividend Professor Pigou deducts such obsolescence etc as may fairly be called normal and the practical test of normality is that the depletion is suf ciently regular to be foreseen if not in detail at least in the largequot But since this deduction is not a deduction in terms ofmoney he is involved in assuming that there can be a change in physical quantity although there has been no physical change Le he is covertly introducing changes in value Moreover he is unable to devise any satisfactory formula to evaluate new equipment against old when owing to changes in technique the two are not identical I believe that the concept at which Professor Pigou is aiming is the right and appropriate concept for economic analysis But until a sate isfactory system ofunits has been adopted its precise de ne ition is an impossible task The problem of comparing one real output with another and of then calculating net output by setting off new items of equipment against the wastage of old items presents conundrums which permit one can con dently say of no solution iii Thirdly the wellrknown but unavoidable element of vagueness which admittedly attends the concept of the general pricerlevel makes this term very unsatisfactory for the purposes of a causal analysis which ought to be exact Nevertheless these dif culties are rightly regarded as cor nundrumsquot They are purely theoreticalquot in the sense that they never perplex or indeed enter in any way into busir ness decisions and have no relevance to the causal sequence of economic events which are clearrcut and determinate in spite of the quantitative indeterminacy of these concepts It is natural therefore to conclude that they not only lack precision but are unnecessary Obviously our quantitative analysis must be expressed without using any quantitatively vague expressions And indeed as soon as one makes the attempt it becomes clear as I hope to show that one can get on much better without them The fact that two incommensurable collections ofmiscelr laneous objects cannot in themselves provide the material for a quantitative analysis need not of course prevent us from making approximate statistical comparisons depending on some broad element ofjudgment rather than of strict calr culation which may possess signi cance and validity within certain limits But the proper place for such things as net real output and the general level of prices lies within the eld of historical and statistical description and their purpose should be to sate isfy historical or social curiosity a purpose for which perfect precisionisuch as our causal analysis requires whether or not our knowledge of the actual values of the relevant quanr tities is complete or exactiis neither usual nor necessary To say that net output today is greater but the price elevel lower than ten years ago or one year ago is a proposition ofa similar character to the statement that Qieen Victoria was a better queen but not a happier woman than Qieen Elizabethia proposition not without meaning and not without interest but unsuitable as material for the differential calculus Our precision will be a mock precision ifwe try to use such partly vague and nonrquantitative concepts as the basis of a quanr titative analysis 111 On every particular occasion let it be remembered an entrepreneur is concerned with decisions as to the scale on which to work a given capital equipment and when we say that the expectation of an increased demand Le a raising of the aggregate demand function will lead to an increase in aggregate output we really mean that the rms which own the capital equipment will be induced to associate with it a greater aggregate employment of labour In the case of an individual rm or industry producing a homogeneous product we can speak legitimately ifwe wish of increases or decreases of output But when we are aggregating the active ities ofall rms we cannot speak accurately except in terms of quantities of employment applied to a given equipment The concepts ofoutput as awhole and its pricerlevel are not required in this context since we have no need of an absolute measure of current aggregate output such as would enable us to compare its amount with the amount which would result from the association of a different capital equipment with a different quantity of employment When for purposes of description or rough comparison we wish to speak of an increase of output we must rely on the general presumpr tion that the amount of employment associated with a given capital equipment will be a satisfactory index of the amount of resultant output ithe two being presumed to increase and decrease together though not in a de nite numerical proportion In dealing with the theory of employment I propose therefore to make use of only two fundamental units of quantity namely quantities of moneyrvalue and quantities of employment The rst of these is strictly homogeneous and the second can be made so For in so far as differ ent grades and kinds of labour and salaried assistance enjoy a more or less xed relative remuneration the quantity of employment can be suf ciently de ned for our purpose by taking an hour s employment of ordinary labour as our unit and weighting an hour s employment of special labour in proportion to its remuneration is an hour of special labour remunerated at double ordinary rates will count as two units We shall call the unit in which the quantity ofemployment is measured the labourrunit and the moneyrwage of a labour unit we shall call the wagerunit Thus ifE is the wages and salaries bill W the wagerunit and N the quantity of employment E NW This assumption ofhomogeneity in the supply oflabour is not upset by the obvious fact ofgreat differences in the sper cialised skill of individual workers and in their suitability for different occupations For if the remuneration of the work ers is proportional to their ef ciency the differences are dealt with by our having regarded individuals as contributing to the supply of labour in proportion to their remuneration whilst if as output increases a given rm has to bring in labour which is less and less ef cient for its special purposes per wagerunit paid to it this is merely one factor among others leading to a diminishing return from the capital equipment in terms of output as more labour is employed on it We subsume so to speak the nonrhomogeneity of equally rer munerated labour units in the equipment which we regard as less and less adapted to employ the available labour units as output increases instead of regarding the available labour units as less and less adapted to use a homogeneous capir tal equipment Thus if there is no surplus of specialised or practised labour and the use of less suitable labour involves a higher labour cost per unit of output this means that the rate at which the return from the equipment diminishes as employment increases is more rapid than it would be ifthere were such a surplus Even in the limiting case where differ ent labour units were so highly specialised as to be altogether incapable of being substituted for one another there is no awkwardness for this merely means that the elasticity of supply of output from a particular type of capital equipment falls suddenly to zero when all the available labour specialised to its use is already employed Thus our assumption ofa hoe mogeneous unit oflabour involves no dif culties unless there is great instability in the relative remuneration of different labourrunits and even this dif culty can be dealt with ifit arises by supposing a rapid liability to change in the supply of labour and the shape of the aggregate supply function It is my belief that much unnecessary perplexity can be avoided ifwe limit ourselves strictly to the two units money and labour when we are dealing with the behaviour of the economic system as a whole reserving the use of units of particular outputs and equipments to the occasions when we are analysing the output of individual rms or industries in isolation and the use of vague concepts such as the quantity of output as a whole the quantity of capital equipment as a whole and the general level of prices to the occasions when we are attempting some historical comparison which is within certain perhaps fairlywide limits avowedly unprecise and approximate It follows that we shall measure changes in current outr put by reference to the number of hours of labour paid for whether to satisfy consumers or to produce fresh capir tal equipment on the existing capital equipment hours of skilled labour being weighted in proportion to their remur neration We have no need of a quantitative comparison between this output and the output which would result from associating a different set ofworkers with a different capital equipment To predict how entrepreneurs possessing a given equipment will respond to a shift in the aggregate demand function it is not necessary to know how the quantity of the resulting output the standard of life and the general level of prices would compare with what they were at a different date or in another country CHAPTER 8 THE PROPENSITY TO CONSUME I THE OBJECTIVE FACTORS I We are now in a position to return to our main theme from which we broke offat the end ofBookT in order to deal with certain general problems of method and de nition The aggregate demand function relates any given level of employment to the proceeds which that level of employ ment is expected to realise The proceeds are made up of the sum of two quantitiesithe sum which will be spent on consumption when employment is at the given level and the sum which will be devoted to investment The factors which govern these two quantities are largely distinct In this book we shall consider the former namely what factors determine the sum which will be spent on consumption when employ ment is at a given level and in Book TV we shall proceed to the factors which determine the sum which will be devoted to investment The amount that the community spends on consumption obviously depends partly on the amount of its income ii partly on the other objective attendant circumstances and iii partly on the subjective needs and the psychological propensities and habits of the individuals composing it and the principles on which the income is divided between them which may suffer modi cation as output is increased The motives to spending interact and the attempt to classify them runs the danger of false division Nevertheless it will clear our minds to consider them separately under two broad heads which we shall call the subjective factors and the objective factors The subjective factors which we shall consider in more detail in the next chapter include those psychological characteristics of human nature and those social practices and institutions which though not unalterable are unlikely to undergo a material change over a short