1711 – 1776, Scottish philosopher and historian. Born near Edinburgh; entered Univ. of Edinburgh at 11. Major philosophical works: A Treatise of Human Nature(1739 – 40) An Enquiry Concerning Human Understanding(1748) An Enquiry Concerning Human Understanding (1751) The Dialogues Concerning Natural Religion (1779) “I have always considered him, both in his lifetime and since his death, as approaching as nearly to the idea of a perfectly wise and virtuous man, as perhaps the nature of human frailty will admit.” --- Adam Smith David Hume
The Idea of Necessary Connection • Impressions and Ideas • Impressions are lively, immediate perceptions (external or internal); • Simple ideas are faint copies of impressions (which, in turn, compose more complex ideas). According to Hume, all ideas ultimately derive from experience. • What impression underwrites our idea of power or necessary connection typically associated with cause and effect?
Hume’s Answer • Perception of the operation of external objects in a single instance can’t give rise to the idea. • Perception of the working of our own volition can’t give rise to the idea. • So, the idea must be due to the customary drive our mind feels to infer from one event/object to another after observing a number of instances of events similar to the latter following events similar to the former.
Regularity Theory of Causation “ Similar objects are always conjoined with similar. Of this we have experience. Suitably to this experience, therefore, we may define a cause to be an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second. Or in other words where, if the first object had not been, the second never had existed. The appearance of a cause always conveys the mind, by a customary transition, to the idea of the effect. Of this also we have experience. We may, therefore, suitably to this experience, form another definition of cause, and call it, an object followed by another, and whose appearance always conveys the thought to that other.” David Hume, Enquiry (1748)
Causes as Conditions • One way of looking at it is to think of causes as conditions: John S. Mill, A System of Logic (1843) • In this passage Mill seems to identify the cause as sufficient conditions for the effect. But in virtue of what is the cause sufficient for the effect? General regularities or what Mill preferred to call uniformities or laws of causation. • A more sophisticated account links causes to the so-called INUS conditions: an INUS condition for an effect is an Insufficient but Necessary (Non-redundant) part of a Unnecessary but Sufficient condition for that effect. (John Mackie, The Cement of the Universe, 1980)
Logical Positivism/Empiricism • A philosophical movement originating in Europe in the early 1920’s, lead and participated by a group of scientifically minded philosophers and philosophically minded scientists. • Two main centers: • Vienna Circle lead by Moritz Schlick: R. Carnap, H. Feigl, P. Frank, H. Hahn, K. Godel, K. Menger, O. Neurath, … • Berlin Circle lead by Hans Reichenbach: K. Grelling, D. Hilbert, C. Hempel, R. von Mises … • Distinguished by their firm positivist or empiricist stance, their emphasis on philosophical analysis with logical tools, and their rejection of most metaphysical problems as meaningless.
Hempel and Oppenheim • Carl G. Hempel (1905 – 1997), born in Germany; was a (younger) core member of the Berlin circle, and also visited the Vienna circle for a while; moved to the US in 1937; settled eventually as professor of philosophy in Princeton. • Paul Oppenheim (1885 – 1977), born in Germany; a good friend of Reichenbach’s, who introduced Hempel to him; moved to the US in 1939; settled in Princeton, and was a good friend with several leading figures in the Institute for Advanced Study.
Prototype of the D-N Model John S. Mill, A System of Logic (1843)
Deductive Argument • An argument consists of a bunch of statements(declarative sentences). Some of the statements are premises, and others are conclusions. e.g. Premise 1: Some people are philosophers. Premise 2: All philosophers love wisdom. Conclusion: Some people love wisdom. • An argument is deductively validif the truth of its premises would compel the truth of its conclusions. In other words, for a valid argument, if all the premises were true, the conclusions could not possibly be false.
Logical Form • The logical form of an argument abstracts away the specific terms or (basic) sentences in the argument, and only retains logical quantifiers are connectives. • An argument is deductively valid or invalid in virtue of its form. Some people are philosophers. All philosophers are wisdom lovers. Some people are wisdom lovers. Some X’s are Y’s. All Y’s are Z’s. Some X’s are Z’s.
Invalid Arguments • An invalid argument has an invalid logical form. • That means you can find an argument that conforms to the logical form in which all premises are true but the conclusion is false. • e.g., how about the following argument: Some people are philosophers. Some philosophers are freaky. Some people are freaky.
Toy Exercise: Which Are Valid? If P, then Q If P, then Q P Not Q (1) ----------------- (2) -------------------- Hence, QHence, Not P If P, then Q If P, then Q Q Not P (3) ----------------- (4) -------------------- Hence, PHence, Not Q
Answer • (1) and (2) are valid. They are known as Modus Ponens and Modus Tollens. These are probably the most widely used forms of inference. • (3) and (4) are invalid, known as the fallacy of affirming the consequent and the fallacy of denying the antecedent.
Aside: Formal Language • To study the valid forms of inference more precisely, formal language is in many ways preferable to natural language; the latter is filled with vagueness and imprecision. A typical alphabet for (first-order) predicate logic contains: variables: x, y, z, … (intended to range over a given domain of objects) constants: c, d, e, … (intended to name particular objects in the domain) function symbols: f, g, h, … (intended to represent functions) predicate symbols: P, Q, R, … (intended to represent properties or relations) quantifiers: (every, all), (some, there exists) sentential connectives: ~ (not), (and), (or), (if … then) identity: = auxiliary symbols: (, ) * Oftentimes one simply write (x)(Px) to mean x(Px), as Salmon does.
The Deductive-Nomological Model (1) An adequate explanation must be a deductively valid argument. (2) The premises of an adequate explanation, the explanans, must contain at least one general law in an essential way. (3) The explanans of an adequate explanation must be “empirically testable”. (4) The explanans of an adequate explanation must be true.
Example Explanandum: A mercury thermometer is rapidly immersed in hot water, and the mercury column in the glass tube first drops and then quickly rises. (From the H-O paper) What is a D-N explanation of the phenomenon described by the above sentence?
The Concept of General Law • Obviously not just any true general statement is a law. • Intuitively it seems laws are supposed to mean more than just an actual regularity. • A law is supposed to have modal import, to tell us what is physically impossible; • A law is supposed to support counterfactual reasoning: what would happen if things were different than they actually are? • But then how to tell whether a general statement has modal import or supports counterfactual reasoning? Depends on whether it is a law?
A First Attempt • Laws are universal in form. • Laws have unrestricted scope. • Laws do not involve references to particular objects or spatio-temporal locations. • Laws do not contain predicates that are not purely qualitative. * Turns out these are both too strong and too weak. No adequate account so far, which motivates some philosophers to reject the concept.
Putative Counterexamples • Future explains past? – the eclipse example; teleological explanations. • Effect explains cause? – the flagpole example. • Collateral effects explain each other? – the barometer example; the tides example. • Explanatory irrelevance – the hexed salt example and the birth control example. • Symmetry between explanation and prediction (next time)