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# EPISTEMOLOGY PHIL 5340

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This 36 page Class Notes was uploaded by Kenton Grimes on Friday October 30, 2015. The Class Notes belongs to PHIL 5340 at University of Colorado at Boulder taught by Michael Tooley in Fall. Since its upload, it has received 30 views. For similar materials see /class/232149/phil-5340-university-of-colorado-at-boulder in PHIL-Philosophy at University of Colorado at Boulder.

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Philosophy 5340 Epistemology Topic 4 Skepticism Part 2 Michael Huemer on Skepticism Chapter II The Lure of Radical Skepticism 1 Mike Huemer defines radical skepticism as follows Philosophical skeptics hold that one cannot know anything about the external worldquot But this needs to be interpreted as saying that according to the radical skeptic one cannot even know that there is an external world since he later goes on to say that the skeptic maintains that we do not know there is an external worldquot 7 Comment Recall that as I mentioned earlier there is a less radical form of skepticism according to which while one may be able to know that there is an objective world outside of one s mind one cannot know what it is like since one cannot know for example whether it consists of mind independent objects or instead of a Berkeleian God and other immaterial minds 2 Mike Huemer in contrast to a number of epistemologists takes skeptical arguments seriously in one respect since he says that it is important to understand skeptical arguments and to know precisely where they go wrongquot 8 3 At the same time however he says the skeptic s position seems extravagantquot 8 Comment Would Mike Huemer also say that the more limited skepticism mentioned above also seems extravagantquot In view of his later discussion in chapter III it seems clear that he would But suppose for example that one39s parents had been Berkeleians Would one be inclined to think that the idea that one cannot know whether the external world consists of mind independent objects or instead of a Berkeleian God seem extravagant to one 4 Mike Huemer now proceeds to set out four arguments for skepticism the first of which is as follows 1 The Infinite Regress Argument Mike Huemer offers the following summary of this first argument quot1 In order to know something I must have a good reason for believing it 2 Any chain of reasons must have one of the following structures Either a it is an infinite series b it is circular or c it begins with a belief for which there are no further reasons But 3 I cannot have an infinitely long chain of reasons for any of my beliefs 4 Circular reasoning cannot produce knowledge 5 Nor can I gain knowledge by structure 2c for a I would not know my starting beliefs to be true from 1 and b I cannot gain knowledge by deriving it from assumptions that I do not know to be true 6 Therefore I cannot know anythingquot 9 10 5 Mike Huemer points out that most philosophers think that the error in this argument lies in the first premise and they would say that contrary to that premise there are self evident or foundational propositions where a proposition is foundational if one can know it to be true without having a reason for it quot 10 Comments 1 Notice that Mike Huemer defines foundational propositions as ones that one can know without having any reason for thinking that the proposition is true 2 One does not need to be a foundationalist in this strong sense to answer the above argument since one can argue that knowledge can rest upon beliefs that are not justified and afortiori are not known 3 How can this be Suppose that one is slightly inclined to believe that someone told one that p was the case Given that one is only slightly inclined to believe it the probability that it is the case may be very small in which case one will not know that someone did so testify But suppose that one is also inclined to believe that someone else also told one that p was the case Given a sufficiently large number of beliefs of this sort it might well be extremely likely that someone or other told one that p was the case and this in turn might may it likely that p was the case So justified beliefs can rest upon unjustified beliefs 4 Given some accounts of knowledge it will then be possible to argue that knowledge can rest upon unjustified beliefs Here I have in mind for example the view advanced by Chisholm according to which knowledge may be defined as justified true belief where the justification does not also provide a justification for some false belief 6 Mike Huemer next points out that the skeptic has a response namely he or she can contend that one needs to be able to provide a way of distinguishing between propositions that are foundational such as that 2 2 or that one is conscious from propositions that are not such as that there is a twelve headed purple dragon on Venus 7 Mike Huemer next presents a Bonour style argument which can be summarized as follows 1 If proposition A is foundational while proposition B is not then it must be because there is some feature F that A has but B lacks 2 If I am not aware of feature F I cannot know or be justified in believing that proposition A is foundational 3 If I am aware that proposition A has feature F then that fact that proposition A has feature F provides a reason for A and so proposition A is not foundational 4 Hence it is logically i1npossible for there to be foundational propositions Comment One is aware first of certain states of affairs and secondly of the fact that those states of affairs make certain propositions true But this is not to have evidence for the proposition in question since there are no propositions that are distinct from the proposition in question that provide evidence for it 8 This brings us to the second of the skeptical arguments that Mike Huemer considers 2 The Problem of the Criterion Mike Huemer illustrates this second argument in terms of a community that uses the method of the Magic Eight Ballquot and that when this method is challenged uses that method to determine whether the method itself is reliable Mike Huemer offers the following summary of this skeptical argument quot1 All my beliefs are formed by some method 2 I am justified in accepting a belief formed by method M only if I am rst justified in believing method M is reliable 3 I do not have an infinite series of belief forming methods 4 Thus all of my beliefs must rest on beliefs formed by methods whose reliability has not first been established from 1 and 3 5 Therefore none of my beliefs are justified from 2 and 4quot 13 Comment In thinking about this argument there are two challenges to be answered 1 How does one justify the method that one uses in forming basic beliefs about contingent states of affairs 2 How does one justify the methods of reasoning that one uses both deductive and inductive 9 This third skeptical argument that Mike Huemer considers is as follows 3 How Can You Get outside Your Head This argument has the following overall structure 1 One cannot have any knowledge of a world external to one s mind unless either direct realism is true or indirect realism is true 2 Direct realism is false 3 Indirect realism is false 4 Therefore one cannot have any knowledge of a world external to one s mind How are 2 and 3 to be established In the case of 2 Mike Huemer mentions the sort of argument alluded to in the first chapter which he summarizes as follows quot1 As your focus shifts to the background the fingerlike thing you are seeing splits in two 2 No physical object splits in two at this time 3 Therefore the thing you are seeing is not a physical object quot 14 Comments 1 In a footnote Mike Huemer points out that terminology differs among indirect realists and that some do not speak of seeing mental images 2 Mike Huemer introduces the technical expression sense dataquot to refer to the mental items that allegedly exist whenever we exercise any of the five sensesquot 3 The term allegedly suggests that he does not think there are any such items The next question is how 3 is to be established Here Mike Huemer sets out Hume s famous argument This he summarizes as follows quot1 In order to have knowledge of the physical world we must be able to know that our sense data are caused by physical objects 2 In order to know that A causes B one must have experience of A and B 3 We have no experience of physical objects 4 Therefore we do not know that physical objects cause our sense data from 2 3 5 Therefore we have no knowledge of the physical world from 1 4quot 16 10 The fourth skeptical argument that Mike Huemer considers is as follows 4 The Brain in a Vat Mike Huerner summarizes this argument as follows quot1 H 0 N 901 Your sensory experiences are the only evidence you have for propositions about the external world The BIV scenario predicts that you would be having the same sort of sensory experiences as you are actually having Therefore the sensory experiences that you are actually having are not evidence that the BIV scenario isn t true from 2 Therefore you have no evidence that the BIV scenario isn t true from 1 3 Therefore you don t know that you are not a BIV from 4 Therefore you do not know anything about the external world from 5quot Comments 1 The crucial assumption in this formulation of the brain in a vat argument is that if you don t have evidence against a theory you are not justified in rejecting it 2 But this assumption is clearly false since the a priori probability of a theory may be very low and so you may be justified in rejecting it even though you have no evidence against it 3 Here is a different way of formulating the brain in the vat argument 4 Your sensory experiences are the only evidence you have for propositions about the external world N The BlV scenario predicts that you would be having the same sort of sensory experiences as you are actually having 3 When two theories predict precisely the same sensory experience for you you cannot be justified in assigning a higher probability to one than to the other Therefore the sensory experiences that you are actually having cannot make it the case that the view that you are perceiving an external world is more likely to be true