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The basis of logic

Parakeet
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Posted 10/01/08 - 06:42 PM:	#11
Logic is logical because it works. If it didn't correspond with reality, or at least how we observe reality, then it wouldn't be logical.

sqeecoo
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Posted 10/02/08 - 02:48 AM:	#12
A quote from this article by Miller, http://www2.warwick.ac.uk/fac/soc/philosophy/staf..., where he discusses "the status of logical rules" in the last section: A more promising approach, more congenial to critical rationalism, is to volunteer the rules of deduction as conjectures, and to invite all comers to identify counterexamples to them. Critical rationalists will not be flustered by the platitude that, here as elsewhere, a failure to falsify a conjecture provides no shred of justification for it; a rule is not justified because no counterexample has been found. More worrying is the suggestion (attributed by Nilsson 2006 to Apel, Habermas, Thomas Nagel, and Bartley) that there is some small set of logical laws that are immune to criticism because, it is claimed, they constitute an â€˜absolute presupposition of argumentâ€™, and can thus be conclusively and irrevocably justified by showing that any attempt to deny them leads to â€˜performative contradictionsâ€™ (ibidem, p. 110). This transcendental mode of argument leads easily to a rejection of the view that â€˜someone who is trying to inquire and reason rationally can and should treat logic as criticizable and revisableâ€™ (ibidem, p. 112). It is evident that this predicament is similar to that encountered in Â§ 2 above. I hope to show how elegantly critical rationalism can once more weather the storm (on this point see also Miller 1994, Chapter 4, Â§ 3c), and in particular, to give a more satisfying response than that given by Nilsson, who also writes from the perspective of critical rationalism. He poses the problem like this (ibidem): The idea . . . seems to be applicable [when an attempt is made to establish the invalidity of some rule]. If the criticism is aimed at showing that an inference rule is invalid, then it is of course problematic if in the critical argument one presupposes the validity of the same rule. Similarly, if the argument is intended to show that an inference rule is unjustifiable and hence that reasoning in accordance with it is not rationally permitted, it is problematic if the critical argument is based on the presuppositions that the rule is valid and that reasoning in accordance with it is rational. This is plainly incorrect, unless â€˜presupposeâ€™ means something decidedly odd. If a rule R of inference is supposed (or presupposed) to be valid, and a counterexample is derived with its assistance, then either the rule R itself, or one of the other rules used in the derivation, or one of its premises, is not valid. If R is the only rule used in the derivation, then if R is valid it is invalid. It follows that R is invalid. It does not follow that the counterexample to R was not validly derived, since most invalid rules have valid instances (as Nilsson recognizes). Basically, logic is the conjectural attempt to enumerate the truth-transmission rules of our language.

Timothy
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Posted 10/02/08 - 06:52 PM:	#13
Great quote, sqeecoo. It points to what appeared to me to be nonsensical in the first place. But while that diagnosis seems to rely in a circularity, I have another take, a "linear" take if you may. Let's say that you have a classical logic (system/calculi P, let's call it) theorem such as (p -> q) & p :: q Technically speaking, this is not Modus Ponens; MP is not a theorem of the system, but rather is a rule about the system, i.e. it's a metalogical statement. I'm guessing that any attempt to "justify" logic, or plainly to investigate it, must be made within a meta-language. Now, strictly speaking, metalogic does not employ the logical theorems of the system that it is talking about; even when they seem to have a similar structure (quantification would strike a difference enough). Now you could also ask whether this meta-system is itself "justified" in the way that the object-system was; and then ask the same about the meta-meta system and so on ad infinitum. It is this endless chain generated by the OP's question that made me think of it as nonsensical...
""Physics investigates the essential nature of the world, and biology describes a local bump. Psychology, human psychology, describes a bump on the bump." W.V.O. Quine

Deftil
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Posted 10/03/08 - 12:51 AM:	#14
Parakeet wrote: Logic is logical because it works. If it didn't correspond with reality, or at least how we observe reality, then it wouldn't be logical. I basically agree in regards to "logic" in the general sense. Bleedinghamster wrote: What is the basis of logic? I attacked this problem from many directions, only to reach a contradiction: the basis of logic is illogical. Consider this: for logic to be logical, one must assume it is, well, logical. Because logic can't explain how it is logical without using logic, there must be a premise, something that assures us logic is logical (an axiom?). That premise is illogical; it doesn't have any logic behind it, and so the basis of logic is illogical. Essentially all knowledge proceeds from assumed premises. If you then try to prove those premises, you must use other premises that aren't proven in your proof, and the cycle continues on infinitely. I wouldn't say this makes logic, or any other knowledge necessarily illogical, just that complete epistemological certainity isn't available. As stated above, logic in it's general/ informal sense works because it seems to match up with observed reality as we understand it. Proving that it exists independently of our minds is another matter.

