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Lecture 19

Lecture 19 - Deduction & Induction

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University of Ottawa
Daniel Kofman

Nov. 19, 2013  Deductive inference (Lewis Caroll)  Ultimate justification – cannot be itself justified (room for skepticism) -it need not be further justified (the inferences themselves are self-evident)  Inductive inference – to infer from a single event/object something about an unobserved object/event – typically in the future, but can also be in the past or present – some geologists make retrodictions about the past (fossils) and make inferences about the past  What can justify inductive inference?  Ex: Scientists – General Law: water boils @ 100C  Particular event that is observed: this water is being heated to 100C  Deduction: water is boiling Hume on Induction 1. Hume’s Fork: There are only two kinds of knowable propositions – relations of ideas and matters of fact 2. Relations of ideas have two features: 1) They are ether intuitively or demonstratively certin (logical truths, geometric proofs, etc.) 2) They do not assert the existence of non-abstract entities (ex: physical objects or physical states, minds or mental states) 3. Matters of fact have (the opposite two features: 1) they are either intuitively nor demonstratively certain 2) they do assert the existence of non-abstract entities (objects or states) (Some examples: Caesar crossed the Rubicon, the water in the kettle is boiling, water boils at 100C, the sun will rise tomorrow) 4. All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of geometry, algebra, arithmetic, and in short, every affirmation, which is either intuitively or demonstratively certain. That the square of the hypotenuse is equal to the squares of the two dies, is a propostion which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers. Propositions of theis kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Thought there never was a circle or triangle in nature, the truths, demonstrated by Euclid, would forever retain their certainty and evidence. Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction, than the affirmation that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind. (E IV 1, “Skeptical Doubts Concerning the Operations of the Understanding”). -can’t imagine a possible world in which a contradiction is true -a matter of fa
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