02. Explanation. Part 1.

Transcription

1 02. Explanation. Part 1. I. Introduction Topics: I. Introduction II. Deductive-Nomological (DN) Model III. Laws: Preliminary Sketch First blush: A scientific explanation is an attempt to render understandable or intelligible some particular event, or some general fact, by appealing to other particular and/or general facts drawn from one or more branches of empirical science. As Salmon notes, this is pretty vague. Let s get a bit more precise. Terminology: 1. Explanandum - fact (particular or general) to be explained. 2. Explanans - that which does the explaining 3. Explanation - (2 hair-splitting views) (a) A linguistic object consisting of an explanandum-statement and an explanans statement. (b) A collection of facts consisting of explanandum-facts and explanans-facts. (For our purposes, nothing too important rides on this distinction. Just be aware of it.) More Preliminaries: Arguments Since DN views explanations as arguments, we should be clear about what arguments are. An argument is a collection of statements, one of which is identified as a claim (conclusion), and the others are identified as reasons given for the claim (premises). ASIDE: We ve now introduced 2 distinct types of object: (1) an explanation; and (2) an argument. These are not necessarily the same type of object! One attempt to further define what an explanation in science amounts to is the DN account. This particular account claims an explanation is a type of argument. We will investigate the adequacy of this account in the following lectures. But at this point, it is very important to realize that, in general, explanations and arguments are differents sorts of things. 1

2 Two Main Types of Argument (not explanation!) Deductive 1. Non-ampliative: Content of conclusion is present in premises. 2. Truth-preserving: If premises are true, conclusion must be true. 3. Erosion-proof: Addition of new premises does not affect strength of argument (as long as original premises are left alone). 4. Deductive validity is all-or-nothing. A deductive argument is either valid or invalid. Inductive 1. Ampliative: Conclusion contains information beyond that expressed in premises. 2. Not necessarily truth preserving. 3. Not erosion-proof: Addition of premises may strengthen/weaken argument. 4. Inductive strength comes in degrees. Some inductive arguments are stronger/weaker than others. Ex1: All animals with wings can fly. Pigs have wings. Pigs can fly. This is a valid deductive argument: 1. It is non-ampliative: the conclusion is already implicit in the premises. 2. It is truth-preserving: If it is true that all animals with wings can fly, and if it is true that pigs have wings, then it must also be true that pigs can fly. ASIDE: Of course, pigs don t have wings, and not all animals with wings can fly (penguins, for example). Note, however, that the truth-preserving property simply requires that it can never be the case that all the premises are true and the conclusion false. So long as this holds, the argument is valid. This does allow any other combination of truthvalues for the premises and conclusion. For instance, a valid argument could have all false premises and a true conclusion; or all false premises and a false conclusion; or some combination of false/true premises together with a false/true conclusion. Again, the only combination that is prohibited by property (2) is the combination of all true premises and a false conclusion. 3. It is erosion-proof: If we added the premise Wilbur has butterfly wings, the conclusion would still follow in the required truth-preserving way. ASIDE: If we explicitly added Pigs don t have wings as a third premise, then the conclusion Pigs can fly would still be true if all the premises were true. To see this, note that this new third premise contradicts the second premise Pigs have wings -- they can t both be true at the same time (or false at the same time). So adding Pigs don t have wings prevents the argument from ever having all true premises and a false conclusion; and this is just the truth-preserving property (2). Similarly, adding Pigs can t fly as a third premise would contradict the conclusion, which is already implicit in the first two premises. So again, we could never have a situation in which all the premises were true and the conclusion false. So again, property (2) would be upheld. 4. Finally, as we ve seen, it s validity is all-or-nothing. We ve established that it is valid, and shown that nothing we can do to it (short of destroying it) obviscates this fact. 2

3 Ex2: 95% of observed smokers developed lung cancer. Smoking causes lung cancer. This is an inductive argument. 1. It is ampliative: The conclusion contains information not already present in the premise. 2. It is not necessarily truth-preserving: If it is true that a certain survey found that 95% of smokers surveyed went on to develop lung cancer, then it does not necessarily follow that smoking was to blame. There could have been other causal factors that influenced the development of cancer in those 95%. 3. It is not erosion-proof. Suppose we added a second premise that states 100, 000 smokers were surveyed. This would strengthen the conclusion, all things remaining equal. It would establish that the sample size of the survey was very big. However, if we then added a fourth premise that states All smokers surveyed lived in coal mines, this would weaken the conclusion. It would establish that the sample was pretty biased; in this case, it would lead us to think that perhaps the large incidence of cancer was due to inhaling coal dust, as opposed to smoking. 4. Finally, (3) shows how inductive strength comes in degrees. II. Deductive-Nomological (DN) Model of Scientific Explanation Hempel & Oppenheim (1948) Studies in the Logic of Explanation DN explanation - an account of the explanandum that indicates how it follows deductively from a law of nature ( covering-law account). Key characteristics are given by: Conditions of Adequacy 1. Must be a valid-deductive argument with premises stating the explanans and the conclusion stating the explanandum. 2. Premises (explanans) must contain a law. 3. Explanans must have empirical content. 4. Explanans must be true. The conditions of adequacy define what a DN explanation is. In other words, an explanation is a DN explanation if and only if it satisfies conditions 1-4. CLAIM: Scientific explanations are DN explanations. 3