period of time except in abnormal or revolutionary circumstances In an historical enquiry or in comparing one social system with another ofa different type it is necessary to take account of the manner in which changes in the subjective factors may affect the propensity to consume But in general we shall in what follows take the subjective factors as given and we shall assume that the propensity to consume depends only on changes in the objective factors 11 The principal objective factors which in uence the propensity to consume appear to be the following I A emnge in tbe wagerunit Consumption C is obi viously much more a function of in some sense 7eaZ inr come than of moneyrincome In a given state of technique and tastes and of social conditions determining the distribr ution of income a man s real income will rise and fall with the amount of his command over labourrunits ie with the amount of his income measured in wage runits though when the aggregate volume of output changes his real income will owing to the operation of decreasing returns rise less than in proportion to his income measured in wagerunits As a rst approximation therefore we can reasonably assume that ifthe wagerunit changes the expenditure on consum 7 tion corresponding to a given level of employment will like prices change in the same proportion though in some cir cumstances we may have to make an allowance for the pose sible reactions on aggregate consumption of the change in the distribution of a given real income between entreprer neurs and rentiers resulting from a change in the wagerunit Apart from this we have already allowed for changes in the wagerunit by de ning the propensity to consume in terms of income measured in terms ofwagerunits 214 emnge in tbe d ereme between income and net income We have shown above that the amount of consumption der pends on net income rather than on income since it is by de nition his net income that a man has primarily in mind when he is deciding his scale ofconsumption In a given site uation there may be a somewhat stable relationship between the two in the sense that there will be a function uniquely relating different levels ofincome to the corresponding levr els of net income If however this should not be the case such part of any change in income as is not re ected in net income must be neglected since it will have no effect on consumption and similarly a change in net income not re ected in income must be allowed for Save in exceptional circumstances however I doubt the practical importance of this factor We will return to a fuller discussion of the effect on consumption of the difference between income and net income in the fourth section of this chapter 3 Windfall Manger in capitaZr MZuex not allowedfm in calf whiting net income These are of much more importance in modifying the propensity to consume since theywill bear no stable or regular relationship to the amount of income The consumption of the wealthrowning class may be extremely susceptible to unforeseen changes in the moneyrvalue of its wealth This should be classi ed amongst the major factors capable ofcausing shortrperiod changes in the propensity to consume 4 Cyzmgex in tbe mtg aftimerdixcaunting is in tbe mtia of ext31mg betweenprexmz goadx andfutme goody This is not quite the same thing as the rate of interest since it allows for future changes in the purchasing power ofmoney in so far as these are foreseen Account has also to be taken of all kinds ofrisks such as the prospect of not living to enjoy the future goods or of con scatory taxation As an approximation however we can identify this with the rate of interest The in uence of this factor on the rate of spending out ofa given income is open to a good deal of doubt For the classical theory of the rate of interest which was based on the idea that the rate of interest was the factor which brought the supply and demand for savings into equilibrium it was convenient to suppose that expenditure on consumption is 551 pm negatively sensitive to changes in the rate of interest so that any rise in the rate of interest would appreciably dir minish consumption It has long been recognised however that the total effect of changes in the rate of interest on the readiness to spend on present consumption is complex and uncertain being dependent on con icting tendencies since some of the subjective motives towards saving will be more easily satis ed ifthe rate ofinterest rises whilst others will be weakened Over a long period substantial changes in the rate ofinterest probably tend to modify social habits considerably thus affecting the subjective propensity to spendithough in which direction itwould be hard to say except in the light of actual experience The usual type of shortrperiod uctuation in the rate of interest is not likely however to have much direct in uence on spending either way There are not many people who will alter their way of living because the rate of interest has fallen from 5 to 4 per cent if their aggregate income is the same as before lndir rectly there may be more effects though not all in the same direction Perhaps the most important in uence operating through changes in the rate of interest on the readiness to spend out ofa given income depends on the effect of these changes on the appreciation or depreciation in the price of securities and other assets For ifa man is enjoying a wind fall increment in the value of his capital it is natural that his motives towards current spending should be strengthened even though in terms ofincome his capital is worth no more than before and weakened if he is suffering capital losses But this indirect in uence we have allowed for already under 3 above Apart from this the main conclusion suggested by experience is I think that the shortrperiod in uence of the rate of interest on individual spending out of a given income is secondary and relatively unimportant except per haps where unusually large changes are in question When the rate of interest falls very low indeed the increase in the ratio between an annuity purchasable for a given sum and the annual interest on that sum may however provide an impor tant source of negative saving by encouraging the practice of providing for old age by the purchase of an annuity The abnormal situation where the propensity to consume may be sharply affected by the development of extreme uni certainty concerning the future and what it may bring forth should also perhaps be classi ed under this heading 5 Cyzmgex in rmZpaZiey In so far as the inducement to the individual to save depends on the future return which he expects it clearly depends not only on the rate of inr terest but on the scal policy of the government lncome taxes especially when they discriminate against unearned income taxes on capitalrpro ts deathrduties and the like are as relevant as the rate ofinterest whilst the range ofposr sible changes in scal policy may be greater in expectation at least than for the rate ofinterest itself lf scal policy is used as a deliberate instrument for the more equal distribution of incomes its effect in increasing the propensity to consume is of course all the greater We must also take account of the effect on the aggregate propensity to consume of government sinking funds for the discharge of debt paid for out of ordinary taxation For these represent a species of corporate saving so that a policy of substantial sinking funds must be regarded in given cir cumstances as reducing the propensity to consume It is for this reason that a changerover from a policy of government borrowing to the opposite policy ofproviding sinking funds or wire vemz is capable ofcausing a severe contraction or marked expansion of effective demand 6 Cyzmgex in expectatiom aftbe relation between tyeprexem and tyefuz me e veZ afimome We must catalogue this factor for the sake offormal completeness But whilst it may affect considerably a particular individual s propensity to consume it is likely to average out for the community as a whole Moreover it is a matter about which there is as a rule too much uncertainty for it to exert much in uence We are left therefore with the conclusion that in a given situation the propensity to consume may be considered a fairly stable function provided that we have eliminated changes in the wagerunit in terms of money Windfall changes in capitalrvalues will be capable of changing the propensity to consume and substantial changes in the rate of interest and in scal policy may make some difference but the other objective factors which might affect it whilst they must not be overlooked are not likely to be important in ordinary circumstances The fact that given the general economic situation the expenditure on consumption in terms of the wagerunit der pends in the main on the volume ofoutput and employment is the justi cation for summing up the other factors in the portmanteau function propensity to consume For whilst the other factors are capable of varying and this must not be forgotten the aggregate income measured in terms of the wagerunit is as a rule the principal variable upon which the consumptionrconstituent of the aggregate demand function will depend III Granted then that the propensity to consume is a fairly stable function so that as a rule the amount of aggregate consumption mainly depends on the amount of aggregate income both measured in terms ofwagerunits changes in the propensity itself being treated as a secondary in uence what is the normal shape of this function The fundamental psychological law upon which we are entitled to depend with great con dence both aprimi from our knowledge of human nature and from the detailed facts of experience is that men are disposed as a rule and on the average to increase their consumption as their income increases but not by as much as the increase in their income That is to say if Cw is the amount of consumption and Yw is income both measured in wagerunits ACw has the same sign as AYw but is smaller in amount ie is positive and less than unity This is especially the case where we have short periods in view as in the case of the sorcalled cyclical uctuations of employment during which habits as distinct from more permanent psychological propensities are not given time enough to adapt themselves to changed objective circumr stances For a man s habitual standard of life usually has the rst claim on his income and he is apt to save the differ ence which discovers itself between his actual income and the expense of his habitual standard or if he does adjust his expenditure to changes in his income he will over short periods do so imperfectly Thus a rising income will often be accompanied by increased saving and a falling income by decreased saving on a greater scale at rst than subsequently But apart from shortrperiod cmngex in the level of in come it