than that you are a BIV from 3 If p and a are two incompatible propositions and p is no more likely than a then you are not justified in believing p 6 Therefore you are not justified in believing that that you are not a 31V from 4 5 7 Therefore you don t know that you are not a BIV from 6 8 Therefore you do not know anything about the external world from 7 H 01 4 This alternative formulation involves a different erroneous premise namely the assumption that when two theories entail the occurrence of precisely the same sensory experiences for you you cannot be justified in assigning a higher probability to one than to the other 5 The reason this assumption is false is that the two theories need not have the same a priori probability 11 This concludes what Mike Huemer regards as the four most important skeptical arguments He now goes on to consider different forms of skepticism 5 Skepticism and Common Sense 12 First Mike Huemer offers the following more general definition of skepticism than that offered earlier in Chapter 1 I define skepticism as any philosophical theory that challenges a signi cant class of common sense beliefs 18 13 Mike Huemer then defines common sense beliefsquot in terms of the following three characteristics i They are accepted by almost everyone except some philosophers and some madmen regardless of what culture or time period one belongs to ii They tend to be taken for granted in ordinary life iii If a person believes a contrary to one of these propositions then it is a sign of insanityquot Comments 1 To believe something that is contrary to the ordinary belief that there is a spatiotemporal world containing physical objects is not treated as a sign of insanity when as in the case of Berkeley arguments are offered in support of the opposing view 2 It is important to note that acting in ways that would be rational if certain beliefs were true while rejecting that belief need not be irrational in any way provided there is some other belief that it is rational to accept and that makes precisely the same actions rational So consider for example Bas van Fraassen s view that while we are not justified in believing that certain scientific theories are true we are justified in believing that those scientific theories are empirically adequate Or consider the corresponding view with regard to the proposition that there are physical objects In short in the case of physical objects one may act in the way that it would be rational to act if there were physical objects if rather than believing that there are physical objects one believes instead that the theory of the existence of physical objects is experientially adequate either because there really are such objects or because Berkeley s theory of reality is correct 3 As I discuss in more detail in connection with the G E Moore response to skepticism it is crucial whether the common sense beliefs in question are inferential For if they are inferential the correctness of the inference is very much something that one may change one s mind about given philosophical considerations For example if ordinary beliefs about physical objects involve as a matter of fact an inference to the best explanation then consideration of alternative theories such as Berkeley s may lead to one s forming a much lower estimate of the plausibility of the original beliefs 14 Mike Huemer goes on to discuss the second of the three characteristics listed above pointing out that philosophical skeptics continue to act in ordinary life as if the beliefs that they claim to be unjustified were true 15 Next Mike Huemer explains what he means by a challenge to P Q is a challenge to P if P and Q are not rationally cotenable 16 Mike Huemer argues very plausibly that his definition of skepticism is preferable to standard definitions such as the definition of skepticism as the view that no one can know anythingquot For one thing it applies to skepticism about justified belief as well as skepticism about knowledge For another skeptics typically grant that one has some knowledge 6 Skepticism and Internal Justification 17 Given the above definition of skepticism skeptical challenges can both be directed against different sets of beliefs and can take the following different forms 1 Certain beliefs are not true 2 Certain beliefs are not knowledge 3 Certain beliefs are not justified 18 Mike Huemer says that it is the last of these three sorts of claims that he wants to label radical skepticismquot He also says that the radical skeptic that he wishes to respond to is not saying merely that certain beliefs are not all that highly justified The radical skeptic I will be confronting holds that some significant class of common sense beliefs are not at all justified which is to say there is no reason to believe that they are true it is no more rational to think they are true than to think they are falsequot 20 19 Mike Huemer s final point in this section is that radical skepticism is concerned with the internalist sense of justification with what is justified from one s own point of view Chapter III Easy Answers to Skepticism 1 Is Skepticism SelfRefuting 1 Mike Huemer points out that regardless of what may be the case with regard to radical universal skepticism skepticism about the external world is not self refuting 2 He then goes on to argue that radical universal skepticism is self refuting not because it is self contradictory but because its truth would entail our lack of justi cation for asserting it 28 3 The gist of Mike Huemer s argument is that the universal skeptic will not be able to claim either that his or her premises are justified or that given those premises the conclusion is justified 4 A crucial point is that the universal skeptic cannot even advance a reductio ad absurdum argument since this presupposes that deductive reasoning is a justified method of arriving at beliefs Comment I think that Mike Huemer is right about radical universal skepticism 5 One conclusion that Mike Huemer wants to draw is that the first two skeptical arguments considered in the previous chapter are self refuting since they are defenses of universal skepticism Comment 1 Those two arguments can be recast however so that they are defenses not of radical universal skepticism but of skepticism with regard to the external world 2 This can be done in the case of the infinite regress argument by holding that some propositions expressing necessary truths can be noninferentially justified 3 Similarly in the case of the quotproblem of the criterionquot argument one can hold first that self contradictory propositions are necessarily false and secondly that the form of a proposition is something that one can directly recognize 2 The G E Moore Shift 1 Mike Huemer points out that G E Moore actually responds to Hume s argument for skepticism in Hume s Theory Examined in Some Main Problems of Philosophy 2 In this section Mike Huemer sets out a defense of the following argument quot1 Given a conflict between two beliefs it is rational to reject the less initially plausible one rather than the more plausible one Common sense beliefs have the highest level of initial plausibility Philosophical theories do not Therefore given a con ict between a philosophical theory and common sense it is rational to reject the philosophical theory rather than common sensequot 3 F9 3 In support of the second premise that is Common sense beliefs have the highest level of initial plausibility Mike Huemer argues that while massive scientific testimony could convince one that something like the Theorem of Pythagoras was false it would not convince one for example that there were no rocks Comments 1 It is not true that all common sense beliefs have the highest level of plausibility since some common sense beliefs have a higher level of plausibility than others For example my common sense belief that I am now having experiences has a higher plausibility for me that my common sense belief that I am now seeing a desk Moreover my treating the former belief as more plausible than the latter is surely justified since the truth of the latter belief entails the truth of the former but not vice versa 10 2 Similarly the common sense belief that there are other human bodies should have a higher initial plausibility for one than the common sense belief that those bodies have minds that enjoy experiences 3 Scientific testimony has convinced people that some beliefs that were common sense beliefs are false Thus it was once a common sense belief that a quality with which normal perceivers are directly acquainted namely the occurrent sensible property of redness was a quality out there on the surfaces of objects such as ripe tomatoes lf physics is right there is no reason for believing that there is any such property on the surfaces of ripe tomatoes 4 Other common sense beliefs that science has given us good reason for abandoning are for example the belief that when one touches an orange the matter in one39s hand comes in contact with the matter in the orange and the belief that most of the space occupied by a coin is occupied by matter in the coin 4 In support of the third premise that is Philosophical theories do not have the highest level of initial plausibility Mike Huemer argues that the disagreement over philosophical claims shows that they do not have the highest level of initial plausibility Comments 1 Mike Huemer refers here to philosophical theories 2 It is true that philosophical theories do not generally elicit a high level of agreement and it is fair to say that that shows that philosophical theories do not possess the highest level of initial plausibility 3 On the other hand there can be philosophical claims that do not involve philosophical theories in an ordinary sense and that may have very high initial plausibility so one needs to consider the possibility of a collision between such philosophical claims and common sense beliefs Comments on this Argument as a Whole 1 Consider the following claims a Reality consists of nothing except God plus finite immaterial minds and their mental states b Berkeley39s theory is not significantly more complex than the theory that there are mind independent external objects c The predictions of Berkeley39s theory are the same as the predictions of