Lecture Notes for Philosophy & Science, Study notes of Philosophy

Download Lecture Notes for Philosophy & Science and more Study notes Philosophy in PDF only on Docsity!

Lecture Notes for Philosophy & Science

J. Dmitri Gallow

Draft of Spring, 2018

Contents

• 1 Course Intro
• I Induction
• 2 Naïve Inductivism, day
  • 2.1 Inference
  • 2.2 Naïve Inductivism
• 3 Naïve Inductivism, day
  • 3.1 The Logic of Hypothesis Testing
  • 3.2 Hempel’s Criticisms of Naïve Inductivism
• 4 The Problem of Induction, day
  • 4.1 Some Prefatory Terminology
  • 4.2 Hume on Induction
• 5 Laws of Nature, day
  • 5.1 Laws and Accidentally True Universal Generalizations
• 6 Laws of Nature, day
  • 6.1 The “Best Systems” Account of Laws
  • 6.2 The Universals Account of Laws
• 7 The Problem of Induction, day
  • 7.1 Review: Hume’s First Problem
  • 7.2 Hume’s Second Problem
• 8 The Problem of Induction, day
• II Falsification
• 9 Popper’s Falsificationism, day
  • 9.1 Popper’s Solution to the Problem of Demarcation
  • 9.2 Popper’s ‘Solution’ to the Problem of Induction
• 10 Popper’s Falsificationism, day
  • 10.1 Problems with Anti-Inductivism
• 11 Popper’s Falsificationism, day
• III Confirmation Theory
• 12 Confirmation Theory, day
  • 12.1 Review
  • 12.2 Back to the Problem of Induction
  • 12.3 Confirmation Theory
• 13 Confirmation Theory, day
  • 13.1 Review
  • 13.2 You can’t always get what you want
  • 13.3 The New Riddle of Induction
• 14 Confirmation Theory, day
  • 14.1 Review
  • 14.2 A Probabilistic Theory of Confirmation
  • 14.3 The Theory of Probability
• 15 Confirmation Theory, day
  • 15.1 Bayesian Confirmation Theory
  • 15.2 Why the Bayesian Thinks You Can’t Always Get What You Want
  • 15.3 Objections to Bayesian Confirmation Theory
• 16 Objective Chance
  • 16.1 Objective Chance
  • 16.2 The Classical Account of Objective Chance
  • 16.3 Actual Frequentism
• IV Scientific Realism
• 17 Scientific Realism, day
  • 17.1 Eddington’s Two Tables
  • 17.2 Scientific Realism
• 18 Scientific Realism, day
  • 18.1 The “No Miracles” Argument for Scientific Realism
  • 18.2 The Underdetermination Argument Against Scientific Realism
• 19 Logical Positivism
  • 19.1 Logical Positivism
    • 19.1.1 The Verificationist Criterion of Meaningfulness
    • 19.1.2 Analytic and Synthetic Statements
    • 19.1.3 Observational and Theoretical Terms
    • 19.1.4 One Final Objection
• 20 Constructive Empiricism
  • 20.1 Constructive Empiricism
    • 20.1.1 van Fraassen’s Reply to the ‘No Miracles’ Argument
    • 20.1.2 van Fraassen on Supra-empirical Theoretical Virtues
    • 20.1.3 On Observability
    • 20.1.4 Is van Fraassen selectively skeptical in an unmotivated way?
• V Scientific Explanation
• 21 Scientific Explanation, day
  • 21.1 Scientific Explanation
  • 21.2 The Deductive Nomological Account of Scientific Explanation
• 22 Scientific Explanation, day
  • 22.1 The DN Account
    • 22.1.1 Probabilistic Explanations
  • 22.2 Objections to the DN Account
  • 22.3 The Missing Ingredient
• VI Paradigms and Scientific Revolutions
• 23 Kuhn’s Theory of Scientific Development
  • 23.1 Pre-Paradigm Science
  • 23.2 Paradigm Work
  • 23.3 Normal Science
  • 23.4 Crisis & Scientific Revolution
• 24 Kuhn on Scientific Revolutions
  • 24.1 Incommensurable Meaning
  • 24.2 Incommensurable Standards
  • 24.3 Incommensurable Observations
  • 24.4 Off the Deep End

