Jon, List,
the fallacy of intuitionistic logic in my hypothesis is, that it first includes belief into the concept of truth, then sees, that belief is not two-valued, and then denies the law of the excluded middle for both. But the NOT-operator can only be applied for truth-problems, and so for knowledge-problems, not for belief-problems. It is meant like that.
The fallacy is based on the hypothesis, that truth in general is not detectable. But I think, that Steven has shown with Goedel, that there is a clear, noncontinuous distinction between belief and truth, meaning, that truth exists, the only thing, that the NOT-operator applies to, due to the agreement about this symbol.
The clear distinction -mathematically proven by Goedel- between belief and truth is, that, if the proposition is about a system the propositioner is part of, it must be belief, and therefore (I think), if the propositioner is not part of the proposition´s object, the proposition may be true or false, such as: "This bucket is made of zinc.".
Even if it was so, that intuitionalistic logic would admit, that it throws belief and knowledge (of truth) in one basket, this would be a performative fallacy, because, since there is a clear distinction between both, and both exist, blending both together, and widening the symbolic meaning of the NOT-operator, is an unnecessary, confusing thing to do.
At least, they should not use the NOT-operator, but invent a new one, such as MNOT (maybe not), like Peirce has done with not using the normal cut, but a dotted cut for insecurity-problems.
Best, Helmut
24. Dezember 2020 um 03:34 Uhr
"Jon Alan Schmidt" <jonalanschm...@gmail.com>
"Jon Alan Schmidt" <jonalanschm...@gmail.com>
Helmut, Steven, List:
HR: For me it is not clear, what exactly is claimed to justify intuitionistic logic.
What would it mean to justify intuitionistic logic? What kind of reasoning would one use to do so? From my standpoint, it is "justified" by not imposing excluded middle as if it were an exceptionless law, as in classical logic. I agree with Peirce that the underlying assumption of the latter--"that there is a perfectly definite body of propositions which, if we could only find them out, are the truth, and that everything is really either true or in positive conflict with the truth" such that "reality is so determinate as to verify or falsify every possible proposition"--is "utterly unwarranted" and not "strictly true" (NEM 3:758-760, 1893). In other words, it is not always the case that "what is not true, is false" and vice-versa; for example, since there are real possibilities, a "conditional proposition whose antecedent does not happen to be realized" (CP 4.580, 1906) is not false but also not necessarily true, which is why "if A then C" is not equivalent to "not-(A and not-C)."
SS: About the world we live in, we're all "believers that" and "knowers not" even if we think and say we are "knowers that”. (Where “belief” is an understanding one's prepared to act on.)
Only if we equate knowledge with certainty rather than accepting its standard philosophical definition as justified true belief. For Peirce, a belief itself is a habit of conduct; a belief is justified if it is the conclusion of a valid argument, whether abductive/retroductive (plausible), deductive (certain), or inductive (probable); and a belief is true if the corresponding habit would never be contradicted by any future experience. "[U]pon innumerable questions, we have already reached the final opinion," while "some finite number of questions, we can never know which ones, will escape getting answered forever"; and "there is nothing to distinguish the unanswerable questions from the answerable ones, so that investigation will have to proceed as if all were answerable" (CP 8.43, 1885).
SS: One can never know with infallibility the state of ontology if the knower is within the system ("that what is") under consideration, right? I think that was shown by Goedel, right?
One can never know anything with infallibility--according to Peirce, not even that twice two is four, although we have no good reason to doubt it--but in any case, that is not my understanding of Gödel's famous proofs. What he demonstrated is that there are undecidable sentences in any formal axiomatic system powerful enough to express basic arithmetic.
SS: In terms of logic and the big questions, don’t we live more in a state of "fuzzy logic" where things have likelihoods--percentages of truth? And then things begin to feel pretty intuitionistic.