the theory that there are mind independent objects 11 d If two theories S and T generate the same observational predictions and theory S is only slightly more complex than T then the ratio of the a priori probability of S to that of the a priori probability of T will be only slightly different from one e The a priori probability of Berkeley39s theory is not significantly lower than the a priori probability of the theory that there are mind independent objects f Bayes s Theorem is true Or The definition of conditional probability is consistent Only the first of these would naturally be characterized as a philosophical theory At the same time the other four claims are very relevant to the question of the epistemic status of the first 2 To see this let us introduce the following abbreviations p There is a certain sort of world of mind independent objects m Berkeley39s view of the world is correct but all one s experience are as they would be if proposition p were true 8 The conjunction of all of the propositions about sensory experiences that are entailed by proposition p Probq the a priori probability that q is the case Probq r the probability that q is the case given that r is the case If claims b c and d above are correct or at least near enough then it is the case that 1 If Probm Probp is less than one it is only slightly less than one But by the definition of conditional probability one has that 2 Probm e x Probe Probm amp e Probem x Probm and similarly that 3 Probp e x Probe Probp amp e Probep x Probp But in view of the definition of quotequot we have that 4 Probep 1 But then in view of c above we must also have 5 Probem 1 Substituting 5 and 4 into 2 and 3 then gives us respectively 6 Probm e x Probe Probm and 7 Probp e x Probe Probp 12 Dividing equation 6 by equation 7 then yields 8 Probm eProbp e ProbmProbp But this means in view of its being the case that if Probm Probp is less than one it is only slightly less than one that 9 Probm e Probp e is only slightly less than one In short the a posteriori probability that Berkeley39s view of reality is correct relative to the totality of experiences that one has is only slightly less than the a posteriori probability that there is a world of mind independent physical objects 3 Notice the following important contrast lf Berkeley39s view of the world is true that is a contingent truth In contrast claims b through f if true are necessary truths 4 This is very important For necessary truths can have an initial plausibility that is greater than that of a common sense belief such as that there are rocks In addition even in the case of necessary truths whose initial plausibility is not especially high investigation can show that the proposition in question is extremely plausible and more plausible than common sense beliefs concerning the external world 5 To sum up then it is a mistake to think that the only way of challenging a common sense belief is by opposing it by a philosophical theory One can instead appeal to philosophical claims that do not involve advancing any philosophical theories and argue that those claims lead to the conclusion that a certain common sense belief does not have the probability that is being assigned to it Moreover the philosophical claims in question may be necessary truths and they can have an initial plausibility that is higher than that of common sense beliefs about the external world Further Comments Inferential Versus Noninferential Beliefs 1 The vast majority of common sense beliefs are inferential beliefs Thus for example in the case of beliefs about present but not currently perceived objects all such beliefs rest upon everyday conservation principles 2 Even if one confines oneself to beliefs about currently perceived objects those beliefs typically go beyond what one is directly acquainted with in the following ways a One believes that the things one sees are not facades b One believes that the things one sees have insides of a certain sort c One believes that the things one sees have tactile qualities d One believes that the things one sees would also be seen by others if they were present 13 e One believes that the things one sees would exist even if one were not seeing them 3 When beliefs are inferential the fact that their plausibility is not substantially reduced by certain sorts of challenges is compatible with its being the case that challenges specifically directed against the underlying inferences may radically reduce their plausibility 4 When a common sense belief is inferential it is apparent that the plausibility of that belief is a function of the plausibility of the inference involved and it may then very well be the case that confronted with a competing inference leading to an incompatible conclusion one s estimate of the plausibility of the original inference and so also of the original belief plummets 5 Suppose in particular that the following things turned out to be true a Our beliefs about external objects that we are currently perceiving are inferential beliefs b The inference is an inference to the best explanation c Berkeley s theory does not differ much from the theory of physical objects with regard to simplicity Then it would seem that the plausibility of the theory that there is a spacetirne world containing mind independent physical objects should drop very significantly 3 Stroud s Defense 1 Stroud s criticism of Moore s response to skepticism is not as clear as it might be from Mike Huemer s account but the basic idea seems to be as follows 1 If a claim is challenged by directing an objection against an argument on which the claim rests that objection needs to be answered reiterating the claim is worthless 2 Moore needs to consider where the claims that he is defending stand in a structure of epistemic justification and this he totally fails to do 2 Mike Huemer introduces at this point the idea that some beliefs may be justified on the basis of other beliefs 38 4 He also says that psychological certainty counts for nothing if the belief in question rests upon an argument that an objection has been directed against 39 5 Mike Huemer grants accordingly that to the extent that the skeptic is able to identify specific deficiencies or alleged deficiencies in the justification of common sense beliefsquot Moore cannot prove that beliefs about the external world are justified in the face of the skeptic39s objections by simply appealing to his knowledge that this is a pencilquot 40 14 6 Nevertheless Mike Huemer says that he sides with Moore against Stroud 7 His reason for doing so is connected with the idea that epistemic justification is not a one direction relationship 8 The crucial idea that Mike Huemer appeals to is that the unreasonableness of a conclusion calls into question the reasoning leading to itquot 41 9 Mike Huemer then claims that the conclusion that no one ever knows anything or that no one ever knows anything about the physical world is no more plausible prirna facie than the conclusion that nothing ever moves or that the earth is only 32 miles in circumferencequot 42 Comments 1 The idea that an implausible conclusion provides one with a good reason for thinking that one s reasoning may well have gone astray is not in itself unreasonable 2 However it is still true that if the reasoning supporting one s common sense beliefs has been challenged one must answer that challenge by defending the reasoning 10 Mike Huemer concludes his discussion in this section by pointing to the following differences between Stroud s case of the detective and his assistant and Moore s response to skepticism 1 The assistant s belief is not one that it is at all close to being a common sense belief 2 The detective is challenging an isolated belief held by his assistant whereas the skeptic is challenging an enormous set of beliefs 3 The detective s criticism of his assistant s belief does not involve controversial premises whereas the skeptic s criticism of knowledge claims does involve claims that though not without some plausibility are controversial Comments 1 I don t think that there is anything objectionable in the idea that it is likely that principles that if right lead to the conclusion that a massive set of beliefs are wrong are very likely to be wrong 2 But that thought should never replace a close examination of the principles in question and if after that examination the principles in question still seem right so that the inferences used to arrive at the common sense beliefs in question still seem faulty then the common sense principles should be questioned 11 Mike Huemer s basic contention here is as follows 15 The point I want to make here is that the Moorean argument or something very much like it can supplement and strengthen the presentation of an alternative nonskeptical theory of knowledge Once we have two alternative initially plausible epistemological theories before us if one of them is consistent with our everyday prephilosophical beliefs about what people know while the other one is radically revisionary this fact becomes a strong argument in favor of the formerquot 44 Comments 1 My view is first that one should be able to establish which epistemological theory is correct without using any such argument 2 The argument that I set out earlier involved in effect the following elements a The idea of there being logical probabilities is a sound one and so there are numbers that are the a priori probabilities of the Berkeleian hypothesis and of the mind independent world hypothesis b The extensive isomorphisms between these two hypotheses and the fact that the Berkeleian hypothesis is not significantly more complex than the mind independent world hypothesis makes it likely that the former hypothesis does not have a significantly smaller a priori probability than the latter c These two metaphysical theories make the same predications with regard to all experiences that humans will have d In view of c the logical probability of the occurrence of any experience E should be the same on either hypothesis e In view of and d the a posteriori probability of the Berkeleian hypothesis will not be significantly smaller than the a posteriori probability of the mind independent world hypothesis f Given that this is so one cannot be justified in