is also obvious that a higher absolute level ofincome will tend as a rule to widen the gap between income and r i For the ati faction ofthe J4 rimary needs ofa man and his family is usually a stronger motive than the motives towards accumulation which only acquire effective sway when a margin of comfort has been attained These reasons will lead as a rule to a gmzz erpmpon im of income being saved as real income increases But whether or not a greater proportion is saved we take it as a fundamental psychological rule of any modern community that when its real income is increased it will not increase its consump tion by an equal abmlm e amount so that a greater absolute amount must be saved unless a large and unusual change is occurring at the same time in other factors As we shall show subsequently the stability of the economic system essentially depends on this rule prevailing in practice This means that if employment and hence aggregate income increase not a the additional employment will be required to satisfy the needs of additional consumption On the other hand a decline in income due to a decline in the level of employment if it goes far may even cause conr sumption to exceed income not only by some individuals and institutions using up the nancial reserves which they have accumulated in better times but also by the government which will be liable willingly or unwillingly to run into a 13 budgetary de cit or will provide unemployment relief for example out ofborrowed money Thus when employment falls to a low level aggregate consumption will decline by a smaller amount than that by which real income has declined by reason both of the habitual behaviour of individuals and also of the probable policy of governments which is the ex planation why a new position of equilibrium can usually be reached within a modest range of uctuation Otherwise a fall in employment and income once started might proceed to extreme len ths This simple principle leads it will be seen to the same conclusion as before namely that employment can only in crease pmi pmm with an increase in investment unless in deed there is a change in the propensity to consume For since consumers will spend less than the increase in aggrer gate supply price when employment is increased the in creased employment will prove unpro table unless there is an increase in investment to ll the gap Economics 201 CottrellLawlor What are Data Data etymology from the Latin dare to give singular datum plural data That which is given Data are generally not handed to us on a plate by nature the story of Newton and the apple notwithstand ing In the natural sciences datacollection often involves technologies of observation and of record that themselves embody previous hardwon scienti c results Eg extracting the data from a collision in a particle accelerator getting data from a quasar collecting data on the genetic structure of wild grasses In economics data are generally produced by computerassisted bureaucracies working on materials as sembled from surveys tax returns and the like The setup of the surveys depends on both economic theory and commercial practice So in what sense are data given Roughly once they obtained they can t be messed with If theory is in disagreement with the data the data can t be warped to match the theory the theory will have to be adjusted re ned or perhaps rejected This may have to be quali ed in various ways but scienti c fraud is generally detected fairly quickly The a priori and the empirical This theme is raised in the reading from Hume A priori means prior to experience Something known a priori is known by the exercise of reason alone without requiring any sensory or experiential input Contrast with empirical this means pertaining to or founded upon experiment or experience Does this give us a clearcut dichotomy Some philosophers Wittgenstein Quine think not Exercise Consider the following statements For each one say whether you think it is a priori or empirical or perhaps somewhere in between Explain your view Two plus two equals four Equot The car that just went by was red 5 There can be no such thing as a round triangle 3 There can be no such thing as a blue swan V39 This desk is two feet from the wall 9 The earth is 93 million miles from the sun gt1 The boiling point of water at sea level is 100 Celsius 9 The melting point of tungsten is 3422 C gt0 A rational consumer will select that plan of action which appears likely to satisfy hisher desires to the greatest possible eXtent given the available information 0 A rational consumer will arrange hisher expenditure so as to equalize the marginal utility per dollar spent on each of the goods heshe consumes Consumers can generally be regarded as rational N The government eXpenditure multiplier is greater in absolute magnitude than the taX multiplier 5 Investment is the component of aggregate demand that shows the greatest degree of independent variation 5 A high rate of interest discourages investment spending a low rate of interest encourages investment V39 A pro tmaximizing rm equates marginal cost and marginal revenue 9 Monopoly is detrimental to the pace of technical progress in an industry Exercise From the eld of microeconomics identify one proposition that seems clearly a priori and one that seems clearly empirical Write them down and be prepared to justify your choices Economics 201 Cottrell Some Basic Gretl Skills Gretl is a rather fullfeatured econometrics program In this class we will be using only a fraction of its functionality but if you have a good background in statistics you are encouraged to explore some of the more advanced features Note that there is online help available in most contexts and there is also a full manual in PDF format to access this click the Acrobat icon on the toolbar at the foot of gretl s main window Here are some pointers for accomplishing various tasks relating to exploration of a dataset for example the OECD healthspending data The boldfaced phrases below are keyed to the corresponding phrases in the OECD assignment Make a table Make a table displaying the values of one or more selected variables possibly sorted and copyand paste this table into a Word document Select your variable or variables To select a single variable just click on its line in gretl s main window To select a set of contiguous variables drag the mouse over the variables you want To select noncontiguous variables click the rst one you want then with the Ct r1 key held down click on the others Display the variables Rightclick in gretl s main window and select Display values from the popup menu Or from the Data menu on the main menubar select Display values A window will open showing the selected variables let s call this a data window Sort the data If the data should be sorted click the Sort AAZ icon at the top of the data window A dialog box will appear where you select the variable you wish to use for sorting Copy the contents of the data window to the clipboard First click the copy icon at the top of the data window note that you don t have to select data in this window with the mouseiby default all the data will be copied A dialog box appears giving you some options regarding the format in which the data should be copied If you plan to copy into MS Word select the option Tab separated If you re copying into MS Excel select Comma separated To paste the data into Word or Excel Use Edit Paste or the shortcut Ctrl V In Word it will not at rst look like a real table Select the material you just pasted highlight it by dragging the mouse then from Word s Table menu select Table AutoFormat If you want to netune the appearance of the table you may do so at this point or you can come back to this task later by rightclicking on the table in Word Be sure to give your table an informative title and also be sure to note in the accompanying text or in a note under the table the source of the data Find the mean To get summary statistics including mean median standard deviation and so on rst select a variable or variables as described above Then rightclick in gretl s main window and select Descriptive statistics A window will open showing the relevant statistics You can copy and paste this into Word as above In this case the material should appear in Word as a properly formatted table automatically so you don t need the Table AutoForm at step Note that the form at of the information differs depending on whether you selected just one variable or a set of variables One format or the other may be more suitable depending on the context If the table contains information that you don t need feel free to delete the extra stuff To delete rows in a Word table rst select the rows to delete then right click on the table and click Delete Rows in the popup menu simply pressing the Delete key will delete the contents of the table cells but not the cells themselves Make an XY graph To create an XY scatter graph rst select two variables in gretl s main window using Ctrl if they are noncontiguous Then rightclick and select XY scatterplot Or click the graph icon third from the right on the toolbar at the foot of gretl s main window A dialog box will appear in which you select the variable to be shown on the X axis With the graph displayed click on the graph window for a popup menu This menu gives the option of copying the graph to the clipboard from where you can paste it into Word saving the graph in various formats editing the graph and so on If you want to netune the appearance of the graph explore the possibilities that appear when you click Edit in the popup menu Labeling points in a graph If the data le contains identifying labels for the observations as the OECD data les do you have various options in relation to displaying those labels With the graph onscreen individual labels appear when you brush the data points with the mouse To get rid of these select Clear data labels from the popup menu To x them in place so they carry over when you copyandpaste the graph select Freeze data labels If you want to add data labels for every point select Edit from the graph popup and check the box titled Show all data labels This may or may not produce good results since the labels may overlap Further graphing options are available if you go to the Data menu on the menubar in the gretl main window the options Graph speci ed vars and Multiple scatterplots Also worth mentioning are two quite different sorts of graph which give you a x on the distribution of a single selected variable a frequency plot or histogram and a boxplot These are both available via the rightclick popup menu in gretl s main window when just one variable is selected Equation of line of best t When you create a XY graph if there is a reasonable degree of linear t then a line of best t is shown and its equation is displayed at the topleft corner of the