4 General form of DN explanations explanans L 1, L 2,... C 1, C 2,... law(s) conditions underwhich laws are applicable explanandum O 1, O 2,... observed phenomena Ex1: Why do skaters spin faster as they bring their arms in towards their bodies? DN explanation: 1. Angular momentum is conserved. 2. Skater doesn t interact with external objects. 3. Skater has non-zero initial angular momentum. 4. Skater brings arms in towards body (reducing rotational intertia). Skater spins faster. law conditions observed phenomena Subsumption of particular fact (skater spinning faster) under a law (conservation of angular momentum). ASIDE: Ex1 satisfies the 4 conditions of adequacy. In particular, it is a valid-deductive argument -- If the premises are all true, then the conclusion must be true. To see this concretely, note that the argument can be formulated mathematically in the following manner (where the angular momentum L of a spinning object is defined as L = Iω, where I is the object s moment of inertia (it s rotational inertia, which is roughly a measure of the object s tendancy to continue spinning in the absernce of external forces), and ω is its rotational velocity (which measures how fast it is rotating)): 1. L i = L f 2. L i = I i ω i and L f = I f ω f 3. L i = 0 4. I f < I i ω f > ω i (nothing contributes to L other than the skater s I and ω) (Intuitively, to preserve the equation I i ω i = I f ω f when I f is less than I i, the quantity ω f must be greater than ω i to compensate) Ex2: Why did Jan s bracelet melt when it was heated to 1063 C? DN explanation: 1. Gold melts at 1063 C. law 2. Jan s bracelet is made of gold. condition Jan s bracelet melted at 1063 C. observation 4

5 Initial Problem for DN model: What is a law of nature? Preliminary Sketch Claim: Laws must Hempel & Oppenheim (1948) Studies in the Logic of Explanation (a) Describe regularities that hold universally at all times and places. (b) Be capable of supporting counterfactual statements. (c) Be capable of supporting modal statements. counterfactual statement = An if-then statement with a false if -clause. Ex: If Abe Lincoln were alive today, then he d be clawing at the lid of his coffin. modal statement = A statement that asserts a physical necessity or (im)possibility. Ex: It is impossible to construct an enriched uranium sphere with mass > 100,000 kg. To say that a law supports a counterfactual/modal statement is to say that the law makes the counterfactual/modal statement true. Three examples of candidate laws: (1) All the apples in my refrigerator are yellow. (2) No gold sphere has a mass greater than 100,000 kg. (3) No enriched uranium sphere has a mass greater than 100,000 kg. Is (1) lawlike? (Does it satisfy (a), (b), (c)?) It doesn t satisfy (a). It refers to a particular place (and time). Is (2) lawlike? It satisfies (a). (It's reasonable to suppose that in our universe there will never be enough gold to assemble such a massive sphere.) It doesn t satisfy (b). It doesn t support the following true counterfactual statement: If two gold spheres with masses of 50,001 kg each were put together, then they would form a sphere with mass 100,001 kg. It doesn t satisfy (c). It doesn t support the following true modal statement: It is possible to construct a gold sphere with mass greater than 100,000 kg. 5

6 Is (3) lawlike? It satisfies (a). It satisfies (b). It supports the following true counterfactual statement: If 100,000 kg of enriched uranium were assembled, then we would no longer have any uranium. It satisfies (c). It supports the following true modal statement: It is impossible to construct a sphere of enriched uranium with mass greater than 100,000 kg. Accidental generalization = A true generalization that satisfies (a) but not (b) or (c). Lawlike generalization = A true generalization that satisfies (a), (b) and (c). Circularity Problem with this preliminary account of laws This account says a law of nature is a true generalization that statisfies conditions (a), (b) and (c). In particular, laws differ from accidental generalizations solely on the basis of the ability of laws to support counterfactuals and modal statements. BUT: Why do we think certain counterfactuals and modal statements are true in the first place? If it s because we think there are laws of nature that underlie them, then we can t use them to define what we mean by a law, on pain of circularity. SO: This preliminary account works only if we already have a theory of counterfactuals and modal statements that is independent of the notion of a law and which can be used to determine which counterfactuals/modal statements are true and which are false. Such a theory is hard to envision. (And note that it can t simply be based on our intution; i.e., we can say that, intuitively, we think that the modal statement It s physically possible to construct a 100,000 kg gold sphere is true. The question is, What underlies this intuition?) 6