assigning a probability to the mind independent world hypothesis that is significantly greater than one half let alone greater than say 099 3 Notice too that any attempt to argue for the view that the a priori probability of the Berkeleian hypothesis is much smaller than the a priori probability of the mind independent world hypothesis clears the deck for the indirect realist who can then argue that an inference to the best explanation argument allows one to assign a high probability to beliefs about a mind independent world 16 4 Why Study Skepticism 1 Although Mike Huemer thinks that the two answers to skepticism that he has defended are correct he thinks that one should not rest content with thus answering skepticism 2 His reason is that resting content with those answers means that one has not really learned anything positive from the encounter with skepticism 3 In particular the above responses do not tell us anything about precisely what the mistake is in the case of each of the skeptical arguments set out earlier 4 Moreover the principles that are appealed to in skeptical arguments typically are rather plausible and such as one might well accept if one didn t see them embedded in an argument for skepticism But if although those principles seem plausible one still rejects skepticism and thus the conclusions of the valid arguments that lead from such principles to skepticism one s overall epistemological outlook is not consistent 5 Mike Huemer points out that one s acceptance of principles that entail skepticism means that on the one hand one is embracing some of the time very strict standards of justification whereas the fact that one nevertheless rejects skepticism means that on the other hand one is operating some of the time with much looser standards of justification 6 He then suggests that besides being unfortunate in itself this give rise to the danger that one will appeal to the strict standards when confronted with a claim that one doesn t like while appealing to the loose standards when considering a claim that one likes 7 Mike Huemer suggests moreover that this is not a mere possibility since the human capacity for self deception is both vast and subtlequot 47 8 He suggests too that one area in which this operates is morality where on the one hand we often hold that there are no moral truths while on the other we vigorously condemn people who reject certain moral claims 9 Finally Mike Huemer claims first that one cannot have a satisfactory epistemological theory until one can see precisely what is wrong with the various arguments for skepticism and secondly that an epistemological theory is not satisfactory unless it entails conclusions about precisely where skeptical arguments go wrong Comment All of this strikes me as very plausible except that I would say not that an epistemological theory is not satisfactory unless it entails conclusions about precisely where skeptical arguments go wrong but rather that an epistemological theory is not satisfactory unless either it entails conclusions about precisely where any given 17 skeptical argument goes wrong or it shows that the skeptical argument in question is correct Philosophy 5340 Epistemology Topic 4 Skepticism Part 4 Can Skepticism Be Refuted 1 Overview of a Possible Refutation of Skepticism In my View there is only one way of attempting to refute skepticism that is promising The basic idea is to defend a theory of logical probability and then to use that theory to compare the probability that the non skeptical hypothesis in question has relative to the relevant evidence to the probability that the disjunction of the competing skeptical hypotheses has relative to that evidence 1 Probability 11 Different Concepts of Probability What is probability There are different conceptions of probability among which the following five are the more important Subjective Probability The subjective probability of a proposition p for a person S is the degree to which S assents to p One can think of it as being more or less defined by the choices that S would make over lotteries Thus suppose that if S is offered a free ticket in a lottery with 100 tickets numbered from 1 to 100 S does not care which ticket he or she is given Then S is assigning the same subjective probability to the following 100 propositions T1 Ticket 1 will win T2 Ticket 2 will win T3 Ticket 3 will win T100 Ticket 100 will win Now suppose that S who has no tickets in the lottery prefers getting a prize if any one of tickets 1 through 25 is the winning ticket to getting the same prize if proposition p is true Then the subjective probability that S assigns to p s being true is less than 25 100 If on the other hand S prefers getting a prize if proposition p is true to getting the same prize if one of tickets 1 through 24 is the winning ticket then the subjective probability that S assigns to p s being true is greater than 24 100 These two preferences together would then mean that the subjective probability that S assigns to proposition p s being true is greater than 024 and less than 025 The Relative Frequency Conception of Probability A second concept of probability is that of relative frequencies Suppose that a coin has been ipped 100 times and has come down heads 47 times Then the probability of the coins coming down heads according to the relative frequency conception of probability is 047 The Relative Frequency in the Limit Conception of Probability The idea of defining a concept of probability in terms of relative frequencies has certain unappealing consequences What is the probability that a certain coin will if ipped come down heads If the coin is only going to be ipped once in its lifetime the probability has to be either 1 or 0 on the relative frequency conception If it is going to be flipped three times in its lifetime the probability has to be either 1 or 23 or 13 or 0 on the relative frequency conception It does not really seem that this idea of probability as relative frequency is capturing some property of the coin As a result some people who are attracted to the empirically based nature of relative frequencies shift to a conception of probability that equates the probability that a coin w l come down heads not with the relative frequency but instead with the limit of the relative frequency with which the coin would come down heads if it were ipped an infinite number of times But then the question arises as to what the truthmallter is for the subjunctive conditional statement about what would happen if the coin were ipped an infinite number of times Propensities and Objective Probabilities A very different conception of probabilities but one that is also an empirically based one is that of propensities Consider for example the isotope of uranium that has an atomic weight of 238 Uranium 238 has a half life of about 447 billion years so that for any given atom of uranium the probability on the propensity interpretation of probability that that atom will undergo radioactive decay in about 447 billion years is equal to 05 Some philosophers think that propensities are fundamental properties that are irreducible to anything else For reasons that I shall not go into here that conception seems problematic and I think it is much more plausible to view propensities as properties that logical supervene on categorical properties plus probabilistic laws of nature Logical Probabilities Logical probabilities unlillte subjective probabilities have nothing to do with subjective states of a person and unlike relative frequencies and propensities logical probabilities are not based upon contingent facts about the world The logical probability associated with a proposition is a necessary property of the proposition Logical probability will be discussed in more detail in the next section Some Suggestions for Further Readings on Probability If you are interested in reading a little more about different conceptions of probability a very comprehensive survey article is Probability by Max Black in The Encyclopedia of Philosophy edited by Paul Edwards New York Macmillan 1967 Volume 6 pages 464 79 For a much fuller discussion one book that can be recommended as worthwhile is Ian Hacking An Introduction to Probability and Inductive Logic Cambridge Cambridge University Press 2001 Finally for a very good discussion of some different conceptions of probability along with a defense of the idea of logical probability see Rudolf Carnap Chapters 1 and 2 of The Logical Foundations of Probability Second edition Chicago The University of Chicago Press 1962 pages 1 51 12 Logical Probability What is logical probability The basic idea is that for any two propositions p and a there is some number k that presents the likelihood that a is true given evidence that consists only of proposition p Let us use Prap kquot to say that the logical probability of a given p is equal to k Logical probability if it exists is a relation simply between two propositions akin to the relation of logical entailment Moreover because it is a relation simply between two propositions it is necessary relation In the case where p logically entails a Prap 1 In the case where p logically entails the negation of a Prap 0 In all other cases the value of k is equal to or greater than 0 and equal to or less than 1 If k can take on infinitesimal values then there is reason to require that Prap 1 only if p entails a and that Prap 0 only if p entails the negation of a If p is a logically necessary truth then Prapquot represents in effect the a priori logical probability of a the probability that a is true given no evidence at all This can be written as Praquot Given the a priori logical probability that a proposition is true Pra the logical probability of one proposition relative to another can be defined via the standard definition of conditional probability which is as follows Prp a def Prgy amp g provided that Pra 14 0 PM So if one can specify the a priori logical probabilities of every proposition where this is the probability that a proposition is true given no evidence at all then the logical probability of any proposition p relative to any proposition 0 whose a priori probability is not equal to 0 is automatically defined But how is the a priori logical probability that a proposition is