graph To get details on this click for the graph popup and select OLS estimates OLS Ordinary Least Squares which is the most common method for nding the best linear t The OLS output can also be copied into Word if you wish Km 2 rmer 7L0 d S W 39c PDI39fco ry New 745m 84 13mm MSG Oriana0 1k Gum1434 CHAPTER I A SURVEY OF SOME FUNDAMENTAL PROBLEMS A SCIENTIST whether theorist or experimenter puts forward statements or systems of statements and tests them step by step In the eld of the empirical sciences more particularly he constructs hypotheses or systems of theories and tests them against experience by observation and experiment I suggest that it is the task of the logic of scientific discovery or the logic of knowledge to give a logical analysis of this procedure that is to analyse the method of the empirical sciences But what are these methods of the empirical sciences And what do we call empirical science I The Problem of Induction According to a widely accepted view to be opposed in this book the empirical sciences can be characterized by the fact that they use inductive methods as they are called According to this view the logic of scienti c discovery would be identical with inductive logic ie with the logical analysis of these inductive methods It is usual to call an inference inductive if it passes from singular statements sometimes also called particular statements such as accounts of the results of observations or experiments to universal statements such as hypotheses or theories Now it is far from obvious from a logical point of view that we are justi ed in inferring universal statements from singular ones no matter how numerous for any conclusion drawn in this way may always turn out to be false no matter how many instances of white swans we may have observed this does not justify the con clusion that all swans are white 27 FUNDAMENTAL PROBLEMS The question whether inductive inferences are justi ed or under what conditions is known as the problem of induction e problem of induction may also be formulated as the question of how to establish the truth of universal statements which are based on experience such as the hypotheses and theoretical systems of the empirical sciencesjor many people believe that the truth of these universal statements is known by experiente yet it is clear that an account of an experience of an observation or the result of an experi ment can in the rst place be only a singular statement and not a universal one Accordingly people who say of a universal statement that we know its truth from experience usually mean that the truth of this universal statement can somehow be reduced to the truth of singular ones and that these singular ones are known by experience to be true which amounts to saying that the universal statement is based on inductive inference Thus to ask whether there are natural laws known to be true appears to be only another way of asking whether inductive inferences are logically justified Yet if we want to find a way of justifying inductive inferences we must rst of all try to establish a principle of induction A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form In the eyes of the upholders of inductive logic a principle of induction is of supreme importance for scienti c method this principle says Reichenbach determines the truth of scienti c theories To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories Without it clearly science would no longer have the right to distinguish its theo ies om the fanciful and arbitrary creations of the poet s mind 1 glow this principle of induction cannot be a purely logical truth like a tautology or an analytic statement Indeed if there were such a thing as a purely logical principle of induction there would be no problem of induction for in this case all inductive inferences would have to be regarded as purely logical or tautological trans formations just like inferences in deductive logic Thus the principle of induction must be a synthetic statement that is a statement Whose negation is not self contradictory but logically possibl So the question arises why such a principle should be accepted at all and how we can justify its acceptance on rational grounds 1 H Reichenbach Erleenntnis I 1930 p 186 also p 64 i 28 I THE PROBLEM OF INDUCTION Some who believe in inductive logic are anxious to point out with Reichenbach that the principle of induction is unreservedly accepted by the whole of science and that no man can seriously doubt this principle in everyday life either Yet even supposing this were the case for after all the whole of science might err I should still contend that a principle of induction is super uous and that it must lead to logical inconsistencies That inconsistencies may easily arise in connection with the principle of induction should have been clear from the work of Humefquot1 also that they can be avoided if at all only with dif culty or the principle of induction must be a universal statement in its turn Thus if we try to regard its truth as known from experience then the very same problems which occasioned its introduction will arise all over again To justify it we should have to employ induc tive inferences and to justify these we should have to assume an inductive principle of a higher order and so on Thus the attempt to base the principle of induction on experience breaks down since it must lead to an infinite regresg Kant tried to force his way out of this difficulty by taking the principle of induction which he formulated as the principle of universal causation to be a priori valid But I do not think that his ingenious attempt to provide an a priori justi cation for synthetic statements was successful My own view is that the various di iculties of inductive logic here sketched are insurmountableCSo also I fear are those inherent in the doctrine so widely current today that inductive inference although not strictly valid can attain some degree of reIiabiIity or of probabilityg According to this doctrine inductive inferences are probable inferences393 We have described39 says Reichenbach the principle of induction as the means whereby science decides upon truth To be more exact we should say that it serves to decide upon Tw fobability For it is not given to science to reach either truth or a falsity but scienti c statements can only attain continuous degrees of 55 39Rcichenbach ibid p 67 n The decisive passages from Hume are quoted in appendix vii text to footnotes 4 5 and 6 See also note 2 to section 81 below s aC JM Keynes A Treatise on Probability 1921 O Kiilpe Vorlesungen ber Log by 5612 1923 Reichenbach who uses the term probability implications factual der Wahrsrheinlichkeitruhnung Mathem Zeitsehr 34 1932 and in many err p ces 29 FUNDAMENTAL PROBLEMS probability whose unattainable upper and lower limits are truth and falsity At this stage I can disregard the fact that the believers in inductive logic entertain an idea of probability that I shall later reject as highly unsuitable for their own purposes see section 80 below I can do so because the difficulties mentioned are not eVen touched by an appeal to probability for if a certain degree of probability is to be assigned to statements based on inductive inference then this will have to be justi ed by invoking a new principle of induction appropriately modi ed And this new principle in its turn will have to be justi ed and so on Nothing is gained moreover if the principle of induction inits turn is taken not as true but only as probable39 In short like every other form of inductive logic the logic of probable inference or probability logic leads either to an in nite regress or to the doctrine of apriorism The theory to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic It might be described as the theory of the deductive method of testing or as the view that a hypothesis can only be empirically tested and only after it has been advanced Before I can elaborate this view which might be called deduc tivism in contrast to inductivism395 I must rst make clear the distinction between the psychology of knowledge which deals with empirical facts and the logic of knowledge which is concerned only with logical relations For the belief in inductive logic is largely due to a confusion of psychological problems with epistemological ones It may be worth noticing by the way that this confusion spells trouble not only for the logic of knowledge but for its psychology as well Reichcnbach Erleermmis I 1930 p 186 39 See also chapter x below especially note 2 to section 81 and chapter IIii of the Postscript for a fuller statement of this criticism 5 Liebig in Induktion und Deduktion 1865 was probably the rst to reject the inductive method from the standpoint of natural science his attack is directed against Bacon Duhem in La Theorie physique son objet et sa structure 1906 English translation by P P Wiener The Aim and Structure of Physical Theory Princeton 1954 held pronounced deductivist views But there are also inductivist views to be found in Duhem39s book for example in the third chapter Part One where we are told that only experiment induction and generalization have produced Descartes39s law of diffraction cf the English translation p 45 5 See also V Kraft Die Grandquotomen der Wissenschqftlichen Methoden 1925 and Carnap Erleennmis 2 1932 p 440 30 2 ELIMINATION OF PSYCHOLOGISM 2 Elimination of Psychologism I said above that the work of the scientist consists in putting forward and testing theories The initial stage the act of conceiving or inventing a theory seems to me neither to call for logical analysis nor to be susceptible of it The question how it happens that a new idea occurs to a man whether it is a musical theme a dramatic con ict or a scienti c theory may be of great interest to empirical psychology but it is irrelevant to the logical analysis of scienti c knowledge This latter is concerned not with questions of fact Kant s quid facti but only with questions ofjusti cation or validity Kant39s quidjuris Its questions are of the following kind Can a statement be justi ed And if so how Is it testable Is it logically dependent on certain other state ments Or does it perhaps contradict them In order that a statement may be logically examined in this way it must already have been presented to us Someone must have formulated it and submitted it to logical examination Accordingly I shall distinguish sharply between the process of conceiving a new idea and the methods and results of examining it logically As to the task of the logic of knowledge in contradis tinction to the psychology of knowledge I shall proceed on the assumption that it consists solely in investigating the methods employed in those systematic tests to which every new idea must be subjected if it is to be seriously entertained Some might object that it would be more to the purpose