Some Notes on the Philosophy of Science I. The Problem of Induction We saw in Hume’s Enquiry the classic presentation of the Problem of Induction. Hume’s question was simply: What justification do we have for the beliefs that (a) the future will resemble the past and (b) similar powers will be conjoined with similar sensible effects? (cf. p. 198b) Or, as Wesley Salmon puts it, Hume’s question is this: “How do we acquire knowledge of the unobserved?” (p. 230b) Knowledge of the unobserved is the issue when we say that the future (which is necessarily unobserved) will resemble the past and when we say that x will bring about y (something unobserved). Again, when we say that the future will resemble the past, the past instances of the future’s resembling the past can’t serve as a proof that it will do so in the future – unless we assume the very principle that is in question. One ought to see the power of this question — for it threatens to undermine all of science. (A) Some more detail: Induction is often contrasted with deduction. The latter can be seen as going from general claims (or one general claim) to a particular claim. For example, (P1) All men are mortal. (Major Premise [General Claim]) (P2) Socrates is a man. (Minor Premise) (C) Therefore, Socrates is mortal. (Deductive Conclusion) The conclusion (C) is necessary — for it must follow, given the premises (P1) and (P2). And it cannot be false, if the premises are true. Induction, on the other hand, can be seen as going from particular claims to a general (or universal) claim. For example, (1) Swan1 is white. (Observation) (2) Swan2 is white. (3) Swan3 is white. (n) Swann is white. (C) All swans are white. (Inductive Conclusion) Now, this conclusion is not necessarily true — for it could be false, even though all observations/premises up to this point are true. (For example, every UK student I have known has been a basketball fan; but it need not follow necessarily that the next one I meet cares about basketball. Another example: every student in Phi 100 is under 50 years of age; but that doesn’t mean that all UK students are under 50 years of age.) And Hume’s question is, again, what (if any) rational justification do we have for believing that (C) is true. Introduction to Philosophy: Knowledge and Reality 2 Dr. Brandon C. Look, University of Kentucky (B) The Problem of Induction Extended Immanuel Kant (1724-1804), a philosopher equal to or greater than Hume, realized the importance of Hume’s critique of induction. It is not only that we are not rationally justified in our inductive inferences, but a whole class of propositions are subject to skeptical doubts. Following in Hume’s spirit, but using different lingo, Kant makes two important distinctions. First, he claims that judgments (i.e., claims of the form A is B) can either be a priori (prior to experience or universal and necessary) or a posteriori (dependent upon experience and contingent). Second, he claims that judgments are either analytic or synthetic. An analytic judgment is one in which the concept of the predicate is contained the concept of the subject: e.g., “a bachelor is an unmarried male.” This is analytic because the concept bachelor contains the idea of a being an unmarried male. In other words, analytic truths are true by virtue of meaning. A synthetic judgment is one in which the predicate adds something to the subject. Now, according to Kant, all a posteriori judgments are synthetic, and all analytic judgments are a priori. But, Kant asks, are synthetic a priori judgments possible? To give you an idea of the importance of this question, consider that Hume focused on the issue of causal relations only; but the following kinds of propositions would have to be synthetic a priori (if true and meaningful): (1) God exists. (2) The soul is immortal. (3) The will is free. Again, think of Salmon’s gloss on Hume’s problem: How can we have knowledge of the unobserved? Kant’s answer is that, while synthetic a priori judgments are possible, only those things that are objects of possible experience can be known. Ultimately, Kant argues that God, the soul, and the will are not things about which we can have knowledge. And, concerning causation, Kant argues that we can only have knowledge of the general proposition that there is a cause for every effect. (C) Nelson Goodman’s “New Riddle of Induction” Hume’s writings have forced philosophers to think long and hard about the foundations of science and the rational justification of our inductive inferences. In his Fact, Fiction and Forecast, Nelson Goodman points to a different kind of problem with our inductive practices. We would have no problem in agreeing that All emeralds are green is