true to be defined This is a crucial and very difficult question One natural idea is that the a priori logical probability that p is true is equal to the proportion of the totality of the logically or analytically or metaphysically possible worlds in which p is true But there are various difficulties that stand in the way of this answer The most evident perhaps is that there are presumably an infinite number of possible worlds So what sense can one make for example of the claim that p is true in say 75 of those worlds Another less familiar and less obvious problem is that Carnap set out an argument that appears to show that given this possible worlds or state descriptions conception of logical probability it follows that one cannot learn from experience So if for example one has drawn one thousand marbles from an urn all of which were red the probability that the one thousand and first marble drawn from the urn will be red will be precisely what it was before any marbles were drawn from the urn 13 Some Axioms Definitions and Theorems of Logical Probability Here are some axioms that logical probability must satisfy 1 If p and q are logically equivalent then Prp Prq 2 For any p 0 S Prp S 1 3 If p is necessarily true then Prp 1 4 If p and q are mutually exclusive so that p 3 not 0 and q 3 not p then PrIc7 0r 0 PrP Prvl Given axioms 1 and 4 one can then prove 5 Regardless of the relation between p and q PrIc7 0r 0 PrP Prvl Prla7 amp 0 Next conditional probability can be defined as follows 6 Prqp W provide Prp 0 PrP Given 6 the following Multiplication Rule for logical probabilities then follows immediately 7 Prp amp q Prqp x Prp provided that Prp 0 Finally the following Rule of Total Probabilities follows from axiom 1 together with the definition of conditional probabilities via the Multiplication Rule 8 Prp Prqp x Prp Prq not In x Prnot p provided that 0 lt Prp lt 1 2 Skepticism concerning an External MindIndependent World In the case of skepticism concerning the existence and nature of an external mind independent spatial physical world a natural idea that many philosophers have had is that belief in the existence of such an external world can be justified by abduction inference to the best explanation hypothetico deductive method the method of hypothesis that is by the method that is used to justify scientific theories If one thinks of things in that way there are two basic steps that must be carried out if skepticism is to be defeated Step 1 Justifying the Method The first step involves showing that abduction or inference to the best explanation hypothetico deductive method etc is a legitimate form of non deductive inference Step 2 Showing that that Method Justifies the NonSkeptical Hypothesis The second step involves showing that when that method is applied to the relevant evidence which in the present case will be given by propositions about one s own present sensory experiences and memory beliefs the result is that a given non skeptical hypothesis turns out to have a higher probability or as some would prefer to say is a better explanation of the evidence than any competing skeptical hypothesis or as I think is needed than the disjunction of all relevant skeptical hypotheses 21 Step 1 Justifying Abduction Some philosophers hold it seems that the principle of abductive inference or inference to the best explanation hypothetico deductive method etc is a basic truth for which no justification can be offered This view is rejected by Bas van Fraassen and correctly in my opinion One way of thinking about this issue involves noticing that when philosophers talk about inference to the best explanation the explanation in question is typically though not always a causal explanation Deductive logical principles hoever are content neutral they do not contain any descriptive terms The question arises then of what account is to be given of the concept of explanation that is involved in inference to the best explanation In particular does it involve the idea of causation or can it be cashed out in purely logical terms No one I think has succeeded in doing the latter and this suggests that the concept of causation is needed But why should such a concept figure in an inductive principle Shouldn t inductive principles like deductive principles be free of such descriptive terms My view is that abduction cannot be taken as a primitive form of non deductive inference for which no proof can be offered But what then could such a principle of induction be derived from My suggestion is that it can be derived from a combination of two things 1 An analysis of causation and in particular an analysis that connects up causation with logical probability 2 A theory of logical probability So far however no one has carried out such a derivation So the task of justifying the inductive method that is needed to answer skepticism must be set aside as a task for the future 22 Step 2 Showing that the Method Justifies the NonSkeptical Hypothesis If I m right in thinking that the method of abduction needs to be justified and that this is to be done by appealing along with an analysis of causation to a theory of logical probability then what the method of abduction will generate presumably are the probabilities that different hypotheses have upon the relevant evidence What needs to be shown then is that application of that method leads to the conclusion that the hypothesis that there is a mind independent spatial physical world has an a posteriori probability relative to the propositions describing one s present experiential states and memory beliefs that is greater than the a posteriori probability that any competing skeptical hypothesis has relative to that same body of evidence But that is not sufficient The non skeptical hypothesis must also be more likely to be true than to be false and so the probability of the non skeptical hypothesis must be greater than the probability of the disjunction of all of the competing skeptical hypotheses Nor does even that seem sufficient For if the hypothesis that there is a mind independent spatial physical world has an a posteriori probability relative to the propositions describing one s present experiential states and memory beliefs that is only slightly greater than one half one is still in an epistemologically unsatisfactory state something that is especially clear when one notes that the likelihood that there are other minds is closely tied to the likelihood that there is a mind independent spatial physical world So it would seem that a satisfactory response to skepticism concerning the existence of a mind independent spatial physical world requires that the a posteriori probability of there being such a world is quite close to one 3 The Relation betweenA Priori Logical Probabilities and A Posteriori Logical Probabilities in this Case It is often the case that the a priori probability of some proposition p is greater than the a priori probability of some other proposition 0 but that things are switched when one considers the a posteriori probabilities relative to some evidence 8 the a posteriori probability of a relative to 6 may be less than the a posteriori probability of 5 relative to 8 But the situation is different when one considers a non skeptical hypothesis and a corresponding skeptical hypothesis There the order in the case of the a posteriori probabilities must be the same as in the case of the a priori probabilities 31 The Argument The relevant argument was set out earlier in the second set of seminar notes on skepticism It involves considering the relevant non skeptical hypothesis and a corresponding skeptical hypothesis As before let us take these to be p There is a certain sort of world of mind independent objects m Berkeley39s view of the world is correct but all of one s experiences and memory beliefs are as they would be if proposition p were true Propositions p and m are to be understood in such a way that first of all they are full descriptions of the world as it would be under the relevant hypothesis and secondly they are experientially and memorybelief equivalent at least up until the point where one dies lf then we introduce the following proposition 8 The conjunction of all of the propositions about the sensory experiences and memory beliefs that one has at the present time that proposition will be logically entailed by p and also by m since those propositions are experientially equivalent and they fully describe the world as it is under the respective hypotheses As in section 1 above let us use the following abbreviations Prq the a priori logical probability that q is the case Prq r the a posteriori logical probability that q is the case given that r is the case The argument in question is then as follows By the definition of conditional probability given in section 13 one has the following four equations W W 1 Prpe we and Per Mp W W 2 Prme We and Pre m Mm Multiplying through by the denominators of the fractions in these four equations that is by Pre Prp Pre and Prm respectively then gives us 3 Prp e x Pre Prp amp e Prep x Prp and 4 Prm e x Pre Prm amp e Prem x Prm But in view of the way that quotequot is defined one has the following two entailments 5106 6 21136 These two entailments then entail respectively that 7 Prep 1 and 8 Pre m 1 Substituting 5 and 6 into 3 and 4 then gives us respectively 9 Prp e x Pre Prp and 10 Prm e x Pre Prm Dividing equation 9 by equation 10 then yields 11 Prpe Prp 39 Prme Prm 32 The Upshot The conclusion of the above argument is that the ratio of the a posteriori logical probabilities is exactly equal to the ratio of the a priori logical probabilities Among the important consequences of this are the following 1 It is logically impossible to establish that the a posteriori logical probability of the non skeptical hypothesis is greater than the a posteriori logical probability of the skeptical hypothesis unless the a priori logical probability of the non skeptical hypothesis is greater than the a priori logical probability of the skeptical hypothesis 2 It is logically impossible to establish that the a posteriori logical probability of the non skeptical hypothesis is much greater than the a posteriori logical probability of the skeptical hypothesis unless the a priori logical probability