to regard it as the business of epistemology to produce what has been called a rational reconstmrtion of the steps that have led the scientist to a dis covery40 the nding of some new truth But the question is what precisely do we want to reconstruct If it is the processes involved in the stimulation and release of an inspiration which are to be recon Structed then I should refuse to take it as the task of the logic ofknow ledge Such processes are the concern of empirical psychology but hardly of logic It is another matter if we want to reconstruct rationally the subsequent tests whereby the inspiration may be discovered to be a discovery or become known to be knowledge In so far as the fplentist critically judges alters or rejects his own inspiration we may like regard the methodological analysis undertaken here as d0f rational reconstruction of the corresponding thought ah items 1 PF0E stBut this reconstruction would not describe these processes 31 FUNDAMENTAL PROBLEMS as they actually happen it can give only a logical skeleton of the procedure of testing Still this is perhaps all that is meant by those who speak of a rational reconstruction of the ways in which we gain knowledge It so happens that my arguments in this book are quite independent of this problem However my View of the matter for what it is worth is that there is no such thing as a logical method of having new ideas or a logical reconstruction of this process My view may be expressed by saying that every discovery contains an irrational element or a creative intuition in Bergson s sense In a similar way Einstein speaks of the search for those highly universal laws from which a picture of the world can be obtained by pure deduction There is no logical path he says leading to these laws They can only be reached by intuition based upon something like an intellectual love Einjiihlung of the objects of experience 1 3 Deductive Testing of Theories According to the View that will be put forward here the method of critically testing theories and selecting them according to the results of tests always proceeds on the following lines From a new idea put up tentatively and not yet justi ed in any way an anticipation a hypothesis a theoretical system or what you will conclusions are drawn by means of logical deduction These conclusions are then com pared with one another and with other relevant statements so as to nd what logical relations such as equivalence derivability com patiblity or incompatibility exist between them We may if we like distinguish four different lines along which the testing of a theory could be carried out First there is the logical comparison of the conclusions among themselves by which the internal consistency of the system is tested Secondly there is the investi gation of the logical form of the theory with the object of determining Whether it has the character of an empirical or scientific theory or whether it is for example tautological Thirdly there is the com 1 Address on Max Planck s 60th birthday The passage quoted begins with the words The supreme task of the physicist is to search for those universal laws etc quoted from A Einstein Mein Wsltbx39Id 1934 p 168 English translation by Harris The World a I see It 1935 p 125 Similar ideas are found earlier in Licbig op tit 41 also Mach Principien der Wiz39rmelehre 1896 p 443 at The German word Ein lhlung is dif cult to translate Harris translates sympathetic understanding 0f experience 32 r aw E 3 TESTING THEORIES parison with other theories chie y with the aim of determining whether the theory would constitute a scienti c advance should it survive our various tests And nally there is the testing of the theory by way of empirical applications of the conclusions which can be derived from it The purpose of this last kind of test is to find out how r the new consequences of the theory whatever may be new in what it asserts stand up to the demands of practice whether raised by purely scienti c experiments or by practical technological applications Here too the procedure of testing turns out to be deductive With the help of other statements previously accepted certain singular statements which we may call predictions are deduced om the theory especially predictions that are easily testable or applicable From among these statements those are selected which are not derivable 39om the current theory and more especially those which the current theory contradicts Next we seek a decision as regards these and other derived statements by comparing them with the results of practical ap plications and experiments If this decision is positive that is if the singular conclusions turn out to be acceptable or veri ed then the theory has for the time being passed its test we have found no reason to dis card it But if the decision is negative or in other words if the con clusions have been falsi ed then their falsi cation also falsi es the theory from which they were logically deduced It should be noticed that a positive decision can only temporarily support the theory for subsequent negative decisions may always overthrow it So long as a theory withstands detailed and severe tests and is not superseded by another theory in the course of scienti c progress we may say that it has proved its mettle or that it is corroborated 1 Nothing resembling inductive logic appears in the procedure here outlined I never assume that we can argue from the truth of singular statements to the truth of theories I never assume that by force of veri ed conclusions theories can be established as true or even as merely probable In this book I intend to give a more detailed analysis of the quotEcthods of deductive testing And I shall attempt to show that Vylthin the framework of this analysis all the problems can be dealt quoti For this term See note 1 before secuon 79 and section 29 of my Postscript 33 FUNDAMENTAL PROBLEMS with that are usually called epistemological39 Those problems more especially to which inductive logic gives rise can be eliminated without creating new ones in their place 4 The Problem of Demarcation Of the many objections which are likely to be raised against the view here advanced the most serious is perhaps the following In rejecting the method of induction it may be said I deprive empirical science of what appears to be its most important characteristic and this means that I remove the barriers which separate science from metaphysical speculation My reply to this objection is that my main reason for rejecting inductive logic is precisely that it does not provide a suitable distinguishing mark of the empirical nonmetaphysical character of a theoretical system or in other words that it does not provide a suitable criterion of demarcation The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand and mathematics and logic as well as metaphysical systems on the other I call the problem of demarcation1 This problem was known to Hume who attempted to solve it2 With Kant it became the central problem of the theory of knowledge If following Kant we call the problem of induction Hume s problem we might call the problem of demarcation Kant s problem Of these two problems the source of nearly all the other problems of the theoryof knowledge the problem of demarcation is I think the more fundamental Indeed the main reason why epistemologists with empiricist leanings tend to pin their faith to the method of induction seems to be their belief that this method alone can provide a suitable criterion of demarcation This applies especially to those empiricists who follow the ag of positivism The older positivists wished to admit as scienti c or legitimate only those concepts or notions or ideas which were as they put it derived from experience those concepts that is which they believed to be logically reducible to elements of senseexperience such as sensations or sensedata impressions perceptions visual or auditory 1 With this and also with sections I to 6 and I3 to 24 my note Erleenntnis 3 1933 p 426 It is now here reprinted in translation as appendix i a C the last sentence of his Enquiry Concerning Human Understanding With the next paragraph compare for example the quotation from Reichenbach in the text to note 1 section I 34 4 THE PROBLEM OF DEMARCATION memories and so forth Modern positivists are apt to see more clearly that science is not a system of concepts but rather a system of statements1 Accordingly they Wish to admit as scienti c or legiti mate only those statements which are reducible to elementary or atornic statements of experience to judgments of perception or atornic propositions or protocol sentences39 or what notquot It is clear that the implied criterion of demarcation is identical with the demand for an inductive logic Since I reject inductive logic I must also reject all these attempts to solve the problem of demarcation With this rejection the problem of demarcation gains in importance for the present inquiry Finding an acceptable criterion of demarcation must be a crucial task for any epistemology which does not accept inductive logic Positivists usually interpret the problem of demarcation in a naturalistic way they interpret it as if it were a problem of natural science Instead of taking it as their task to propose a suitable con vention they believe they have to discover a difference existing in the nature of things as it were between empirical science on the one hand and metaphysics on the other They are constantly trying to prove that metaphysics by its very nature is nothing but nonsensical twaddle sophistry and illusion as Hume says which we should commit to the flames quot 3 If by the words nonsensical or meaningless we wish to express no more by de nition than not belonging to empirical science then the characterization of metaphysics as meaningless nonsense would be trivial for metaphysics has usually been de ned as non empirical But of course the positivists believe they can say much more about metaphysics than that some of its statements are non When I wrote this paragraph I overrated the modern positivists as I now see Ishould have remembered that in this respect the promising beginning ofWittgenstein39s Trartutus a The world is the totality of facts not of things was cancelled by its end which denounced the man who had given no meaning to certain signs in his proposi tions Seealso my Open Society and its Enemies chapter 11 section ii and chapter ti of my Postscript especially sections arr note 5 24 the last ve paragraphs and 25 quot Nothing depends on names of course When I invented the new name basic statement or basic proposition see below sections 7 and 28 I did so only because I nccflcd a term not burdened with the connotation of a perception statement But unfortunately it was soon adopted by others and used to convey precisely the kind of W thhil wished to avoid C also my