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U OF T / History and Philosophy of Science / HIST 100 / How many types of propositions are there?

How many types of propositions are there?

How many types of propositions are there?


School: University of Toronto
Department: History and Philosophy of Science
Course: Intro to History and Philosophy of Science
Professor: Hakob barseghya
Term: Fall 2016
Cost: 50
Name: Hps100 Midterm Review
Description: Midterm review
Uploaded: 10/25/2016
13 Pages 17 Views 3 Unlocks

Hps100 Midterm Review 

How many types of propositions are there?

Theory: A set of propositions that attempt to describe something. Scientific Mosaic: A set of all accepted theories. Note that scientific  mosaics have changed over time.

Scientific Change: Any change in the scientific mosaic.

Absolute Knowledge:

Question: Is there anything unchangeable in the mosaic? Is there such a  thing as absolute knowledge?

Case 1: Mathematics

1 + 2 = 3. What makes this statement true?

We've defined 2 as: 1 + 1 = 2

We've defined 3 as: 1 + 1 + 1 = 1 + (1 + 1) = 1 + 2

Mathematics: General Template

- We start with some basic definitions

- Some basic theorems follow immediately from the definitions. - Other theorems follow from definitions and basic theorems. - More theorems can be deduced from those theorems and so on.

Can synthetic propositions be absolutely certain?

Don't forget about the age old question of How do you calculate molecular mass and formula mass?

Case 2: Swans

How can you justify the statement: All swans are white.

The theory that all swans are white is based on our experience (observation)  of individual swans.

Case 3: Gravity

Newton's law of universal gravitation → F = (G * m1 * m2) / r^2

How do we know this is true?

→ It must be somehow based on experience.

Two types of Propositions:

1. Analytic

- deducible from definitions.

- cannot contradict the results of experiments or observations - must necessarily hold true in all possible worlds. i.e. the opposite is  inconceivable

- all propositions of formal sciences (e.g. mathematics, logic) are analytic.

What is an example of an ontology?

If you want to learn more check out Why do firms innovate?

2. Synthetic

- not deducible from definitions

- can contradict the results of experiments or observations - most (not all) propositions of empirical sciences (e.g. physics, biology,  economics) are synthetic because the opposite is conceivable - E.g. We can conceive a world where floating mountains are possible.

Key point to note: Synthetic propositions can be confirmed by  experience and observation but cannot be proved. There is no such thing  as “proof” when it comes to synthetic propositions.


1. Can analytic propositions be absolutely certain? → Yes.

2. Can synthetic propositions be absolutely certain? → No.

Why synthetic propositions can't be absolutely true: 3 Problems: If you want to learn more check out Why use bacteria and bacteriophage model systems?

1. Problem of Sensations:

Our sensations/perceptions are questionable. E.g. Optical illusions. There is a disconnection (or possibility of a disconnection) between reality and  perception. We also discuss several other topics like Which famous italian family were huge patrons of the arts during the renaissance?

2. Problem of Induction: We also discuss several other topics like What is residence time?

How can we arrive at a general conclusion if experience provides us only  singular propositions. (e.g. We see a swan that's white. How do we know that there isn't a black swan somewhere that no one has seen? How could we  know if we've observed all the swans out there? How could we know that  there won't be a black swan in the future?

The point is, our experiences are limited.

3. Problem of Theory-Ladenness:

Let's say you “observe' mountains on the Moon through a telescope. What's  the problem here? → You've placed your trust in the instrument (telescope)  and theories of optics. Even trusting your vision requires trusting things like  having good lighting, you're not under the influence of any drugs, you're not  hallucinating, etc.

Our observations rely on or are laden with theories. Theories can change.  Theories are shaping our perspectives.

Can synthetic propositions be absolutely certain? There are two  stances you can take:

1. Infallibilism: Synthetic propositions can be infallible, i.e. incapable of  making mistakes. Empirical knowledge can be absolutely certain. 2. Fallibilism: No synthetic propositions can be infallible. Empirical  knowledge cannot be absolutely certain. This is the position accepted  nowadays.

Scientific Method:

Theory Assessment - Question: Don't forget about the age old question of What do answers do?

While all theories in empirical science are fallible, we still believe that some  theories are better than others. How do we decide which theories should  become accepted into the scientific mosaic?

Theory Acceptance:

A theory is said to be accepted if it is taken as the best available description  of its object. The object could be something physical (e.g. falling apple,  revolving planet), something social (e.g. a group of people, social  institutions), etc.

Theory Use:

A theory is said to be in use if it is taken as an adequate tool for practical  application, regardless of whether it is accepted or not.

Theory Pursuit:

A theory is said to be pursued if it is considered worthy of further  development, regardless of whether it is accepted or whether there is any  use for it at that moment.