1 | Course Intro

1. The philosophy of science subdivides into two broad categories:

(a) General philosophy of science asks questions about (for instance) what the method- ology of science is in general, whether/how it allows us to know things about the world, and what the scientific enterprise in general reveals or presupposes about the nature of reality. (b) Applied philosophy of science, on the other hand, asks questions about the methodology or the content of particular scientific theories. For instance, some questions in applied Philosophy of Science are: i. What is the best way to make sense of the theory of (non-relativistic) quan- tum mechanics? Is it one according to which the laws of nature are radi- cally non-local—or is it one according to which the universe is constantly branching? Or is it something else altogether? ii. The Theory of Special Relativity tells us that whether two events are simul- taneous depends upon how fast you are moving. This appears to fly in in the face of a traditional philosophical position known as presentism. Pre- sentism claims that only the present is real—the past and the future are not real (at least, not any longer, or not yet). Is presentism really incompatible with special relativity? Or is there a way of making sense of the theory, and accomodating its predictions, which is consistent with presentism? iii. Most sciences make plentiful use of certain methods of statistical inference developed by the statisticians Fischer, Neyman, and Pearson. These meth- ods are collectively known as frequentist. They are the methods taught in almost all undergraduate statistics courses. However, some philosophers and statisticians believe that these methods are flawed. There is a growing debate about which statistical procedures scientists ought to use. Who is right?

2. In this course, we will be focusing mainly on the general philosophy of science— though courses on applied philosophy of science are available through both the Phi- losophy department and the History and Philosophy of Science department here at Pittsburgh.
3. Questions in the general philosophy of science can be subdivided further, into meta- physical questions and epistemological questions.

Part I

Induction

2 | Naïve Inductivism, day 1

2.1 Inference

1. Suppose you have a collection of beliefs—call them p 1 , p 2 , : : : , pN. And, on the basis of these beliefs, you adopt a new belief—call it c.

(a) In general, we’ll put the propositions p 1 , p 2 , : : : , pN above a horizontal line, and the proposition c below a horizontal line, to indicate that we are drawing an inference from p 1 , p 2 , : : : , pN , and to c.

p 1 p 2 .. . pN c

(b) In moving from p 1 , p 2 , : : : , pN to c, you have drawn an inference. (c) We’ll call p 1 , p 2 , : : : , pN premises, and we’ll call c a conclusion. (d) For instance, P1. Whoever committed the murder had the gate key

P2. The butler had the gate key.

C. The butler committed the murder.

2. Inferences can be divided into two kinds, which we will call inductive and deductive.^1

(a) In a deductive inference, the conclusion follows necessarily from the premises. More carefully, in a deductive inference, it is not possible for the premises to all be true at once, and yet for the conclusion to be simultaneously false. i. For instance, consider P1. The legs of an isosceles triangle have length l.

C. The hypotenuse has length

p 2 l^2. (^1) Beware: philosophical usage here is far from uniform. Some use ‘ampliative’ for the inferences we are calling ‘inductive’, and reserve ‘inductive’ for the inferences we will call ‘enumerative inductions’.

1. Observe and record facts.
2. Classify and analyze these facts.
3. Inductively derive generalizations from these facts.
4. Submit these generalizations to test. (b) To understand these steps, let’s walk through an example. Suppose that we ob- serve the following facts:

• Clarence Oveur ate fish, drank coffee, & fell ill
• Roger Murdock ate fish, drank coffee, & fell ill
• Ted Striker ate chicken, drank soda, & didn￿t fall ill
• Elaine Dickinson ate chicken, drank coffee, & didn￿t fall ill
• Victor Basta ate fish, drank soda, & fell ill (c) First, we should write these facts down (record them). Next, we should find some way of classifying these facts. For Bacon, this involved drawing up a table like the following: Name Drink Dinner Health Oveur Coffee Fish Sick Murdock Coffee Fish Sick Striker Soda Chicken Healthy Dickinson Coffee Chicken Healthy Basta Soda Fish Sick (d) Once the facts have been classified, we should begin to analyze them. This in- volves looking for patterns. We notice that there is no firm correlation between coffee and health, nor soda and health. However, there is a correlation between fish and health. Everyone who ate fish got sick. (e) So, next, form the analyzed data, we inductively derive generalizations. Using enumerative induction, we have P1. Oveur ate fish and got sick.