Postscript 29 Humc thus condemned his own Enquiry on its last page just as later Wittgenstein own Tractatus on its last page See note 2 to section 10 3S FUNDAMENTAL PROBLEMS empirical The words meaningless or nonsensical convey and are meant to convey a derogatory evaluation and there is no doubt that what the positivists really want to achieve is not so much a successful demarcation as the nal overthrow3 and the annihilation of meta physics However this may be we find that each time the positivists tried to say more clearly what meaningful39 meant the attempt led to the same result to a de nition of meaningful sentence in contra distinction to meaningless pseudosentence which simply reiterated the criterion of demarcation of their inductive logic This shows itself very clearly in the case of Wittgenstein according to whom every meaningful proposition must be logically reducible to elementary or atomic propositions which he characterizes as descriptions or pictures of reality 5 a characterization by the way which is to cover all meaningful propositions We may see from this that Wittgenstein s criterion of meaning alness coincides with the inductivists criterion of demarcation provided we replace their words scienti c or legitimate by meaning il And it is precisely over the problem of induction that this attempt to solve the problem of demarcation comes to grief positivists in their anxiety to annihilate metaphysics annihilate natural science along with it For scienti c laws too cannot be logically reduced to elementary statements of experience If consistently applied Wittgenstein s criterion of meaningfulness rejects as meaningless those natural laws the search for which as Einstein says6 is the supreme task of the physicist they can never be accepted as genuine or legitimate statements This view which tries to unmask the problem of induction as an empty pseudo problem has been expressed by Schlick M in the following words Camap Erleennmis 2 1932 p 219 Earlier Mill had used the word meaninglcss39 in a similar way no doubt under the in uence of Comte Comte s Early Essays on Social Philosophy ed by H D Hutton 1911 p 223 See also my Open Society note 5r to chapter II Wittgenstein Tractatus LogicoPhilosophicus 1918 and 1922 Proposition 5 MM this was written in 1934 I am dealing here of course only with the Tractatus 5 Wittgenstein op cit Proposition 401 403 2221 Cf note 1 to section 2 The idea of treating scienti c laws as pseudopropositions thus solving the problem of induction was attributed by Schlick to Wittgenstein Cf my Open Society notes 46 and 51 j to chapter 11 But it is really much older It is part of the instrumentalist tradition which can be traced back to Berkeley and further See for example my paper Three Views Concerning Human Knowledge in Contemporary British Philosophy 1956 and A Note on Berkeley as a Precursor of Mach in The British Journal for the Philosophy of Science iv 4 1953 pp 26 now in my Conjectures and Refu tations 1959 Further references in note 1 before section 12 p 59 The problem is also treated in my Postscript sections 11 to 14 and 419 to 39026 36 4 THE PROBLEM OF DEMARCATION The problem of induction consists in asking for a logical usti cation of universal statements about reality We recognize with Hume that there is no such logical justi cation there can be none simply because they are not genuine statements 7 This shows how the inductivist criterion of demarcation fails to draw a dividing line between scientific and metaphysical systems and why it must accord them equal status for the verdict of the positivist dogma of meaning is that both are systems of meaningless pseudostatements Thus instead of eradicating metaphysics from the empirical sciences positivism leads to the invasion of metaphysics into the scienti c realm8 In contrast to these anti metaphysical stratagems anti meta physical in intention that is my business as I see it is not to bring about the overthrow of metaphysics It is rather to formulate a suitable characterization of empirical science or to de ne the concepts empirical science39 and metaphysics in such a way that we shall be able to say of a given system of statements whether or not its closer study is the concern of empirical science My criterion of demarcation will accordingly have to be regarded as a proposal for an agreement or convention As to the suitability of any such convention opinions may differ and a reasonable discussion of these questions is only possible between parties having some purpose in common The choice of that purpose must of course be ultimately a matter of decision going beyond rational argumentf 5 Thus anyone who envisages a system of absolutely certain irrevocably true statementsquot as the end and purpose of science will certainly reject the proposals I shall make here And so will those 7 Schlick Naturwissensthaften 19 1931 p 156 The italics are mine Regarding natural laws Schlick writes p 151 It has often been remarked that strictly we can never speak of an absolute veri cation of a law since we always so to speak tacitly make the reservation that it may be modi ed in the light of further experience If I may add by way of parenthesis Schlick continues a few words on the logical situation the abovementioned fact means that a natural law in principle does not have the logical etc of a statement but is rather a prescription for the formation of statements 39 Formation no doubt was meant to include transformation or derivation Schlick attributed this theory to a personal communication of Wittgenstein s See also section 12 Of my Postscript 39 Cf Section 78 for example note 1 See also my Open Society notes 46 51 and 52 to Chapter I and my paper The Demarcation between Science and Metaphysics cpitflmbuted 111 January 1955 to the planned Camap volume of the Library of Living iggophers edited by P A Schilpp a in Higheheve that a reasonable discussion is always possible between parties interested a 1 d39ready to pay attention to each other Cf my Open Society chapter 24 This istglers View gf note 1 to section 19 37 FUNDAMENTAL PROBLEMS who see the essence of science in its dignity which they think resides in its wholeness and its real truth and essentiality 10 They will hardly be ready to grant this dignity to modern theoretical physics in which I and others see the most complete realization to date of What I call empirical science The aims of science which I have in mind are different I do not try to justify them however by representing them as the true or the essential aims of science This would only distort the issue and it would mean a relapse into positivist dogmatism There is only one way as far as I can see of arguing rationally in support of my pro posals This is to analyse their logical consequences to point out their fertility their power to elucidate the problems of the theory of knowledge Thus I freely admit that in arriving at my proposals I have been guided in the last analysis by value judgments and predilections But I hope that my proposals may be acceptable to those who value not only logical rigour but also freedom from dogmatism who seek practical applicability but are even more attracted by the adventure of science and by discoveries which again and again confront us with new and unexpected questions challenging us to try out new and hitherto undreamedof answers The fact that value judgments in uence my proposals does not mean that I am making the mistake of which I have accused the positivists that of trying to kill metaphysics by calling it names I do not even go so far as to assert that metaphysics has no value for empirical science For it cannot be denied that along with meta physical ideas which39 have obstructed the advance of science there have been others such as speculative atomism which have aided it And looking at the matter from the psychological angle I am inclined to think that scienti c discovery is impossible without faith in ideas which are of a purely speculative kind and sometimes even quite hazy a faith which is completely unwarranted from the point of view of science and which to that extent is metaphysical 11 Yet having issued all these warnings I still take it to be the rst task of the logic of knowledge to put forward a concept of empirical science in order to make linguistic usage now somewhat39uncertain 1 This is the view of 0 Spam Kategorienlehre I924 Cf also Planck Positivismus und reale Aussenwelt I931 and Einstein Die Religiositiit der Forsthung in Main Weltbild 1934 p 43 English translation by A Harris TheWorId as I See It 193 5 p 23 quot tSee also section 85 and my Postscript 38 5 EXPERIENCE AS A METHOD as de nite as possible and in order to draw a clear line of demarcation between science and metaphysical ideas even though these ideas may have furthered the advance of science throughout its history 5 Experience as a Method The task of formulating an acceptable de nition of the idea of empirical science is not without its di iculties Some of these arise from the fact that there must be many theoretical systems with a logical structure very similar to the one which at any particular time is the accepted system of empirical science This situation is sometimes described by saying that there are a great many presumably an in nite number of logically possible worlds Yet the system called empirical science is intended to represent only one world the real world or the world of our experience quot 1 In order to make this idea a little more precise we may distinguish three requirements which our empirical theoretical system will have to satisfy First it must be synthetic so that it may represent a non contradictory a possible world Secondly it must satisfy the criterion of demarcation sections 6 and 21 139e it must not be metaphysical but must represent a world of possible experience Thirdly it must be a system distinguished in some way from other such systems as the one which represents our world of experience F But how is the system that represents our world of experience to be distinguished The answer is by the tct that it has been sub mitth to tests and has stood up to tests This means that it is to be distinguished by applying to it that deductive method which it is my aim to analyse and to describe Experience on this view appears as a distinctive method whereby one theoretical system may be distinguished from others so that empirical science seems to be characterized not only by its logical fQImllltinaddition by its distinctive method This of course is also the view of the inductivists who try to characterize empirical science by its use of the inductive method The theory of knowledge whose task is the analysis of the method or procedure peculiar to empirical science may accordingly be described as a theory of the empirical method a theory of what is quot I l i jexperience 39 quot1 Cf txi 39 FUNDAMENTAL