of the non skeptical hypothesis is much greater than the a priori logical probability of the skeptical hypothesis 3 On the positive side if one can establish that the a priori logical probability of the non skeptical hypothesis is much greater than the a priori logical probability of the skeptical hypothesis that then entails that the a posteriori logical probability of the non skeptical hypothesis is much greater than the a posteriori logical probability of the skeptical hypothesis 4 One Key Idea The Probabilities of Laws of Nature Versus the Probabilities of Accidental Generalizations 41 The Probability that a Generalization Is True But how can one establish that the a priori logical probability of the non skeptical hypothesis is much greater than the a priori logical probability of any of the competing skeptical hypotheses To begin to answer this question we need to turn to the epistemology and metaphysics of laws of nature Suppose that four marbles are drawn from an um and that all four are a certain shade of red Relative to that proposition what is the probability that the fifth marble drawn from the urn will also be that same shade of red According to Rudolf Carnap s theory of logical probability the answer depends upon the size of the family of mutually exclusive and jointly exhaustive color properties to which the property of being that shade of red belongs Suppose for silnplicity that there are only two color properties Then the probability that the fifth marble drawn from the urn will be the same color as the first four What if there are k color properties Then according to Carnap s theory of logical probability the probability that the fifth marble drawn from the urn will be the same color as the first four More generally if n marbles have 4 k 4 k been drawn from an um and all of them have been a certain shade the probability 11 1 that the n lth marble drawn from the urn will be the same shade k 11 For silnplicity however let us consider the case where the family of mutually incompatible properties has only two members Then if four marbles have been drawn from the urn that are all the same color the probability that the fifth will be 5 the same color is as noted above Next let us consider what the probability is if four marbles have been drawn from the urn all of which are the same color that both the fifth and the sixth marbles will be that color The answer is that for that to be so the fifth marble must match the color of the first four the probability of which is 2 and then if that happens the color of the sixth marble must match the color of the first five What is the probability of that The answer is gotten by putting n 5 and k 2 in the general n1 th tth b bil39t 39 lt 7 k so a epro a 1y1sequa o 7 formula 11 For both the fifth and the sixth marble to be the same color as the first four two things have to happen the first of which has a probability of 2 and the second 10 of which has a probability of To get the probability that both of these things will happen one has to multiply the two probabilities So if four marbles have been drawn from the urn all of which are the same color the probability that both the fifth and the sixth will be that color 2 X In similar fashion one can show that if four marbles have been drawn from the urn all of which are the same color the probability that the fifth the sixth and the seventh marble will all be that color 2 X g X More generally if four marbles have been drawn from the urn all of which have the same color property the probability that the next In marbles will be that 6 7 8 9 gtlt4m 1gtlt 4m xix 7 W7 8 9 10 4m 4m1 Looking at this formula one can see that the denominator of any given fraction is equal to the numerator of the next fraction This means that one can use cancellation to write the above product of fractions in a much simpler form Thus we have that if four marbles have been drawn from the urn all of which are the same color the probability that the next In marbles will be that color 5 4 31 1 5 m Next what is the situation as the number of marbles in the urn is larger and larger In particular what is the probability that all of the marbles in the urn are the 5 the 5 m probability will not only be smaller and smaller as m is larger and larger but if the number of marbles in the urn is infinite then as m gets larger and larger the 5 5 m same color as the first four The answer is that since the probability probability will approach 0 in the limit I have been focusing on the case where one is dealing with a family of properties that contains only two members How would the argument be affected if there were more properties in the family If the family of properties contains three members say red green and blue and four marbles have been drawn from the urn all of which have been red then the probability that the next marble will be red will be equal to 3 rather than to 2 and the probability that the next three marbles will all be red will be equal to g X g X Z 9 rather than to 2 X g X g What one can see is that cancellation still takes place but now it occurs between the denominator of one fraction and the numerator not of the next fraction but of the one after that What that means is that the probability that 11 the next In marbles will all be red rather than being equal to is equal to 5 m 5 X 6 4 m5 121 so the argument is unaffected and the same is true regardless of the number of properties in the relevant family of properties But once again the limit of this fraction as m goes to infinity is still 0 Conclusion If there are an infinite number of marbles in the urn and if four marbles have been drawn from the urn all of which are the same color then the probability that all of the marbles will be that color is infinitesimally close to zero Four marbles is of course a very small sample Suppose then that a trillion marbles have been drawn from the urn all of which are the same color Then in the case where the family of properties contains only two members the probability that L000000000001 the next In marbles are all that same color L000000000001 111 But if there are an infinite number of marbles in the urn then the probability that all of them are that same color will still be infinitesirnally close to 0 since L000000000001 L000 000 000001 m 42 The Problem of Justifying the Belief that a Law Obtains This result looks disturbing For consider a universe with non probabilistic laws for example a Newtonian universe Newton s Laws of Motion and the Newtonian Law of Gravitation will have an infinite number of instances if time never ends They will also have an infinite number of instances if time ends but the temporal series is dense that is there is a temporal instant between any two temporal instants So how in a Newtonian universe could one ever be justified in believing that the Newtonian laws had no exceptions and so were true approaches 0 as m tends to infinity If as many philosophers following Hume maintain laws of nature are merely certain cosmic regularities then the answer is that in view of the above result whenever one was justified in believing that there would be an infinite number of instances falling under the cosmic generalization in question one would never be justified in believing that the probability that the generalization in question was true was more than infinitesirnally greater than zero and so one would never be justified in believing that the exceptionless regularity in question obtained There are however other views of laws According to one which I favor laws rather than being regularities are second order relations between the relevant properties Suppose for example that it is a law that all Fs and Gs Then according to the view in question what makes this a law is that the property of F ness and the property of G ness stand in a certain relation call it the relation of nomic 12 necessitation If this relation obtains then it entails that all Fs are Gs so that the cosmic regularity obtains But the cosmic regularity is not itself the law How does this help The answer is that the state of affairs that consists of the property of F ness standing in the relation of nomic necessitation to the property of G ness is an atomic state of affairs in sharp contrast to the regularity which consists of an infinite number of states of affairs of the form a has the property of F ness and also the property of G ness It is then possible to argue that the atomic state of affairs that consists of the property of F ness standing in the relation of nomic necessitation to the property of G ness has an a priori logical probability that is greater than zero and that is not an infinitesimal This in turn enables one to show that as the number of F5 that have been observed to be Gs increases with no counterexamples appearing the a posteriori logical probability that it is a law that all Fs are Gs not only increases but increases quite rapidly and moreover is soon very close to 1 43 Conclusions If this is right we can draw the following important conclusions 1 If laws are simply cosmic regularities then the a posteriori logical probability that a non probabilistic law with an infinite number of instances will obtain is infinitesirnally close to zero 2 By contrast if laws are second order relations between universals then the observation of instances falling under the law with no counterexamples will result in a rapid increase in the a posteriori logical probability that the law obtains and moreover that a posteriori logical probability will also rapidly approach the value of 1 5 The Relevance of this to the Problem of Skepticism How is this relevant to our problem Though I am not confident that all the details are in place the basic ideas are as follows 51 The Earlier Skeptical Argument Recall the earlier skeptical argument that I set out The key idea was that since there is a very extensive mapping for example from propositions concerning how things would be in a certain mind independent physical world at a given time to an exactly corresponding representation in the mind of a Berkeleian deity there are extremely extensive similarities between the two theories and this together with the fact that they differ very little in complexity is grounds for holding that their a priori logical