swstephe
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Posted 10/03/08 - 01:14 AM:	#15
Dr.Black wrote: Considering the above, are you questioning the objective Truth of logic, or whether logic systems in themselves are logical (your first post seems to imply the latter)? Are you more interesting in knowing whether validity has anything to do with Truth? I'm saying that logic doesn't need to refer to "Truth", (with a capital T). It is merely one of many possible self-consistent systems, one which matches our perceptions of the world fairly closely. Logic isn't illogical as long as it is self-consistent and can be applied to every situation. It is about the same as "math", (or "maths" for people outside the Americas). Numbers don't exist in reality, but the relationship between numbers help us to model what we observe well enough for practical purposes.
Ethics is the measuring of morality. Morality is the measuring of good. Good is the measuring of benefit. Benefit is the measure of values.

muaz jalil
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Posted 10/03/08 - 11:02 PM:	#16
swstephe wrote "I'm saying that logic doesn't need to refer to "Truth", (with a capital T). It is merely one of many possible self-consistent systems, one which matches our perceptions of the world fairly closely." I couldn't have agreed more. Russell, I think in his book called "Problem of Philosophy", wrote that self consistency and truth are not necessarily synonymous. Consistency is a necessary condition for a system to be true (whatever that means) but definitely not a sufficient condition. Frankly there is no reason to assume that there is a single self consistent system of logic, to avoid the same mistake mathematician made before Reiman came. I have another thought, thanks to swstephe and Parakeet, it seems to me and correct me if i am wrong, the interpretation/defense of logical system provided here has an eerie similarity to the Copenhagen Interpretation of Quantum Mechanics where Neils Bohr suggested along a similar line that QM is set of theories which are consistent or rather correlates well with our experiments, whether they are true or not is entirely a different question.

Toobsock
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Posted 10/08/08 - 10:40 AM:	#17
Using logic to logically explain logic? Seems illogical...

raf0208
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Posted 10/30/08 - 05:35 PM:	#18
Bleedinghamster wrote: What is the basis of logic? I attacked this problem from many directions, only to reach a contradiction: the basis of logic is illogical. Consider this: for logic to be logical, one must assume it is, well, logical. Because logic can't explain how it is logical without using logic, there must be a premise, something that assures us logic is logical (an axiom?). That premise is illogical; it doesn't have any logic behind it, and so the basis of logic is illogical. Thoughts? Read Robert Brandom Articulating reasons. The foundations of logic refer to a non-inferential truth condition or meta-theory that creates this mysterious or mystical understanding of the world. Wittgensteinien in a sense.

How Absurb!
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Posted 11/05/08 - 05:48 PM:	#19
muaz jalil wrote: swstephe wrote "I'm saying that logic doesn't need to refer to "Truth", (with a capital T). It is merely one of many possible self-consistent systems, one which matches our perceptions of the world fairly closely." I couldn't have agreed more. Russell, I think in his book called "Problem of Philosophy", wrote that self consistency and truth are not necessarily synonymous. Consistency is a necessary condition for a system to be true (whatever that means) but definitely not a sufficient condition. Frankly there is no reason to assume that there is a single self consistent system of logic, to avoid the same mistake mathematician made before Reiman came. I have another thought, thanks to swstephe and Parakeet, it seems to me and correct me if i am wrong, the interpretation/defense of logical system provided here has an eerie similarity to the Copenhagen Interpretation of Quantum Mechanics where Neils Bohr suggested along a similar line that QM is set of theories which are consistent or rather correlates well with our experiments, whether they are true or not is entirely a different question. Agreed, a much more coherent version of what I was considering writing.

cjwalker89
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Posted 12/17/08 - 03:10 PM:	#20
Should we analyze a system from the point of view of the system itself? Wouldn't that be circular? Shouldn't we reach outside the system of logic and ask Why be logical? But If we do that, no matter what the anwser, will it not lead to infinite regress?
MIND, n. A mysterious form of matter secreted by the brain. Its chief activity consists in the endeavor to ascertain its own nature, the futility of the attempt being due to the fact that it has nothing but itself to know itself with.

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