PROBLEMS 6 Falsi ahility as a Criterion of Demarcation The criterion of demarcation inherent in inductive logic that is the positivistic dogma of meaning is equivalent to the requirement that all the statements of empirical science or all meaningful39 statements must be capable of being nally decided with respect to their truth and falsity we shall say that they must be conclusively decidable This means that their form must be such that to verify them and to zlsify them must both be logically possible Thus Schlick says a genuine statement must be capable of conclusive veri cation and Waismann says still more clearly If there is no possible way to determine whether a statement is true then that statement has no meaning whatsoever For the meaning of a statement is the method of its verification 2 Now in my view there is no such thing as inductionquot 1 Thus infer ence to theories from singular statements which are verified by experi ence whatever that may mean is logically inadmissible Theories are therefore never empirically veri able If we wish to avoid the positivist s mistake of eliminating by our criterion of demarcation the theoretical systems of natural science then we must choose a criterion which allows us to admit to the domain of empirical science even statements which cannot be veri ed But I shall certainly admit a system as empirical or scienti c only if it is capable of being tested by experience These considerations suggest that not the veri ability but the falsi ability of a system is to be taken as a criterion of demarcation In other words I shall not 1 Schlick Naturwissenschaften I9 1931 1931 p 150 3 Waismann Erkenntnis l I930 p 229 1 am not of course here considering so called mathematical induction39 whatI am denying is that there is such a thing as induction in the so called inductive sciences39 that there are either inductive procedures or inductive inferences39 quot In his Logical Syntax 1937 p 321 f Camap admitted that this was a mistake with a reference to my criticism and he did so even more fully in Testability and Meaning39 recognizing the fact that universal laws are not only convenient for science but even essential Philosophy of Science 4 1937 p 27 But in his inductivist Logical Foundations of Probability 1950 he returns to a position very like the one here criticized nding that universal laws have zero probability p 511 he is compelled to say p 575 that though they need not be expelled from science science can very well do without them 3 Note that I suggest falsi ability as a criterion of demarcation but not of meaning Note moreover that I have already section 4 sharply criticized the use of the idea of meaning as a criterion of demarcation and that I attack the dogma of meaning again even more sharply in section 9 It is therefore a sheer myth though any number of refutations of my theory have been based upon this myth that I ever proposed falsi ability as a criterion of meaning Falsi ability separates two kinds of perfectly meaningful statements the falsi able and the nonfalsi able It draws a line insi e meaningful language not around it See also Appendix ti and chapter ii of my Postscript especially sections 17 and 19 40 m3 Effie 6 FALSIFIABILITY AND DEMARCATION require of a scienti c system that it shall be capable of being singled out once and for all in a positive sense but I shall require that its logical form shall be such that it can be singled out by means of empirical tests in a negative sense it must be possible for an empirical scienti c system to be refuted by experience3 Thus the statement Itwillrain or not rain here tomorrow will not be regarded as empirical simply because it cannot be refuted whereas the statement It will rain here tomorrow will be regarded as empirical Various objections might be raised against the criterion ofdemarca tion here proposed In the rst place it may well seem somewhat wrong headed to suggest that science which is supposed to give us positive information should be characterized as satisfying a negative requirement such as refutability However I shall show in sections 31 to 46 that this objection has little weight since the amount of positive information about the world which is conveyed by a scienti c statement is the greater the more likely it is to clash because of its logical character with possible singular statements Not for nothing do we call the laws of nature laws the more they prohibit the more they say Again the attempt might be made to turn against me my own criticism of the inductivist criterion of demarcation for it might seem that objections can be raised against falsi ability as a criterion of demarcation similar to those which I myself raised against veri ability This attack would not disturb me My proposal is based upon an asymmetry between veri ability and falsi ability an asymmetry which results from the logical form of universal statements For these are never derivable from singular statements but can be contra dicted by singular statements Consequently it is possible by means of purely deductive inferences the help of the modus tollens of classical logic to argue from the truth of singular statements to the fill 1t9 universal statements Such an argument to the falsity of umversal statements is the only strictly deductive kind of inference that proceeds as it were in the inductive direction39 that is from Smgular to universal statements A third objection may seem more serious It might be said that Cr Related ideas are to be found for example in Frank Die Kausalitiz39t und ihre C quot79quot 1931 ch 1 IO p 15f Dubislav Die De nition 3rd edition 1931 p 100 f 315 30 1 to section 4 above F1333 35ch is now more fully discussed in section 22 of my Postscript 4r FUNDAMENTAL PROBLEMS even if the asymmetry is admitted it is still impossible for various reasons that any theoretical system should ever be conclusively falsi ed For it is always possible to find some way of evading falsi fication for example by introducing ad hoc an auxiliary hypothesis or by changing ad hot a de nition It is even possible without logical inconsistency to adopt the position of simply refusing to acknowledge any falsifying experience whatsoever Admittedly scientists do not usually proceed in this way but logically such procedure is possible and this fact it might be claimed makes the logical value of my proposed criterion of demarcation dubious to say the least I must admit the justice of this criticism but I need not therefore withdraw my proposal to adopt llsi ability as a criterion of demarcation For I am going to propose in sections 20 that the empirical method shall be characterized as a method that excludes precisely those ways of evading falsification which as my imaginary critic rightly insists are logically admissible According to my proposal what characterizes the empirical method is its manner of exposing to falsi cation in every conceivable way the system to be tested Its aim is not to save the lives of untenable systems but on the contrary to select the one which is by comparison the fittest by exposing them all to the fiercest struggle for survival The proposed criterion of demarcation also leads us to a solution of Hume s problem of induction of the problem of the validity of natural laws The root of this problem is the apparent contradiction between what may be called the fundamental thesis of empiricism the thesis that experience alone can decide upon the truth or falsity of scienti c statements and Hume s realization of the inad missibility of inductive arguments This contradiction arises only if it is assumed that all empirical scientific statements must be con clusively decidable ie that their verification and their falsi cation must both in principle be possible If we renounce this requirement and admit as empirical also statements which are decidable in one sense only unilaterally decidable and more especially falsi able and which may be tested by systematic attempts to falsify them the contradiction disappears the method of falsi cation presupposes no inductive inference but only the tautological transformations of deductive logic whose validity is not in dispute For this see also my paper mentioned in note I to section 4 Imow here reprinted as appendix i and my Postscript esp section 2 42 tun 31 in ruar w I 7 THE EMPIRICAL BASIS 7 The Problem of the Empirical Basis39 If falsi ability is to be at all applicable as a criterion of demarcation then singular statements must be available which can serve as premisses in falsifying inferences Our criterion therefore appears only to shift the problem to lead us back from the question of the empirical character of theories to the question of the empirical character of singular statements 39 Yet even so something has been gained For in the practice of scienti c research demarcation is sometimes of immediate urgency in connection with theoretical systems whereas in connection with singular statements doubts as to their empirical character rarely arise It is true that errors of observation occur and give rise to false singular statements but the scientist scarcely ever has occasion to describe a singular statement as nonempirical or metaphysical Problems of the empirical basis that is problems concerning the empirical character of singular statements and how they are tested thus play a part within the logic of science that differs somewhat from that played by most of the other problems which will concern us For most of these stand in close relation to the practice of research whilst the problem of the empirical basis belongs almost exclusively to the theory of knowledge I shall have to deal with them however since they have given rise to many obscurities This is especially true of the relation between perceptual experiences and basic statements What I call a basic statement or a basic proposition is a statement which can serve as a premise in an empirical falsi cation in brief a statement of a singular fact Perceptual experiences have often been regarded as providing a kind of justi cation for basic statements It was held that these statements are based upon these experiences that their truth becomes mifmfes t by inspection through these experiences or that it is made ev1dent by these experiences etc All these expressions exhibit the perfectly sound tendency to emphasize the close connection between the basic statements and our perceptual experiences Yet it was also nghtly felt that statements can be logically justi ed only by statements usthe connection between the perceptions and the statements ImuaeinCd ObSCure and was described by correspondingly obscure cx t sions39yvhich elucidated nothing but slurred over the dif culties or at bestadumbrated them through metaphors FUNDAMENTAL PROBLEMS Here too a solution can be found I believe if we clearly separate the Psychological tom the logical