Example: Today,

 Accepted: Quantum Physics, General Relativity

 Used: Classical Newtonian Physics

 Pursued: String Theory

Two incompatible theories can be simultaneously used, pursued but not  accepted. Only one of the alternatives can be accepted at a time.

How do we decide which theory is the best available description of its object? We need a list of rules, criteria.

We need a method of appraisal to determine which theory is better in light of the available evidence.

Scientific Method:

Method: A set of requirements (criteria, rules, standards, etc.) for  employment in theory assessment (evaluation, appraisal, comparison, etc.) Example of methods (not necessarily good methods): Accept theories that  are simpler. Accept theories with confirmed novel predictions. Accept  theories that solve more problems. Accept more precise and accurate  theories.

Methods should not be confused with methodologies.

Methodology: A set of explicitly formulated rules of theory assessment.

Methodologies are the rules openly prescribed by the community as the  correct way of doing science.  

Methods are the actual (implicit) expectations of the scientific community.  

Our openly formulated requirements are often very different from our actual  expectations.

You may or may not have an openly stated methodology, but you do have a  method. You may or may not be aware of what is it that guides you in your  choices (that would be your methodology) but you do have a method (your  implicit expectations which allow you to choose between competing movies  for example).

Methodologies are what scientists say they should be doing; methods are  what scientists actually do.

Focus on the method, not on the methodologies.

Methods of theory assessment are not to be confused with techniques used  by scientists to construct theories.

Research Technique: A set of procedures for theory construction  (generation, invention). E.g. brainstorming.

If there were a fixed set of rules employed by the scientific community in  theory assessment then we would be in a position to say that our current  theories are better than the theories of the past.

The whole process of scientific change would be governed by this fixed  scientific method.


Are there such unchangeable rules of theory assessment?

What are the requirements of the scientific method? How can they be  explicated? To answer this question we must study how theories actually  become accepted into the mosaic.

Why is it that, in some cases, theories become accepted simply because they are more precise and accurate than their predecessors, while in other  cases, theories are required to provide confirmed novel predictions in  order to become accepted?

Accepted Ontology: The accepted views on the types of entities and  interactions that populate the world.

Our attitude seems to depend on whether the theory attempts to modify the  accepted ontology.

Does a new theory try to modify the accepted ontology?

 No: In order to become accepted, the new theory must fit the known  data with more precision and accuracy than the accepted theory.  Yes: In order to become accepted, the new theory must also provide  confirmed predictions of hitherto unobserved phenomena.


Precision and Accuracy: Coulomb’s Law

This law didn’t introduce any new ontological elements. It merely quantified  a known relation.

Coulomb’s Law became accepted because it fit the data. It had no confirmed  novel predictions.

Novel Predictions: Wave theory of Light

Light is a wave that spreads in a universally present medium, ether. Light  waves can diffract and interfere when they meet obstacles similar to water  waves in a way. The theory’s prediction was confirmed and the theory was  accepted after that.

Novel Predictions: Superstring theory

All known particles and fundamental forces are vibrations of tiny  supersymmetric strings – superstrings. This theory introduces new  ontological element -> superstrings.

Hypothetico-deductive method: A hypothesis is allowed to introduce  unobservable entities (e.g. particles, forces, superstrings, etc.) provided that  it predicts something novel, hitherto unobserved, and some of these novel  predictions are confirmed.

Among other things, nowadays, new theories must satisfy these  requirements in order to become accepted.

Question: Is this scientific method fixed (unchangeable, transhistorical)? ->  No

Laws of Scientific Change:

General Theory of Scientific Change

Both scientific theories and methods of theory evaluation are changeable.


Is the choice of methods arbitrary, or is there a logic that governs the  process of method change?

Is scientific change a rational (law-governed) process?

Can there be a general theory of scientific change?

 Yes: Generalism: There can be a general theory of scientific change. A theory that explains all the transitions from one theory to the next and from one method to the next.

 No: Particularism: There cannot possibly be such a thing as a general theory of scientific change. Two reasons:

o There is no universal and fixed method of science. This says the  method is changeable.

o There is nothing universal in science; each historical episode is  unique. This says there is nothing permanent is science.  

Everything is changeable. (This is a stronger argument than the  first one).

 The details of each scientific change in the mosaic are so  specific that no two changes will be explained in the same  way. There is nothing universal guiding those changes.

Particularism is what’s accepted today.  


Why would we believe that there can be a general theory of scientific  change?

Drug Testing 1: Experimental Confirmation -> Problem: Unaccounted affects Drug Testing 2: Controlled Trial -> Problem: Placebo effect

Drug Testing 3: Blind Trial -> Experimenter’s bias

Drug Testing 4: Double-Blind Trial

Hypothetico Deductive Method:

Even this method is based on some assumptions.