probabilities should not be very different That conclusion together with the results of the argument set out in section 3 above then entails that the a posteriori logical probability of the hypothesis that there is a mind independent physical world should at best be only slightly greater than the a posteriori logical probability of the hypothesis that one lives in a Berkeleian world 13 The discussion in section 4 enables one to see why that argument is problematic For compare the following two hypotheses Hypothesis 1 Hypothesis 2 There are an infinite number of Fs There are an infinite number of Fs All Fs are Gs All Fs are Gs Object 1 is both F and G Object 1 is both F and G Object 2 is both F and G Object 2 is both F and G Object 1 trillion is both F and G Object 1 trillion is both F and C It is a law that all Fs are Gs There are no laws that entail that all Fs are Gs Hypotheses 1 and 2 agree with regard to 1000000000002 statements and disagree only with regard to one claim So one might very well think that hypotheses 1 and 2 differ only by the slightest amount with regard to siInplicity Nevertheless the probability of hypothesis 1 upon the one trillion statements concerning objects 1 through 1 trillion is extremely high whereas the probability of hypothesis 2 upon that same set of one trillion statements concerning objects 1 through 1 trillion is infinitesirnally close to zero Two theories that differ only in that one postulates a law where the other postulates an accidental regularity can therefore differ enormously in probability 52 The BraininaVat Skeptical Hypothesis 1 Consider for simplicity a deterministic world such as a Newtonian world In such a world suppose that the state of the universe at some time t is I while the state of the universe at some later ti1ne u is Then the existence of state I at ti1ne 15 together with the laws of that deterministic universe logically entail that the universe at time u must be in state States of the universe at different tiInes are then nomologically linked and the state of the universe at any earlier time nomologically or causally necessitates that the universe will be in the relevant state at any later ti1ne that one chooses 2 Consider now the skeptical hypothesis that one is a brain in a vat If that hypothesis is to be experientially equivalent to the hypothesis that there is a real physical world located in space and time then it would seem that one of the following things much be the case 1 One possibility is that first of all the computer that is controlling the experiences that one is having as a brain in a vat contains some sort of map that represents how things would be at a given ti1ne in a physical world of the sort that the person associated with the brain in the vat is apparently experiencing So at ti1ne t the computer contains some representation of state I call it RI Secondly the 14 computer then constantly applies rules to update that representation rules that parallel the laws that would exist if the world were as it seems to be to the person associated with the brain in the vat so that at time u the computer contains instead a representation of state call it Then thirdly the computer calculates the type of experience call it E I that the person associated with the brain in the vat would be having at time t if he were located in a physical world in the way that it seems to him he is and the computer then stimulates the person s brain to produce an experience of type EI Similarly at time u the computer produces an experience of type E 2 A second possibility is that the computer that is controlling the experiences that one is having as a brain in a vat rather than containing some sort of map that represents how things would be at one given time in a physical world of the sort that the person associated with the brain in the vat is apparently experiencing a map which the computer then constantly updates contains instead a total map of what the relevant world would be like at absolutely every time The computer in that case does not have to update its map at any time But it has instead to access different parts of that total map at different times in order to work out how to stimulate the brain at those different times to produce the appropriate experiences 3 A third possibility is this The computer is somehow running a program that causes it to be in a state at time t call it St that is not a representation of state I but that nevertheless causes the computer to cause the person who is the brain in the vat to have an experience of type E Similarly the computer winds up in state Su at time u that is not a representation of state but that nevertheless causes the computer to cause the person who is associated with the brain in the vat to have an experience of type EU at the relevant time 3 The crucial point is now this First in the case where the computer is in different representational states at different times the computer s being in representational state RI at time 15 does not nomologically or causally necessitate that the computer will be in state RU at the later time u Secondly and similarly in the case where the computer has a complete map of how the apparent physical world would be at absolutely every time the part of that total map that represents how the apparent world would be at time 15 does not nomologically or causally necessitate the part of that total map that represents how the apparent world would be at the later time u Nor does the computer s accessing one part of the total map at time t nomologically or causally necessitate its being the case that the computer will access the right part of the total map at the later time u Finally and again similarly in the case where the computer does not have states that represent how the apparent physical world is at any time the non representational state St of the computer at time 15 does not nomologically or 15 causally necessitate its being the case that the computer will be in state S u at the later time u One reason these things are not the case is that it is nomologically possible that there are things outside of the computer that can interact with the computer to shut it down or to modify its program or to damage it etc Another reason is that there may be a failure of the computer s memory at any point or a failure of its processing system 4 In contrast to the case of the two hypotheses discussed in section 51 the difference between the non skeptical mind independent spatial world hypothesis and the skeptical brain in a vat hypothesis is not that where the former postulates laws of nature connecting states the latter postulates simply a cosmic coincidence The reason is that laws of nature do play a role in linking together a computer s states at different times even though earlier states do not nomologically or causally necessitate later states For earlier states of the computer do causally give rise to the later states But they do so only as long as the correct background conditions continue to be satisfied So later states of the computer are a function of earlier states of the computer plus laws of nature together with the obtaining of a generalization concerning the continued eadstence of the relevant background conditions such as no failure of memory or of processing etc One has in short a generalization that is not nomically true that is not entailed by laws of nature but that at the same time is not a purely accidental generalization It holds partly as a matter of accident and partly as a matter of laws of nature The upshot is that there is therefore some nonzero probability that that generalization will fail at any point of time The problem is to assess the likelihood of that 5 How likely is such a failure That depends on a number of factors One factor that appears to be relevant is the nature of time If time is infinitely divisible then between any two moments of time there will be an infinite number of instants and so one might think that the probability that there will be no failure of the background conditions in any period of time no matter how short will be infinitesirnally close to zero That would seem however not to be right at last given only what we have considered so far since it seems clear that the probability of something going wrong with any given computer depends upon a number of factors such as how well it is protected against outside interference whether it involves backup systems etc Computers break down but they can also go for long periods of time without that happening 6 But there is a second factor that is surely relevant and that is the compleadty of the world that the computer is so to speak imitating The larger that world is the more complicated the computer s states have to be regardless of whether the states are representational or non representational The intuition is then that as those states 16 become larger and larger the greater the likelihood of a breakdown is a breakdown that will have the result that the computer fails to bring about the type of experience in the person associated with the brain in the vat that the person would have if he or she were located in the a physical world of the relevant type Some such divergences may of course be small and not noticeable But others surely will be noticeable 7 The idea in short is that if one is a brain in a vat apparently experiencing a very complex physical world such as the world that you and I think we are experiencing one should expect that there will be failures in the computer at some points that will have the result that one s experiences will not be what they should be there will be for example discontinuities in successive visual experiences or there will be gaps in one s visual field or one s visual field will freeze at some point There will in short be computer glitches 8 This much then seems to me plausible the probability that the brain in vat hypothesis is true is less than the probability of the non skeptical mind independent spatial world hypothesis given that the relations of nomological or causal necessitation between state I and state that exist if the non skeptical hypothesis is true get replaced by relations between representational states RH and RU or between non representational states St and Su that are not relations