and methodological aspects of the problem We must distinguish between on the one hand our subjective experience or our feelings of conviction which can never justify any statement though they can be made the subject of psychological investigation and on the other hand the objective logical relations subsisting among the various systems of scienti c statements and Within each of them The problems of the empirical basis will be discussed in some detail in sections 25 to 30 For the present I had better turn to the problem of scienti c objectivity since the terms objective39 and subjective which Ihave just used are in need of elucidation 8 Scienti c Objectivity and Subjective Conviction The words objective and subjective are philosophical terms heavily burdened with a heritage of contradictory usages and of inconclusive and interminable discussions My use of the terms objective and subjective is not unlike Kant s He uses the word objective39 to indicate that scienti c knowledge should be justi able independently of anybody s whim a justi cation is objective if in principle it can be tested and under stood by anybody If something is valid he writes for anybody in possession of his reason then its grounds are objective and sufficient 1 Now I hold that scienti c theories are never fully justi able or veri able but that they are nevertheless testable I shall therefore say that the objectivity of scienti c statements lies in the fact that they can be intersuly39ectively testedquot 1 The word subjective39 is applied by Kant to our feelings of conviction of varying degreesa To examine how these come about 1 Kritik der reinen Vernunft Methodenlehre 2 Haupst ck 3 Abschnitt 2nd edition p 848 English Translation by N Kemp Smith 1933 Critique of Pure Reason The Transcendental Doctrine of Method chapter ii section 3 p 645 1 I have since generalized this formulation for intersubjective testing is merely a very important aspect of the more general idea of intersubjective criticism or in other words of the idea of mutual rational control by critical discussion This more general idea discussed at some length in my Open Society and Its Enemies chapters 23 and 24 and in my Poverty of Historicism section 32 is also discussed in my Postscript especially in chapters i ii and vi 39 Ibid 44 8 SCIENTIFIC OBJECTIVITY is the business of psychology They may arise for example in accordance with the laws of association 3 Objective reasons too may serve as subjectivc causes ofjudging39 in so far as we may re ect upon these reasons and become convinced of their cogency Kant was perhaps the first to realize that the objectivity of scienti c statements is closely connected with the construction of theories with the use of hypotheses and universal statements Only when certain events recur in accordance with rules or regularities as is the case with repeatable experiments can our observations be tested in principle by anyone We do not take even our own observations quite seriously or accept them as scienti c observations until we have repeated and tested them Only by such repetitions can we convince ourselves that we are not dealing with a mere isolated coincidence but with events which on account of their regularity and reproducibility are in principle intersubjectively testable Every experimental physicist knOWS those surprising and inex plicable apparent eEects39 which can perhaps even be reproduced in his laboratory for some time but which nally disappear without trace Of course no physicist would say in such a case that he had made a scienti c discovery though he might try to rearrange his experiments so as to make the effect reproducible Indeed the scienti cally signi cant physical mfect may be de ned as that which can be regularly reproduced by anyone who carries out the appro priate experiment in the way prescribed No serious physicist would offer for publication as a scienti c discovery any such occult e ect39 as I propose to call it one for whose reproduction he could give no instructions The discovery would be only too soon rejected as chimerical simply because attempts to test it would lead to negative 39 Cf Krill der reinen Vemuvgft Transcendentale Elementarlehre I9 2nd edition p 142 English translation by N Kemp Smith 1933 Critique of Pure Reason Transcen dental Doctrine of Elements 19 p r 59 foI er39tile der reinen Vemuft Methodenlehre 2 Haupstiick 3 Abschnitt 2nd edmony p 849 English translation chapter ii section 3 p 646 Kant realized that from the required objectivity of scienti c statements it follows that they must be at any time intersubjectively testable and that they must therefore have the form of universal laws or theories He formulated this discovery somewhat bsc 1YbYhls 39principle of temporal succession according to the law of causality 111911 ltEfunple he believed that he could prove a priori by employing the reasoning m n V 16 I do not postulate any such principle gf section Ia but I agree that mum sutcmfmsi smce they must be intersubjectively testable must always have the I cter of universal hypotheses See also note 1 to section 22 45 FUNDAMENTAL PROBLEMS results 3 It follows that any controversy over the question whether events which are in principle unrepeatable and unique ever do occur cannot be decided by science it would be a metaphysical controversy We may now return to a point made in the previous section to my thesis that a subjective experience or a feeling of conviction can never justify a scienti c statement and that within science it can play no part but that of the subject of an empirical a psychological inquiry No matter how intense a feeling of conviction it may be it can never justify a statement Thus I can be utterly convinced of the truth of a statement certain of the evidence of my perceptions overwhelmed by the intensity of my experience every doubt may seem to me absurd But does this afford the slightest reason for science to accept my statement Can any statement be justified by the fact that K R P is utterly convinced of its truth The answer is No39 and any other answer would be incompatible with the idea of scienti c objectivity Even the fact for me so rmly established that I am experiencing this feeling of conviction cannot appear within the eld of objective science except in the form of a psychological hypothesis which of course calls for intersubjective testing from the conjecture that I have this feeling of conviction the psychologist may deduce with the help of psychological and other theories certain predictions about my behaviour and these may be confirmed or refuted in the course of experimental tests But from the epistemo logical point of view it is quite irrelevant whether my feeling of conviction was strong or weak whether it came from a strong or even irresistible impression of indubitable certainty or 39self evidence or merely from a doubtful surmise None of this has any bearing on the question of how scienti c statements can be justi ed Considerations like these do not of course provide an answer to the problem of the empirical basis But at least they help us to see its main difficulty In demanding objectivity for basic statements as well as for other scientific statements we deprive ourselves of any logical means by which we might have hoped to reduce the truth of In the literature of physics there are to be found some instances of reports by serious investigators of the occurrence of effects which could not be rleproduced since further tests led to negative results A well known example from recent times is the unexplained positive result of Michelson s experiment observed by Miller 19211926 at Mount Wilson after he himself as well as Morley had previously reproduced Michelson s negative result But since later tests again gave negative results it is now customary to regard these latter as decisive and to explain Miller s divergent result as due to unknown sources of error See also section 22 especially footnote 1 46 8 SCIENTIFIC OBJECTIVITY scienti c statements to our experiences Moreover we debar ourselves from granting any favoured status to statements which represent experiences such as those statements which describe our perceptions and which are sometimes called protocol sentences They can occur in science only as psychological statements and this means as hypotheses of a kind whose standards of intersubjective testing considering the present state of psychology are certainly not very high Whatever may be our eventual answer to the question of the empirical basis one thing must be clear if we adhere to our demand that scienti c statements must be objective then those statements which belong to the empirical basis of science must also be objective ie inter subjectively testable Yet intersubjective testability always implies that from the statements which are to be tested other testable statements can be deduced Thus if the basic statements in their turn are to be inter subjectively testable there can be no ultimate statements in science there can be no statements in science which cannot be tested and therefore none which cannot in principle be refuted by falsifying some of the conclusions which can be deduced from them We thus arrive at the following View Systems of theories are tested by deducing from them statements of a lesser level of universality These statements in their turn since they are to be intersubjectively testable must be testable in like manner and so ad in nitum It might be thought that this view leads to an in nite regress and that it is therefore untenable In section I when criticizing induction I raised the objection that it may lead to an in nite regress and it might well appear to the reader now that the very same objection can be urged against that procedure of deductive testing which I myself advocate However this is not so The deductive m 33151th of testing cannot establish or justify the statements which are being tested nor is it intended to do so Thus there is no danger of an in nite regress But it must be admitted that the situation to which I have drawn attention testability ad in nitum and the absence 0f ultimate statements which are not in need of tests does create a Problem For clearly tests cannot in fact be carried on ad in nitum 303nmquot or later we have to stop Without discussing this problem hag396 detail I only wish to point out that the fact that the tests 3mm go on for ever does not clash with my demand that every 47 FUNDAMENTAL PROBLEMS scienti c statement must be testable For I do not demand that every scienti c statement must have in fact been tested before it is accepted I only demand that every such statement must be capable of being tested or in other words I refuse to accept the view that there are statements in science which we have resignedly to accept as true merely because it does not seem possible for logical reasons to test them