1. Complexity: The world as it appears in observations is a product of  some more fundamental inner mechanism. We believe there are things that are not directly observable. This is an assumption implicit in all of  contemporary science. That’s the reason why we posit the existence of such unobservables such as particles (e.g. atoms) or forces. The idea is that there is more to the world than meets the eye.

∙ We wouldn’t tolerate unobservables if we thought the world is  composed only of what is immediately observable.  

2. Post hoc explanations: Any phenomenon can be given many  different contrasting post hoc explanations which are equally  precise. Post hoc means after that fact.

∙ Novel predictions wouldn’t be necessarily if there were no risks of cooked up post hoc explanations.

Method: A hypothesis is allowed to introduce unobservable entities (e.g.  microparticles, forces, supersrings, etc.) provided that it predicts something  novel, hitherto unobserved (not yet been observed), and some of these  novel predictions are confirmed.

Since assumptions are changeable, methods are changeable.

Aristotelian-Medieval Method: Assumptions

1. Nature of Things: A thing has its nature, an indispensable  (substantial) quality that makes a thing what it is.

2. Intuition Grasps Nature: The nature of a thing can be grasped  intuitively by an experienced person.

Aristotelian-Medieval Method: A proposition if acceptable if it grasps the  nature of a thing through intuition schooled by experience or it is deduced  from the general intuitive propositions.

Scientific Change: The Laws (These are NOT accepted and NOT used  but are pursued)

The Third Law: Method Employment

A method becomes employed only when it is deducible from other employed  methods and accepted theories of the time. This is true for all cases of  method employment. (This is to do with how methods change; nothing to do  with changes in theories)

The Zeroth Law: Compatibility

At any moment of time, the elements of the scientific mosaic are  compatible with each other.

The First Law: Scientific Inertia

An element of the mosaic maintains its state in the mosaic unless replaced  by some other elements. The theory or method will stay in the scientific  mosaic until it is replaced.

The Second Law: Law of Theory Acceptance:

In order to become accepted into the mosaic, a theory is assessed by the  method actually employed at the time. (How theories change. Nothing to do  with changes in methods)

1st Law for Theories:

An accepted theory remains accepted unless replaced by other theories.

A theory is assessed only if it attempts to become accepted, not when  already accepted.

Contextual Appraisal Theorem:

Theory assessment is an appraisal of a proposed modification of the mosaic  by the method of the time.

Theory Rejection:

A theory becomes rejected only when other theories that are incompatible  with the theory become accepted.

A new theory is often incompatible with some parts of the mosaic.


How do we decide if two theories are or aren’t compatible?

Method: Three Components

Method: A set of criteria for employment in theory evaluation. A method can consist of different criteria.

1. Acceptance Criteria: Criteria for determining whether a theory is  acceptable or unacceptable.

2. Demarcation Criteria: Criteria for determining whether a theory is  scientific or unscientific.

3. Compatibility Criteria: Criteria for determining whether two theories  are compatible or incompatible.

Since methods are changeable, compatibility criteria are also  changeable.

Formal Science: Inconsistency-Intolerant

In formal sciences, we are inconsistency intolerant.

Empirical Science: Inconsistency-Tolerant

In empirical sciences, we are inconsistency tolerant.

Two analytic propositions are compatible only when they are mutually  consistent.

Two synthetic propositions can be compatible even if they contradict each  other. Contradictory propositions cannot both be true at the same time, but  they can both be quasi-true (truthlike). Synthetic propositions can be only  quasi-true. Only analytic propositions can be strictly true.


What happens when two incompatible theories satisfy the requirements of  the method of the time?

Mosaic Split Theorem:

When two incompatible theories meet the requirements of the method at the time, the mosaic splits in two.

There is no universal fixed method of science <- This is true but it doesn’t  mean you cannot have a theory on how the methods of science change  (general theory of scientific change).

Particularism is wrong in insisting that there is nothing permanent in science. All cases of scientific change seem to obey certain logic; there is a certain  pattern. Scientific change is a rational (law-governed) process.

Scientific Progress:

Scientific Realism:

Given that even time-honoured theories become rejected, can we still claim  that our current theories succeed in describing the world?

Do our best scientific theories correctly describe the nature of the external  (mind-independent) world?

Do our theories describe things as they actually are? Or do they only  describe things as they appear to us?

Yes -> Scientific Realism: Our best scientific theories correctly describe  the nature of the mind-independent world. Thus, we can both use theories in practical applications and accept them as best available descriptions of the external world.

No -> Scientific Anti-Realism (Instrumentalism): We do not know  whether our correctly describe the nature of the mind-independent world.  Note this does not say our theories fail to describe the nature of the mind independent world. Thus, we shouldn’t accept theories, but should only  use them in practical applications, for theories are nothing more  than useful tools. It doesn’t say we can’t know (at some time), we don’t  know currently.

