# What is it for something to be logical?

Camerama

Fri 11 Dec, 2009 05:32 pm
@kennethamy,
kennethamy;110243 wrote:
But what you wrote about "denying logic" does not seem to have anything to do what R. said about truth. I am not a mind-reader. How could I tell that from what you wrote?

Im not pretending that i was very clear

Zetetic11235

Fri 11 Dec, 2009 05:35 pm
@Reconstructo,
Reconstructo;110269 wrote:

5. Is much of what is called logic founded on questionable axioms? For instance, should we consider Hegel's criticism of the Law of Excluded Middle?

This is precisely what constructive mathematics does. The law of excluded middle as it applies to mathematical proofs is thrown out. This is because constructive mathematics comes from a computational perspective; i.e. it does not suffice to say "there exists an x in the natural numbers such that property P holds"; you have to provide a finite algorithm to find that x. So a proposition is not only true or false. It can be the case that such an algorithm cannot be provided, and this is provable within first order logic, hence we have 3 possibilities rather than P v~P (the proposition is or is not true) we have P V ~P V U where U is undecidable, i.e. the algorithm for both P and not P is provably non existent. So we might have an algorithm for P or an algorithm for ~P or we might be able to show that neither is decidable/computable/derivable etc.

Also note that there are many formal logics with many sets of rules. I would thus claim that 'logic' in at least one usage, refers to a process of deduction given certain rules, as opposed to reason which refers to the act of selecting the appropriate rules/parameters to which logic will then be applied. In this manner, logic is procedural whereas reason requires a leap of some sort, though experience can certainly illuminate patterns of reasoning that are more appropriate than others given a certain context.

Typically, when someone asks 'Is this logical?" they mean something very different but derivable from the context. For instance, there was a computer science major who came up with a solution that was nonstandard and kind of strange, he asked "I guess this solution isn't totally logical, but...". Of course the solution was procedurally correct or it would not work. He simply mean that the solution came to him through more of a mental leap than a set of memorized procedures. I would say that this use, by my above formulation, is arguably correct. As has been shown earlier, there are many contexts in which 'logical' can be used and each context type gives the name 'logical' a different semantic object/meaning.

kennethamy

Fri 11 Dec, 2009 06:49 pm
@Camerama,
Camerama;110343 wrote:
Im not pretending that i was very clear

Then how would you expect anyone to comment on it?

Reconstructo

Fri 11 Dec, 2009 07:41 pm
@Camerama,
Camerama;110241 wrote:
I was contending Reconstructo's interpretation of logic, i wanted him to clarify the impact of persuasion on truth, and his idea that there is no absolute reality in a world of change. That is how i interpreted his post and mine was a response to it. I saw him as subordinating logic to whim and subjectivity. I however, believe there is a reality completely independent of humanity, and there will be after we are gone. This may be a diversion from the original topic, but is not irrelevant, since metaphysics is the fundamental premise for any argument.

I also agree in an external reality, and that it is important for this discussion. Please don't mistake me for some kind of solipsist. It's my passion for logic (in my sense of the word) that leads me to question the validity of logic, to sniff out its limitations. Perhaps you are familiar with the correspondence theory of truth? For most practical purposes, this theory is great, but it can easily breed confusion, as it contains a questionable redundancy. If a statement is true because it corresponds to reality and at the same time science and philosophy continue to interpret and redescribe reality, how can this non-static reality be a foundation for anything but provisional truth?

And this is to ignore all the knowledge that is not associated with objective physical science.

jeeprs

Fri 11 Dec, 2009 08:49 pm
@kennethamy,
so what is at issue is not logic as such but its range of applicability. I suppose in traditional logic there was a belief that such laws as the law of the excluded middle applied in all times, places and situations, whereas subsequently it has been shown that this is not the case. This was also associated with the classical era which tended to 'objectify the ideal' in that the heavens themselves were supposed to correspond to the perfect mathematical forms within which the rules of formal logic were indubitable. But then Kepler came along with his ellipses and the classical outlook got 'mugged by reality' as the saying has it.

---------- Post added 12-12-2009 at 01:53 PM ----------

but given that, there are still a range of cases within which formal logic is perfectly correct and applicable. But it is no longer regarded as absolute as it once was.

kennethamy

Sat 12 Dec, 2009 02:41 am
@jeeprs,
jeeprs;110421 wrote:
so what is at issue is not logic as such but its range of applicability. I suppose in traditional logic there was a belief that such laws as the law of the excluded middle applied in all times, places and situations, whereas subsequently it has been shown that this is not the case.

