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Hume posited a well known critique of causality that goes back to al-Ghazali - that there is no necessary connection between a cause and an effect.

The same argument it seems can be targeted to logical deduction itself - intuitively seeing deduction temporally, and the premises being the 'cause' of the conclusion.

More formally, we have a premise and a rule. By applying that rule to the premise we get a conclusion, but why should we apply this rule and in this way? Of course, these are the rules of the deductive game, but it remains true, I think, that they do not necessarily apply.

Did Hume offer a similar argument? I seem to recall something similar offered by Lewis Carroll that was picked up by the Tortoise in Hofstadter's Gödel, Escher, Bach: an Eternal Golden Braid, but I may (and probably am) mistaken here.

And if Hume did offer such an argument, did Kant offer a riposte as his work was clearly responding to Hume (amongst other things)?

For example, Kant showed that some of the conditions for empirical knowledge, are time, space and causality. This was in response to Hume (to reiterate the above) who argued that causality when strictly empirically construed can be no more than coincidence. Hence something additional is required.

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    As far as I know, there is no well developed logical formalism for causality. Material implication, despite some of its seemingly counter-intuitive results, seems to be the only form of implication you need for any application. – Dan Christensen Jun 19 '14 at 4:58
  • @Christensen: I'm not arguing that logic ought to be temporalised; I'm merely suggesting a hopefully evocative analogy; the question is focusing on whether a criticism similar to that which Hume made can be leveled at material implication. – Mozibur Ullah Jun 19 '14 at 15:55
  • Can you sharpen up the headline a little bit? Was having a hard time framing it myself; it of course is going to optimize the chances of getting a great answer if we can specify really clearly exactly you'd like someone to explain; at any rate I'm having trouble framing this point about 'similar criticisms for material implication' in a straightforward way -- maybe you could reflect and try to reformulate towards a question? – Joseph Weissman Jun 20 '14 at 2:06
  • "that there is no neccesary connection between a cause and an effect." I am a little confused by this. Doesn't that violate the very meaning of the word "cause?" Perhaps Hume meant to say correlation. At the very least, we modern readers should make that distinction. A cause is in fact a cause, not a correlation. When you flip the light switch, it causes the light to turn on. When I pat my belly and a cloud passes by overhead, that's a correlation, not a cause. – user4894 Jun 20 '14 at 17:53
  • @user4894:sure - good point, Your analysis of cause is what Aristotle called the efficient cause - its not a modern distinction; Hume was being sceptical about the empirical claims of science - he was writing after Newtonian determinism had been discovered; the picture you've drawn already takes for granted a certain world-picture; its the basis of this world-picture that Hume is attacking. – Mozibur Ullah Jun 20 '14 at 19:18
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First, it might be useful to recall that Hume claimed that all propositions can be classified into two categories: 1) relations of ideas and 2) matters of fact. The truth of relations of ideas is known a priori, without the aid of experience. Logical or mathematical propositions are such relations of ideas and we can be sure of their truth because denying them would involve a contradiction. As for matters of fact, their truth depends on how the world is and thus can only be justified a posteriori, i.e. with experience. That X causes Y or that the colour of Napoleon's horse is white are propositions whose truth depends on experience of the world. This distinction is often called 'Hume's Fork' and it mirrors to some extent the necessary/contingent, analytic/synthetic, a priori/a posteriori divide.

To come back more specifically to your question, I think Hume would say that the necessary connection between a cause and an effect is a matter of fact, but the 'necessary connection' (this term is perhaps misleading) between premisses and a conclusion in a deduction is a relation of ideas. The following proposition, 'Were the premisses of a valid deductive argument be true, the conclusion would necessarily follow.', is true in virtue of the meaning we ascribe to the words involved like 'valid, 'deductive' or 'argument'. Basically, one is only spelling out the meaning of the proposition and what this meaning logically entails.

So is it the case that "the rules of the deductive game" necessarily apply? Here I might be deviating from Hume, but the short answer is no. It is relative to a language and there are many types of logics, paraconsistent logic, fuzzy logic, relevance logic, free logic, modal logic, etc. But in a language where 'deduction' means what it commonly means, yes, the rules necessarily apply. One cannot deny that the conclusion of a valid deductive argument necessarily holds provided the premisses are true. That would contradict one's own concept of deduction. But it doesn't mean that necessarily 'deduction' ought to mean that, if that is what you asked.

Finally, concerning Kant, one central idea of the Critique of Pure Reason is that some a priori concepts, the categories of understanding, necessarily apply to all the objects of human knowledge. They structure all our thoughts and experience. One such category is of 'Causality and Dependence' and contains the idea of the necessary connection between a cause and its effect. Also, Kant didn't buy Hume's Fork. The Critique's main motivation was to show that synthetic a priori judgments were possible, i.e. that it is possible to know a priori some propositions about the world.

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