P2. Murdock ate fish and got sick.

P3. Basta ate fish and got sick.

C. Everyone who eats the fish gets sick. (f) Finally, we must submit our inductively derived generalization to a test. For in- stance, we could feed Striker the fish. If our hypothesis is true, then Striker will get sick. In Striker gets sick, our hypothesis has been verified (or confirmed). If Striker does not get sick, then our hypothesis has been refuted (or disconfirmed). In that case, we must start afesh.

5. For Bacon, it is very important that we complete stages 1 and 2 without any precon- ceived hypotheses in mind, and without any preconceived notions about which facts or classifications are important.

3 | Naïve Inductivism, day 2

3.1 The Logic of Hypothesis Testing

1. In order to test a hypothesis, we must first find some test implication of the hypoth- esis.

(a) For instance, suppose we have the following hypothesis: the reason water can- not be lifted above 10 meters with a vacuum is that water rises in a vacuum only because of the force exerted upon it by the atmospheric pressure. This hypothesis implies that, if we take our vacuum to a higher altitude, where the atmospheric pressure is lower, then we will only be able to lift water above 10 meters. (b) In general, in order to submit a hypothesis to test, we must discover something observation we would expect to make if the hypothesis were true. That is, in order to test a hypothesis H, we must discover some potential evidence E, such that we are assured of the following conditional: If H, then E (c) For instance, with respect to our hypothesis about the height of the water in a vacuum, in order to subject this hypothesis to tests, we must assure ourselves of this conditional: If the hypothesis is true, then, at higher altitudes, we will be able to lift water higher than 10 feet with a vacuum pump

2. Once we have a test implication, we must go out and perform the test to see whether the hypothesis’s implication in fact obtains.

(a) For instance, we may bring a vacuum pump to the top of a high mountain and record how high water may be lifted there.

3. Suppose that the test implication is borne out—e.g., suppose that a vacuum pump can raise water higher than 10 feet at the top of a high mountain. This is taken as a reason to accept the hypothesis. Formally, we will perform the following inference:

If H, then E

E H

1. Observe and collect facts (without a preconceived hypothesis in mind).
2. Classify and analyze these facts (without a preconceived hypothesis in mind).
3. Inductively derive generalizations from these facts.
4. Submit these generalizations to test.

(a) Hempel objects to the first two steps of Naïve Inductivism. In particular, he objects to the parenthetical imperative to not let your observation and analysis be directed by any particular hypothesis. (b) First, consider the injunction to collect facts without a preconceived hypothesis in mind. i. In Semmelweis’s case, the evidence he collected depended crucially upon the hypothesis he was considering. He considered how crowded the 1st and 2nd divisions were when he was entertaining the hypothesis that over- crowding causes childbed fever. Such information was irrelevant when he was considering the hypotheses that harsh treatment, the priest, or cadav- eric matter causes childbed fever. ii. Moreover, this feature of Semmelweis’s investigation was, Hempel alleges, unavoidable. For there are an infinite number of facts. We must have some idea of where to start collecting facts, and some idea of which facts are relevant. And the natural place to look for guidance is the hypotheses we are considering. (c) Next, consider the injunction to classify and analyze facts without a precon- ceived hypothesis in mind. i. In Semmelweis’s case, he could have classified women by age, fingernail length, eye color, etc. Instead, how he classified them depended crucially upon the hypothesis he was considering. When he was considering the hy- pothesis that harsh treatment by the medical students was causing childbed fever, he classified women by whether they were receiving examinations. When he was considering whether seeing the priest was responsible, he classified them by whether they had seen the priest or not. ii. In general, there are infinitely many ways of classifying the facts. We must have some guidance as to which classifications might be relevant. And the natural place to look for this guidance is the hypotheses we are considering.