I was aware, of course, that some people have argued that the LEM does not apply to some situations. But I was not aware that we know these arguments are sound. The difference between theory and application is often vexed. Just which cases did you have in mind?

jeeprs

Sat 12 Dec, 2009 03:24 am
@kennethamy,
It's not so much particular cases but types of cases. I would think (and am no expert here) that there are types of situations to which the rules of classical logic can be applied very successfully - many such cases, in fact. I suppose, speaking intuitively, these are where the essential facts can be discerned, and the connection between the premisses and the conclusions reasonably ascertained.

But I think what has happened as society and knowledge have developed, is that we now often confronted with very complex, fluid, or chaotic situations, whether these be scientific, political, economic, or whatever. Market dynamics, or the way epidemics behave, or chaotic systems, often would seem to throw up problems that are not amenable to strictly logical analysis.

Also I think that Aristotlean logic in particular, and the laws of identity and the excluded middle and so on, really don't cope very well with 'the new physics' which is in fact one of the reasons that people are casting about for other logical and metaphysical systems within which they can be interpreted.

That is what I had in mind. I am just improvising here and anyone with more training in logic and so on may know a great deal more.

kennethamy

Sat 12 Dec, 2009 09:26 am
@jeeprs,
jeeprs;110485 wrote:
It's not so much particular cases but types of cases. I would think (and am no expert here) that there are types of situations to which the rules of classical logic can be applied very successfully - many such cases, in fact. I suppose, speaking intuitively, these are where the essential facts can be discerned, and the connection between the premisses and the conclusions reasonably ascertained.

But I think what has happened as society and knowledge have developed, is that we now often confronted with very complex, fluid, or chaotic situations, whether these be scientific, political, economic, or whatever. Market dynamics, or the way epidemics behave, or chaotic systems, often would seem to throw up problems that are not amenable to strictly logical analysis.

Also I think that Aristotlean logic in particular, and the laws of identity and the excluded middle and so on, really don't cope very well with 'the new physics' which is in fact one of the reasons that people are casting about for other logical and metaphysical systems within which they can be interpreted.

That is what I had in mind. I am just improvising here and anyone with more training in logic and so on may know a great deal more.

Everything depends on the argument for the inapplicability of the rule to the particular case. I don't want to be dogmatic about the matter. There might be reasons to restrict the scope of some of the laws of logic. But it would depend. I think we should be reluctant to do so unless there is a compelling reason to do so.

Emil

Sat 12 Dec, 2009 10:39 am
@kennethamy,
kennethamy;110520 wrote:
Everything depends on the argument for the inapplicability of the rule to the particular case. I don't want to be dogmatic about the matter. There might be reasons to restrict the scope of some of the laws of logic. But it would depend. I think we should be reluctant to do so unless there is a compelling reason to do so.

You should extend the same courtesy to the law of non-contradiction.

kennethamy

Sat 12 Dec, 2009 10:49 am
@Emil,
Emil;110539 wrote:
You should extend the same courtesy to the law of non-contradiction.

Oh, I do. In fact, I must, since all three laws are L-equivalent. Never worry.

Zetetic11235

Sat 12 Dec, 2009 12:24 pm
@kennethamy,
kennethamy;110520 wrote:
Everything depends on the argument for the inapplicability of the rule to the particular case. I don't want to be dogmatic about the matter. There might be reasons to restrict the scope of some of the laws of logic. But it would depend. I think we should be reluctant to do so unless there is a compelling reason to do so.

Theory of computation/recursion is based heavily on intuitionist logic/contructivist mathematics, that is, they are based on first order logic without the law of excluded middle (and infact, with bounded quantification). Also, quantum logics and fuzzy logics require different rule sets to achieve certain ends. Fuzzy logics need to allow for gradated set inclusion because it takes sets of 'red' objects or 'thick' objects into account, these status types occur practically in a continuum so truth values range from [0,1] on the real number line.

The logic with which you manipulate your data or axioms needs to reflect the behavior of the objects you are considering. This is why quantum logic is needed. In reality, logic is quite a bit like mathematics.

kennethamy

Sat 12 Dec, 2009 12:32 pm
@Zetetic11235,
Zetetic11235;110571 wrote:
Theory of computation/recursion is based heavily on intuitionist logic/contructivist mathematics, that is, they are based on first order logic without the law of excluded middle (and infact, with bounded quantification). Also, quantum logics and fuzzy logics require different rule sets to achieve certain ends. Fuzzy logics need to allow for gradated set inclusion because it takes sets of 'red' objects or 'thick' objects into account, these status types occur practically in a continuum so truth values range from [0,1] on the real number line.