of nomological or causal necessitation since they depend upon the obtaining of a background generalization that does not express a law 9 Moreover what is true of the brain in a vat hypothesis should also be true of any skeptical hypothesis given that any skeptical hypothesis that is experientially equivalent to the non skeptical hypothesis depends upon the obtaining of a generalization that is not entailed by laws of nature it would seem that the a priori probability of any such skeptical hypothesis must be lower than the a priori probability of the corresponding non skeptical hypothesis The same must then be true of the corresponding a posteriori probabilities 10 There is another issue that is very relevant and that needs to be considered To this point I have simply supposed that the computer that is controlling the experiences that one is having as a brain in a vat somehow is in states either representational states RU or non representational states S t that it makes use of to determine what experiences to cause at any given time But let us now ask what the computer must be like to have such states Suppose in particular that the way it operates is by being in representational states If the brain in a vat hypothesis is to be experientially equivalent to the non skeptical real physical world hypothesis then it would seem that state RU must contain complete information concerning what properties would be present in the spatiotemporal universe at the time in question if there really were a physical world of the sort in question This is an enormous amount of information Indeed given that every property every relation and every spatial location would need to be represented I think it could be argued that the space required for storing that information could 17 not be less than the space that would be occupied by the physical world in question if the latter were real Moreover if space is infinitely divisible there will be a non denumerable infinity of locations and in each case the computer has to contain information about what particles or fields etc are or are not present at each of those locations So it looks as if the required computer will itself have to be at least as large as the physical universe that exists if the non skeptical hypothesis is true 11 l have considered only the possibility of representational states I suspect however that one can argue that there is no way that one can use non representational states St to encode information that will enable the computer to calculate what experiences to produce and that will require less space 12 It is not enough however for the computer to store information about how the physical universe if it existed as it seems to the person associated with the brain in the vat is at any given time The computer has under the first of the three scenarios mentioned above to update that information with the passage of time and the information covers how things are at every apparent spatial location In updating that information then the computer must be accessing information that if the earlier conclusion concerning the size of the regions where that information is stored is correct is distributed throughout a space that is as large as our physical universe is assuming the latter is real How can the computer work on such widely scattered information at any given time The answer is that the processor in the computer would have to be causally connected with all of the locations where the information is stored All of those causal connections would depend however upon pathways that could break down either due to interference from without or by internal deterioration So again we have places where things can fail and these places moreover and as we have just seen would seem to constitute a region at least as large as our universe assuming it exists 13 Moreover consider how quickly the computer must work If time is infinitely divisible the computer cannot take any finite length of time to update how things are at any given spatial location it must work infinitely fast But even if time is not infinitely divisible even if there is a small temporal interval related perhaps to the Planck constant the speed of the computer would have to be enormous in the extreme 14 On the second scenario mentioned above the computer has a total map representing how the apparent world would be at every moment if it were real so no updating is needed But this saving is bought at the cost of requiring sufficient space to store information about the complete state of the universe at every time The computer would need space whose size is comparable to that of our apparent spatiotemporal world Moreover this increase in the amount of information stored requires a comparable increase in the accessing networks which in turn translates 18 into many more possibilities for breakdowns Indeed if ti1ne is infinitely divisible the possibilities for breakdowns will be infinitely greater 15 These processes either of accessing information or of performing calculations to update it or both are not ones in which successive states stand in relations of causal necessitation Consequently there must be some non zero probability that there will be a failure either with regard to the original creation and storing of the information or with regard to the calculations by which the information is updated and then in either case with regard to the retrieving of information Then given the overwhelming amount of information involved and the lengthy causal processes needed for its retrieval and also in the first case the astounding nature of the calculations involved it would seem extremely likely that something would go wrong even in a brief stretch of ti1ne Conclusion Here in contrast with the comparison of laws of nature with regularities that involve cosmic accidents discussed in section 4 I am unable to calculate a probability Nevertheless it seems to me that there are excellent grounds for concluding that the brain in a vat hypothesis has a much lower probability than the hypothesis that there is a mind independent physical world governed by natural laws 53 A Second Skeptical Hypothesis Berkeley s Immaterial World 1 But mightn t one be able to avoid the arguments that I have offered for thinking that the brain in a vat hypothesis is very improbable by shifting to a different skeptical hypothesis In particular what if one switched from the brain in a vat hypothesis to Berkeley s hypothesis Can it be argued that God as an immaterial being will have no problem storing all of the information accessing it and then updating it infinitely quickly 2 If as I am inclined to think the idea of an omnipotent being is logically coherent then Berkeley s hypothesis does seem more difficult to criticize But if that s right and if as some writers such as Richard Swinburne maintain the idea of God is quite a simple idea may not one be able to argue that that a priori logical probability of the existence of God is not that low 3 Re ections on what is involved in the storing accessing and updating of information in the computer case however makes me wonder whether the a priori logical probability of there being an immaterial thing that could do these things isn t in fact extremely low contrary to what some philosophers have claimed and contrary to what one might initially think oneself For mustn t any immaterial being that stores information that accesses that information and that updates it involve causal processes Mustn t there then be causal networks and won t those causal networks be equally complex Won t any calculations involve just as many steps 19 4 Consequently I m inclined to think that the situation is not really different when one shifts from the brain in a vat skeptical hypothesis to the Berkeleian skeptical hypothesis For imagine describing the storing of information the accessing of it the updating of it and the performing of relevant calculations all in a way that does not mention what sort of entity is doing all of that In all of this earlier states do not causally or nomically necessitate later states and because of this there are many and perhaps literally countless opportunities for failures and breakdowns to occur If someone then tells you that by the way all of this is being done by an immaterial being are you then inclined to think that all of those problems vanish 6 Summing Up The result is that while the matter is far from clear cut I am inclined to think that given further development the above lines of thought will provide a refutation of skepticism concerning the existence and nature of an external mind independent physical world There is as we have just seen a serious question of whether the considerations that l appealed to earlier in the case of the brain in a vat skeptical hypothesis in order to argue that that hypothesis has a very low probability can be applied to Berkeley s hypothesis that we live in an immaterial world But if it can be successfully argued that that can be done then I think that we will have a refutation of skepticism concerning the existence of an external mind independent physical world of the sort that most people believe exists The reason is first that while variations are possible it does seem that the only skeptical alternatives are an illusion maintained by a physical thing capable of storing retrieving and manipulating information and an illusion created and maintained by an immaterial being that can do those things So if one can show that the brain in a vat scenario is unlikely and that Berkeley s immaterial world hypothesis is unlikely I think that one can show that any given skeptical hypothesis is unlikely Secondly I think that one has good reasons for thinking that the brain in a vat hypothesis is not only unlikely but extremely unlikely If the same is true of Berkeley s hypothesis then I think one can conclude that the non skeptical mind independent physical world hypothesis is not only much more probable than any given skeptical hypothesis but also much more probable than the disjunction of all possible skeptical hypothesis Finally all of this assumes as I noted earlier that the problem of induction can be solved and that in particular one can justify abduction

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