8. So, Hempel concludes: tentative hypotheses are required in order for scientific in- vestigation to proceed. And these tenative hypotheses must be introduced prior to the collection or analysis of facts.

(a) Moreover, there can be no algorithmic method for selecting these initial hy- potheses. Semmelweis needed the inspiration of his colleague’s accident during the autopsy to have the correct hypothesis occur to him. (b) Hempel concludes that science, just like mathematics, requires imagination and creativity.

9. Note, however, that, while this means that there is no algorithmic procedure for arriving at hypotheses, there could still be an algorithmic procedure for deciding whether or not to accept these hypotheses.

(a) Hempel draws a distinction between the context of discovery and the context of justification. (b) The context of discovery is the stage of scientific investigation at which the scientist discovers a particular scientific hypothesis. For instance, Semmelweis discovered the hypothesis that cadaveric matter causes childbed fever upon ob- serving his colleague’s symptoms after cutting himself during the autopsy. (c) On the other hand, the context of justification is the stage of scientific investi- gation at which the scientist justifies believing in or accepting the hypothesis. (d) While Hempel does not believe that there is any method for telling you how to proceed in the context of discovery, there still may be, on his view, strict canons of inductive inference which tell you when a hypothesis has been verified (or supported or confirmed) by the available evidence. That is: there still may be a method to be followed in the context of justification.

that Trump is president, that I am in Pittsburgh, and that it is sunny outside today, I must rely upon my sense experience. ii. If I were to learn that I was plugged into the Matrix, then I would not be in a position to know that Trump is president, that I am in Pittsburgh, nor that it is sunny today.

2. Here’s another way we may divide our beliefs:^1 on the one hand, there are the beliefs that are necessary. And, on the other hand, there are the beliefs which are contingent.

(a) A belief is necessary iff there is no possible way for it to be false. i. For instance, my belief that there is not a square circle on display at the Smithsonian is necessary. There is no possible way for there to be a square circle, and so there is no possible way for my belief to be false. ii. Here, we do not mean only that there’s no possible way—consistent with the laws of nature—for the belief to be false. We rather mean that there is no way period for the belief to be false. (b) A belief is contingent iff there is a possible way for it to be false, and a possible way for it to be true. i. For instance, my belief that the Earth rotates around the Sun approximately once every 365.25 days is contingent. It could be true, and it could be false.

4.2 Hume on Induction

3. Hume thinks that some of our beliefs are beliefs that we come by through noticing relations between our ideas. He calls these beliefs Relations of Ideas.

(a) These are beliefs, like “All bachelors are unmarried” and “No woman is taller than herself ”, which we can know to be true just by consulting our ideas of “bachelor” and “taller than”. (b) Included in this category will be all of mathematics. To know the Pythagorean Theorem, we need only consult our idea of a right triangle. (c) For Hume, these beliefs are discoverable by reason alone; and, for this reason, these beliefs are a priori. (d) Similarly, we cannot conceive of these beliefs being false. Since conceivability is our guide to possibility (it is possible iff it is conceivable), these beliefs could not possibly be false. So these beliefs are necessary, as well.

4. All beliefs which are not Relations of Ideas, Hume calls beliefs about Matters of Fact.

(a) These are beliefs, like “Trump is president”, “I am in Pittsburgh”, and “The Earth travels around the Sun approximately once every 365.25 days”. In order to come by these beliefs, we need to have some sense experience.

(^1) Attentive students will note that this classification is not exhaustive—that is to say, we may have some beliefs which fall into neither category.

(b) Included in this category will be all of our beliefs about the natural world. In order to know that, e.g., fire produces smoke, we need to observe fire. And in order to know that bread nourishes, e.g., we need to eat some bread. (c) These beliefs are not discoverable by reason alone; and, for this reason, these beliefs are a posteriori. (d) We can easily conceive of these beliefs being false. We can conceive of Trump not winning the election; we can conceive of me not being in Pittsburgh, and we can conceive of the Earth taking longer to travel around the Sun. So these beliefs are contingent.

