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Deductive Completeness

Kelby
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Posted 09/19/09 - 03:25 PM: Subject: Deductive Completeness	#1
I am sorry if this turns out to be a sophomoric post, but I cannot help but thinking about the process of deduction. So many philosophers are skeptical about induction because it is not deductive, as if deduction was a divine arbiter of proof. But can deduction prove anything? Is it not the case that deduction relies on a possibility... as in modus ponens. Modus ponens is deductively valid because it relies on the connection between x and y in x-->y. SO as everyone is aware of if dogs are mammals then cats are felines dogs are mammals therefore cats are felines This is valid but what is the connection between dogs being mammals as proof of cats being felines? Wouldn't the first premise need be some how causally verified? And the assumed premise of that argument also needs to be proven, and so on? If this is the case, wouldn't deduction be just as prone to skepticism as induction? I have a feeling that there is a simple answer to this question, I just can't quite come to terms with the details.

Aetixintro
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Posted 09/19/09 - 04:23 PM:	#2
It's the form that's the guarantee of truth when done right! I have the sense that logic mostly comes to its right in the form of Gödel's incompleteness theorems and the like. The useful logic is not for mortals! F.x. if dogs are cats then cats are elephants dogs are cats therefore cats are elephants Clearly...
Efficacy of "for since it is at present manifest to me that even bodies are not properly known by the senses nor by the faculty of imagination, but by the understanding alone" - Descartes, Meditation II I'm always wanting more, Anything I haven't got, Everything, I want it all, I just can't stop - The Cure, Want

Timothy
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Posted 09/20/09 - 11:49 AM:

There is certainly lots of philosophizing about deduction and its close cousin, logical implication. For example, here's Susan Haack attack on the justification of deduction. You will be pleased to find that she finds deduction as justified as induction.

There's also some buzz regarding different ideas of "logical consequence" that could yield different concepts of deduction (I do not think so myself, but some serious people do). Check this out as a sample.

Attached Files:

The Justification of Deduction.pdf
(753 KB, 16 downloads)

"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson

Timothy
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Posted 09/22/09 - 10:20 AM:	#4
I just found this remark by Nelson Goodman in "The New Riddle of Induction": This looks flagrantly circular. I have said that deductive inferences are justified by their conformity to valid general rules, and that general rules are justified by their conformity to valid inferences. But this circle is a virtuous one. The point is that rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either. Serendipity
"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson

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