Why mathematical logic?: Philosophy Forums

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Why mathematical logic?

lullus
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Posted 10/10/09 - 01:55 PM: Subject: Why mathematical logic?	#1
Why is that mathematical logic works? I mean that when you conclude something from abstract reasoning why is that result true in the real world? It seems like any attempt to show that, without a doubt, mathematical logic is a valid way to work.. must use mathematical logic to prove that. In exactly the same was as assuming the Bible is true leads to the conclusion that God exists.

ClaudeHooper
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1 of 2 people found this post helpful Posted 10/10/09 - 02:30 PM:	#2
Classical logic doesn't work in the real world. That's why physicists are trying to invent a quantum logic.

lullus
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Posted 10/10/09 - 04:12 PM:	#3
Can you elaborate a bit please?

ClaudeHooper
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Posted 10/10/09 - 04:24 PM:	#4
Take the double slit experiment from quantum mechanics. Consider the following statements: Statement A: The electron went through slit A. Statement B: The electron went through slit B. Statement C: The electron went through slit A or slit B. Experimentally, it turns out that statement A is false, statement B is false, but statement C is true. Thus, classical logic doesn't provide an accurate model of the real world.

Gadfly II
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Posted 10/10/09 - 05:09 PM:	#5
ClaudeHooper wrote: Thus, classical logic doesn't provide an accurate model of the real world. To be precise, classical logic does not model quantum phenomena in a useful way. Classical logic does indeed capture relevant features of reality in general. Still, this does not answer that question of the relationship between our abstract representations and physical events. Is it that they capture relevant features of the world? (realist) Are they simply conventions that we arbitrarily assign to phenomena and continue to do so as long as they yield useful results? (conventionalism) The fact that classical logic does not represent features of the world we are interested in does not vitiate the usefulness that it does have. For example, it is true that the world is not euclidean (is not exhausted by euclidean description) but that doesn't mean that the world does not have euclidean features. Of course I'm assuming a realist POV
Dare to use your own reason. Kant

Timothy
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Posted 10/10/09 - 07:03 PM:	#6
lullus wrote: I mean that when you conclude something from abstract reasoning why is that result true in the real world? I don't think this implication holds. What logical reasoning does is to show that If certain premises hold, then certain conclusions are formally implied. Logic does not dictate what is true or what not, only what would be true if certain other things were also true. lullus wrote: It seems like any attempt to show that, without a doubt, mathematical logic is a valid way to work.. must use mathematical logic to prove that. In exactly the same was as assuming the Bible is true leads to the conclusion that God exists. Search a topic named "Completeness of Deduction" on this forum for an article of Susan Haack on how it's circular to try to justify deduction
"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

180 Proof
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Posted 10/10/09 - 08:17 PM:	#7
Timothy wrote: What logical reasoning does is to show that *If certain premises hold, then* certain conclusions are formally implied. Logic does not dictate what is true or what not, only what would be true if certain other things were also true.** As usual, aptly put.
The question isn't "Which explanations do I believe?" but rather "Which explanations do I least disbelieve?" Absence of evidence THAT MUST BE THERE (i.e. implied by any claim, concept, or (its) predicates, that affects changes in/to the world) entails evidence of absence. [What cannot be done?[What cannot be hoped?[What cannot be known?]]]

Kamerynn
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Posted 10/10/09 - 11:07 PM:	#8
Some people find explosion to be a... distasteful result of classical logic (when the assumptions contain a contradiction). I don't believe that it necessitates a "paraconsistent" logic, but I thought I'd mention it. There are certainly ways in which classical logic doesn't resemble the natural language, but that's to be expected. I find it interesting how ~a-->a is assigned a value of "true" whenever the antecedent is false (i.e., a is true); In the natural language, upon hearing the phrase, "if the sky is red, then the sky is blue," we would not congratulate someone on their truthful utterance. We would likely think them insane, or ask what they could possibly mean. I suppose we might say that it's just plain false that the sky is blue if it is not blue. Edited by Kamerynn on 10/12/09 - 04:32 AM
When I'm working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong. -- R. Buckminster Fuller

lullus
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Posted 10/11/09 - 10:40 AM:	#9
so the human brain does not work by logic?

Timothy
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Posted 10/11/09 - 11:39 AM:	#10
the statement is too vague. But if you mean "mathematical logic", then no. The brain works by electrochemical impulses, and formal logic has nothing to do with electrochemical impulses.
"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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