Scientific Realism, nowadays, comes in two basic flavours:  Structural Realism: Although our theories about the natures of the  unobservable entities can be false, our knowledge of the relations  between them is true.

 Entity Realism: Our knowledge about unobservable entities is true,  although our theories concerning relations between those entities can be  false.

Structural Realism: Although our theories about the natures of the  unobservable entities can be false, our knowledge of the relations between  them is true. Although in the future, our theories might be rejected, most of  the equations will survive in one way or another.

Entity Realism: Our knowledge about unobservable entities is true,  although our theories concerning relations between those entities can be  false. Although in the future, our knowledge about relations may change, the accepted entities will remain accepted. We may learn new things about these entities but the entities themselves remain.

Both of those conceptions face serious problems.

Structural Realism is flawed, for our knowledge about relations is not  immune to change. It is a historical fact that our knowledge about relations  between entities is changeable.

Entity Realism is flawed, because for the list of entities that presumably  populate the world has changed through time.

Both Structural Realism and Entity Realism adopt a selective approach.

Scientific Selective Approach (Selective Optimism): Although strictly  speaking all (even our best) theories are false, some aspects of our best  theories are true. This is based on Infallibilism.  

The selective approach is in conflict with the position of Fallibilism -> No  synthetic proposition is infallible. Empirical knowledge cannot be absolute  certain.

The selective approach is incorrect, because every part of our empirical  theories may turn out to be false.

Since all theory assessment is comparative, the only thing we can hope to  know is whether our current theories are closer to the truth than our  past theories.

Scientific Progress:


Does science actually progress towards truth?

In many fields of human endeavor, the notion of progress is problematic. E.g. music, art, sports, etc.

Is it true that our theories simply provide us with different pictures of reality,  none of which is better or worse? Or can we say that our theories gradually  improve our understanding of reality?

If scientific theories are merely different forms of approaching the world then there is no scientific progress, and the external world remains unknown. However, if our theories gradually improve our understanding of reality, then there is scientific progress and the external world Is knowable, albeit always  imperfectly.

Does science actually progress towards truth?

 Yes: Progress Thesis: Science progresses towards truth. i.e. scientific  theories provide increasingly correct descriptions of the external truth.  No: No-Progress Thesis: We can’t know whether science progresses  towards truth, i.e. whether some descriptions are closer to truth than  others.

No-Miracles Argument:

Scientific Community: Progress

The scientific community always holds that compared to previously accepted theories, the currently accepted theory provides a better description of its  object.

The question is not what scientists themselves think about progress but  whether they actually succeed in approximating the truth. We need another  approach.

Empirical Success of Science: Science has been empirically successful;  predictions of our theories become increasingly precise and accurate.

Reality affects Phenomena: The world of phenomena (the world of  experiments and observations) is somehow affected by the external world.

Progress Thesis: Science has been progressing towards truth; the  explanations provided by scientific theories are increasingly correct. The idea in simple; had our theories been far from the truth, their empirical success  would have been a miracle.

No-Miracles Argument: Since our theories become increasingly accurate  and precise in their predictions, this can only indicate that we gradually  uncover the inner structure of the world. We have these successes in  science. We believe these successes are not due to complete chance, but we are actually getting closer to the truth.


But how about constant ontological mistakes? Accepted Ontology is the  accepted views on the types of entities and interactions that populate the  world.

Pessimistic Induction Argument (Pessimistic Meta-Induction  Argument):

Ontological “Mistakes”: The ontologies of past theories are usually  considered mistaken from the perspective of later theories. Progress Definition: A process of acquiring increasingly correct  descriptions of the world (including its ontology) -> Increasingly correct  ontologies.

Because we keep making mistakes, we’re likely to keep making mistakes in  the future. So we can’t ever know if we’re progressing towards the truth. Our  current theories/ontologies will probably be proven to be incorrect as well.

No-Progress Thesis: We can’t know whether science progresses towards  truth, i.e. whether some descriptions are closer to truth than others. Note

that, this doesn’t deny that the predictions get more precise and accurate.  But this doesn’t mean we’re getting closer to the truth.

What is wrong with this argument?

We do not think that our current ontology is absolutely correct, merely that it is a better approximation than the ontologies of the past. Thus, we can’t say  that past ontologies were absolutely fast; they were merely not as correct as  our current ontology.

We believe in a succession of ontologies, where future ontologies try to  improve on past ontologies. Therefore, the premise of Ontological  “Mistakes” is wrong. The whole Pessimistic Induction Argument is  wrong.

The major argument for Progress Thesis is No-Miracles Argument. The major argument for No-Progress Thesis is the Pessimistic Induction  Argument (which is flawed).

Does science progress towards truth? -> Professor’s view is Yes. You can’t  say that this is the accepted view. It is open question for debate.

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