The logic with which you manipulate your data or axioms needs to reflect the behavior of the objects you are considering. This is why quantum logic is needed. In reality, logic is quite a bit like mathematics.

Yes, I know about intuitionism, and not much about the rest. And it may be that (as I said) the scope of the LEM needs to be restricted. But such restriction is not something isolated. It will have implications for all we know. An important contemporary development in philosophy is the notion of anti-realism, which also restricts the use of the LEM and claims, and hold that that propositions that are unverifiable in principle are neither true nor false.

Reconstructo

Sat 12 Dec, 2009 02:23 pm
@kennethamy,
What would any of you describe logic to be founded upon in the first place? Is logic founded upon logic? Is logic founded upon tautology? I haven't studied logic's self-justification so the question is asked in earnest?

Side note: antecedent skepticism: is it refuted by anything other than "common sense," than the fact that man cannot afford it? That it must be an insincere viewpoint for man as he is constituted?

kennethamy

Sat 12 Dec, 2009 03:00 pm
@Reconstructo,
Reconstructo;110616 wrote:
What would any of you describe logic to be founded upon in the first place? Is logic founded upon logic? Is logic founded upon tautology? I haven't studied logic's self-justification so the question is asked in earnest?

Side note: antecedent skepticism: is it refuted by anything other than "common sense," than the fact that man cannot afford it? That it must be an insincere viewpoint for man as he is constituted?

Why must logic be founded on anything? There need be no tortoise at the bottom. Or, maybe, it is tortoises all the way down. There are books on the foundations of logic, but those are mostly books on the axioms and definitions from which all of logic can be deduced. I don't know that skepticism is refutable. Although Descartes gave it the old college try (the Sorbonne) with the Cogito.

Reconstructo

Sat 12 Dec, 2009 03:07 pm
@kennethamy,
Well, if logic is founded upon persuasive intuitions, I think this would change some folk's feelings toward it.

I, too, doubt, that skepticism is refutable. And this just goes to show you that a man must live by faith as well as reason, and perhaps that reason is founded upon faith. But don't exaggerate my meaning here. Force and clarity in prose style -- that's my justification for putting it in such a way.

jeeprs

Sat 12 Dec, 2009 03:41 pm
@kennethamy,
Something that scientists often fail to realise, in my view, and more so in the current 'scientific age', is exactly that logic and mathematical reasoning don't go 'all the way down'. They rest on assumptions and axioms at some point, beyond which they cannot be applied. As for the logical foundations of math, isn't this what Russell and Whitehead tried to establish, and Godel showed couldn't be done? I think logic is very much a tautological system. But skepticism is something that needs to be understood and applied correctly. In my view, scientific skepticism is pseudo-skeptical, because it is all predicated on the type of naive realism which is the first thing that the real skeptic calls into question.

Reconstructo

Sat 12 Dec, 2009 03:55 pm
@jeeprs,
jeeprs;110655 wrote:
Something that scientists often fail to realise, in my view, and more so in the current 'scientific age', is exactly that logic and mathematical reasoning don't go 'all the way down'. They rest on assumptions and axioms at some point, beyond which they cannot be applied. As for the logical foundations of math, isn't this what Russell and Whitehead tried to establish, and Godel showed couldn't be done? I think logic is very much a tautological system. But skepticism is something that needs to be understood and applied correctly. In my view, scientific skepticism is pseudo-skeptical, because it is all predicated on the type of naive realism which is the first thing that the real skeptic calls into question.

I can't find anything to disagree with here. Science still needs philosophy. Concept/metaphor is the cutting edge of speakable. Ultimately the entire system is built on Life, and on the structure of Human Life - which remains in many ways mysterious.

jeeprs

Sun 13 Dec, 2009 04:34 am
@kennethamy,
recognition of which is the difference between science and scientism.

Reconstructo

Sun 13 Dec, 2009 04:37 am
@kennethamy,
Hegel, for all his faults, tried to give the world a Science that would go all the way down. But I don't think he attained "absolute knowledge." I think "the impossibility of closure" is a more likely scenario. Of course we experience moments of transcendence and peace. And this is a passing closure.

kennethamy

Sun 13 Dec, 2009 08:22 am
@Reconstructo,
Reconstructo;110884 wrote:
Hegel, for all his faults, tried to give the world a Science that would go all the way down. But I don't think he attained "absolute knowledge." I think "the impossibility of closure" is a more likely scenario. Of course we experience moments of transcendence and peace. And this is a passing closure.

The quest for foundations and certainty. The heavy hand of Plato. That is why we have to recognize a coherence theory of justification (not of truth) and a correspondence theory of truth.