true. Right? And if I were to present you with a bag of emeralds, you would probably consider yourself justified (in some sense) in predicting that the gem that you draw from the bag will be green. But Goodman proposes a new predicate: grue. X is grue if and only if (1) it is examined before t and is green, or (2) it has not been examined before t and is blue. Introduction to Philosophy: Knowledge and Reality 3 Dr. Brandon C. Look, University of Kentucky Now, let’s suppose t is now. The following inductive inferences would seem to be equally well justified. (1) Emerald1 is green (1) Emerald1 is grue (2) Emerald2 is green (2) Emerald2 is grue (3) Emerald3 is green (3) Emerald3 is grue . (n) Emeraldn is green (n) Emeraldn is grue (C) All emeralds are green. (C) All emeralds are grue. In other words, we are equally justified in expecting the next emerald to be grue as we are in expecting it to be green. But, if it is grue, it is blue and not green. Goodman’s questions are then the following: What makes a statement genuinely lawlike? What allows us to recognize some predicates (like green) as good, respectable predicates and to disregard other predicates? What makes one predicate projectible, another not? Goodman: “The real inadequacy of Hume’s account lay not in his descriptive approach but in the imprecision of his description. Regularities in experience, according to him, give rise to habits of expectation; and thus it is predictions conforming to past regularities that are normal or valid. But Hume overlooks the fact that some regularities do and some do not establish such habits; that predictions based on some regularities are valid while predictions based on other regularities do not… To say that valid predictions are those based on past regularities, without being able to say which regularities, is thus quite pointless. Regularities are where you find them, and you can find them anywhere.” (4th ed., p. 82) II. What is Science? (A) Scientific Method One prominent picture of science suggests that scientists are engaged in the Hypothetico- Deductive Method. According to this view, a scientist proposes a certain hypothesis and makes certain logical deductions from this hypothesis (i.e. predictions), and then compares these deductions (predictions) with observations. If the observations are consistent with the predictions, then the hypothesis has been confirmed or verified (in part at least). If the observations turn out to be different from the deductions (predictions), then the hypothesis has been disconfirmed. (See Salmon, p. 238a) The aim of science on this model is to seek verification. Another Problem: The Paradox of the Ravens. Suppose we observe many ravens and formulate the general scientific claim All ravens are black. It would seem that, when we look around the world, we can confirm or corroborate this by our observations of black ravens. But there’s a catch, too. All ravens are black is logically equivalent to If x is a raven, then x is black. But this, in turn, is equivalent to If x is not black, then x is a non-raven (or All non-black things are non-ravens.) Introduction to Philosophy: Knowledge and Reality 4 Dr. Brandon C. Look, University of Kentucky (Aside: In logic, we call an argument of the following form — (1) If p, then q; (2) p; (3) therefore, q — modus ponens. And an argument of this form — (1) If p, then q; (2) not q; (3) therefore, not p — modus tollens.) So what? So that means that I can confirm the hypothesis or scientific claim All ravens are black by observing that my desk is brown, that my computer is blue and silver, that a piece of paper here is white. Question: Is this how science should work?? Ornithology without looking at birds? In the model of Karl Popper, however, there is a different “logic of scientific discovery.” According to Popper, the aim of science should be to falsify theories. Why? Consider the following two cases, in which T stands for a theory and O for an observation. Verificationism Falsificationism (1) If T, then O (1) If T, then O (2) O (2) not-O (3) Therefore, T (3) Therefore, not-T Deductively invalid. Deductively valid Therefore, whereas the verificationist can only confirm his theory to some degree or make it more probable, the more predictions are consistent with observations, the falsificationist arrives at deductive certainty – in ruling out certain proposed theories because of observations. “The aim of empirical science is to set forth theories to stand the test of every possible serious attempt at falsification. Scientific theories are hypotheses or conjectures; they are general statements designed to explain the world and make it intelligible, but they are never to be regarded as final truths.” (p.