Scientific Explanations

Aristotle’s Explanations Aristotle’s example of an efficient cause Aristotle’s example of an efficient cause The father is uglyThe minor premiss An ugly father will have an ugly childand the major premiss guarantee The child is uglythe conclusion This is an argument This is an argument We need to rephrase this as an explanation We need to rephrase this as an explanation

Explanations Aristotle’s example as an explanation Aristotle’s example as an explanation The father is uglyThe explanantia An ugly father will have an ugly child(or the explanans) explain The child is uglythe explanandum The 1 st line describes a presupposed/known fact The 1 st line describes a presupposed/known fact The 2 nd line describes a Law of Nature The 2 nd line describes a Law of Nature

Explanations Aristotle’s example as an explanation Aristotle’s example as an explanation The father is uglyThe initial condition An ugly father will have an ugly childand a law of nature explain The child is uglythe explanandum Deductive: in the same way that Aristotle required Deductive: in the same way that Aristotle required Nomological: essentially refers to a Law of Nature Nomological: essentially refers to a Law of Nature

Deductive-Nomological Exp. Also known as the Covering Law Model Also known as the Covering Law Model C 1, C 2, C 3, …The initial conditions L 1, L 2, L 3, …and the relevant laws explain Ethe explanandum R1. R1.Explanandum must be a logical consequence of the explanans R2.Explanans must contain laws required for derivation of explanandum R3.Explanans must be capable of test by experiment or observation R4.Sentences constituting the explanans must be true

Deductive-Nomological Exp. An example with gases An example with gases P 1 = 10 kPaThe initial conditions V 1 = 1 l V 2 = ½ l P 1 V 1 = P 2 V 2 and the relevant law explain P 2 = 20 kPa the explanandum Satisfies R1 to R4 Satisfies R1 to R4

Deductive-Nomological Exp. An example with gases An example with gases Doesn’t seem to properly explain the explanandum Doesn’t seem to properly explain the explanandum Why does Why does P 1 V 1 = P 2 V 2 ? 1.This sort of question can always be asked There are always going to be facts that just are facts There are always going to be facts that just are facts That doesn’t mean that higher level explanations aren’t really explanations That doesn’t mean that higher level explanations aren’t really explanations It means that explanations suggest further enquiries It means that explanations suggest further enquiries

Deductive-Nomological Exp. An example with gases An example with gases Doesn’t seem to properly explain the explanandum Doesn’t seem to properly explain the explanandum Why does Why does P 1 V 1 = P 2 V 2 ? 2.This asks for an explanation of a general fact rather than a particular fact like the original example The DN model can handle this sort of request The DN model can handle this sort of request They are called Theoretical Explanations They are called Theoretical Explanations Explain P and V relationship in terms of molecular motion and collisions Explain P and V relationship in terms of molecular motion and collisions This is too hard, try a simpler example This is too hard, try a simpler example

Deductive-Nomological Exp. An example of theoretical explanation An example of theoretical explanation No initial conditions y = v 0,y t + ½ gt 2 Relevant laws x = v 0,x t explain A thrown body travels in a parabolathe explanandum Satisfies R1 to R4 Satisfies R1 to R4

Testing the D-N Model. Insufficiency Insufficiency The length of the shadow of the flagpole is s The sun is at an angle of  When the shadow length is s and the angle of the light is  the pole length is p The pole length is p Satisfies R1 to R4 Satisfies R1 to R4 But doesn’t look like a real explanation But doesn’t look like a real explanation

Testing the D-N Model. Insufficiency Insufficiency Fails to offer an effective cause (c.f. Aristotle) Fails to offer an effective cause (c.f. Aristotle) That’s a deliberate feature of Hempel’s D-N model That’s a deliberate feature of Hempel’s D-N model Hempel agreed with Hume that causation was a problematic notion Hempel agreed with Hume that causation was a problematic notion ‘Cause’ was only definable in terms of such notions as ‘necessity’ or ‘counterfactuality,’ ‘necessity’ in terms of ‘counterfactuality’ and ‘cause,’ etc. ‘Cause’ was only definable in terms of such notions as ‘necessity’ or ‘counterfactuality,’ ‘necessity’ in terms of ‘counterfactuality’ and ‘cause,’ etc. These definitions went in a circle – which is bad These definitions went in a circle – which is bad Therefore the concept should be avoided Therefore the concept should be avoided

Testing the D-N Model. Insufficiency Insufficiency If we think that causation isn’t illegitimate, we can add If we think that causation isn’t illegitimate, we can add R5.One of the laws in the explanans must describe a causal relationship But be careful, we don’t want to eliminate the ‘gas’ explanation for example. But be careful, we don’t want to eliminate the ‘gas’ explanation for example.

Testing the D-N Model. Non-necessity Non-necessity Henry played with Albert Albert had mumps If you play with someone with mumps you will catch mumps Henry caught mumps Seems like a good explanation Seems like a good explanation But the law statement probably isn’t true, so it fails R4 But the law statement probably isn’t true, so it fails R4

Testing the D-N Model. Non-necessity Non-necessity 1.Heroic Denial The mumps explanation really isn’t an explanation The mumps explanation really isn’t an explanation An explanation would tell you why some people who play with people who have mumps get mumps, and some people don’t An explanation would tell you why some people who play with people who have mumps get mumps, and some people don’t This seems an excessive requirement This seems an excessive requirement

Testing the D-N Model. Non-necessity Non-necessity 2.Inductive-Statistical Explanations Allow Natural Laws to be probabilistic Allow Natural Laws to be probabilistic Henry played with Albertthe initial conditions Albert had mumps If you play with someone with and the relevant mumps you are very likely probabilistic law to catch mumps make likely Henry caught mumpsthe explanandum

Testing the D-N Model. Non-necessity Non-necessity 2.Inductive-Statistical Explanations Allow Natural Laws to be probabilistic Allow Natural Laws to be probabilistic This is no longer deductive – it’s inductive This is no longer deductive – it’s inductive And the regularity is not a universal law but a statistical claim And the regularity is not a universal law but a statistical claim The degree of probability required then becomes a problem The degree of probability required then becomes a problem Cigarettes make cancer more likely, but still not very likely Cigarettes make cancer more likely, but still not very likely