5. So, Hume believed that our two distinctions—between the a priori and the a poste- riori, on the one hand, and the necessary and the contingent, on the other—lined up perfectly. He thought that a belief was a priori iff it is necessary and that a belief was a posteriori iff it was contingent. The former variety of beliefs are just the relations of ideas. The latter variety are just the matters of fact.
6. Even though some of our beliefs about matters of fact are based directly on sense experience (or memory), most of our beliefs about matters of fact are not.

(a) For instance, my belief that Wesley Salmon wrote the article assigned for next class is not based directly upon sense experience. I didn’t see him write it (how could I? He wrote it before I was born.). (b) Similarly, my belief that there will be a talk in the Philosophy department this coming Friday is not based directly upon sensne experience. I haven’t seen the talk yet (how could I? It’s in the future.). (c) I view smoke in the distance and believe that there is a fire there. I haven’t seen the fire, so this belief is not based directly upon sense experience of the fire.

7. So, Hume enquires: what is the basis of these beliefs about unobserved matters of fact?

(a) His answer: these beliefs must be based upon relations of cause and effect. (b) I believe that Wesley Salmon’s writing the article would cause (somehow) his name to appear under the title. From this, and the fact that the name does appear there, I infer that Wesley Salmon must have written the article. (c) Similarly, I believe that inviting speakers and organizing talks causes those talks to take place. And I have seen this organization. So I infer that the talk will take place. (d) And I believe that fire causes smoke. So, when I see the smoke, I infer from the effect to the cause, and believe that there is fire causing the smoke.

8. So Hume has discovered an answer to his question: our beliefs about unobserved matters of fact are based on things we have observed, together with relations of cause and effect. Hume is not placated. He pushes on: what, then, is the basis of our beliefs about relations of cause and effect? Why do we believe that writing articles causes your name to appear beneath the title? Why do we believe that inviting speakers

P1. The first fire was followed by smoke.

P2. The second fire was followed by smoke. .. .

PN. The Nth fire was followed by smoke.

UN. Nature operates uniformly.

C. Fire is always followed by smoke. then Hume is happy to accept that reason alone could determine the inference that Fire is always followed by smoke. (c) However, Hume is not so easily satisfied. From where did we derive this belief? It is either a belief about relations of ideas, or a belief about matters of fact. We can conceive of it being false, wherefore we must conclude that it is not necessary, and therefore, not a relation of ideas. So it must itself be a matter of fact.

12. So the belief that nature operates uniformly is itself a matter of fact. We have not directly observed nature operating uniformly in all of the unobserved cases. So what is our basis for this belief?

(a) The most natural answer, it seems, is this: in all of the observed cases, nature has operated in a uniform manner. Thus far, when we go looking for regularities in nature, we have found them, and those discovered regularities have, for the most part, continued into the future. (b) So this is the basis of our belief that nature will operate uniformly, then: because it has always done so in the past. P1. Nature has always operated uniformly in the past.

UN. Nature always operates uniformly

13. But—and this is Hume’s first punchline—we can easily conceive of this premise be- ing true while the conclusion is nevertheless false. We can easily conceive of nature operating uniformly up to the year 2020, and then, thereafter, operating in a hap- hazard, nonuniform manner.

(a) There is no contradiction involved in the supposition that, on Jan. 1, 2020, mas- sive bodies will begin repelling each other instead of attracting each other. (b) Nor is there any contradiction involved in the supposition that, on Jan 1, 2020, bread will stop nourishing and begin poisoning, or that it will keep nourishing blue eyed people and poison brown eyed people. (c) So, our past experience of nature operating uniformly does not provide a con- clusive reason to suppose that nature will continue operating uniformly in the future.

14. So, Hume’s first lesson is this: we cannot know by reasoning from what we’ve ob- served that our method of forming beliefs about the future will not lead us into radical error. We cannot know by reasoning from what we’ve observed that our scientific theories will continue to be true in the future.