No, this confuses our subjective (or perhaps intersubjective) "degrees of belief" at any assignable date with the (absolute) truth as the ultimate opinion that would be affirmed by an infinite community after infinite inquiry. The dynamical object of that "ultimate interpretant of every sign" (EP 2:304, 1904) is reality, that which is as it is regardless of what any individual mind or finite group of minds thinks about it. Also, fuzzy logic is not the same as intuitionistic logic, it ventures even farther away from classical logic by positing multiple truth values rather than merely omitting excluded middle.
HR: So I, up to now, assume, that intuitionistic logic is a fallacy.
What would it mean for intuitionistic logic to be a fallacy? In accordance with what presumed standard of valid reasoning? No one disputes that it does not conform to classical logic since that is pretty much the whole point of it. It might help for you to spell out how you are defining "intuitionistic logic" in this context.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
On Wed, Dec 23, 2020 at 12:35 PM Helmut Raulien <h.raul...@gmx.de> wrote:
Correction: I guess I meant "operator" instead of "quantor". I am not a certified logician.Steven,yes, I nearly totally agree. Interesting, that Goedel said that. An observer cannot know the onologic state of a system the observer is part of. Then calling it knowledge is false, it is belief. Truth can only justifiedly be assumed about a system the observer is not part of, like a thing. This can be analysed. A system the observer is part of can not be merely analysed by him, any investigation partially is a synthesis too. This cannot lead to truth, but only to belief, that can be more and more fixated with the ways Peirce showed. One exception, according to Kant, might be some synthetic statements a-priori, like the Categorical Imperative. This is an open question.I think, belief and truth are two different either-or-categories, so there is no percentage of truth. A hypothesis about a system the observer is part of, must be falsifiable, said Popper too. Either it is belief or truth. To apply the NOT-quantor for belief, is a fallacy. It only applies to truth. "believes that" must not be a quantor or a cut, but written between them as text, is what I think. So I, up to now, assume, that intuitionistic logic is a fallacy.Best, Helmut23. Dezember 2020 um 17:07 Uhr
"Skaggs,Steven" <s.ska...@louisville.edu>Helmut,I think I follow. You guys are clearly expert logicians, but it is easy to get so far into the weeds the way out is lost forever.Now the problem with knowledge is, to call it a classification, there cannot be knowers besides knowers-that-not about one topic.Yes. Logic can kill you. About the world we live in, we're all "believers that" and "knowers not" even if we think and say we are "knowers that”. (Where “belief” is an understanding one's prepared to act on.)Here’s how I think of it… the word “to know” is already assuming some position, from an imputed independent vantage point, outside the system. But with big questions, how do you step outside the system (reality) to make the judgement? One can never know with infallibility the state of ontology if the knower is within the system ("that what is") under consideration, right? I think that was shown by Goedel, right?In terms of logic and the big questions, don’t we live more in a state of "fuzzy logic" where things have likelihoods — percentages of truth? And then things begin to feel pretty intuitionistic.SxSOn Dec 23, 2020, at 9:05 AM, Helmut Raulien <h.raul...@gmx.de> wrote:Supplement: Interesting is the difference between belief and knowledge: The belief values (affirmation, weak, strong negation) classify three groups: Believers, non-believers, and deniers. Affirmation makes believers a class, weak negation makes non-believers and deniers one class, strong negation makes deniers a class. The knowledge values classify three groups too: Affirmation makes knowers a class, weak negation not-knowers, and strong negation knowers-that-not. With knowledge to each value is assigned one group each, while with belief, to the weak negation two groups are assigned. Now the problem with knowledge is, to call it a classification, there cannot be knowers besides knowers-that-not about one topic. About one certain object there can be only either affirmation-knowers, and weak negation-not-knowers (e.g. about the colour red), or weak-negation-not-knowers, and strong-negation-knowers-that-not (e.g. about unicorns). So, knowledge is, other than belief, in general three-valued, but for an instance two-valued. Therefore it is closer than belief related with truth, which is two-valued both in general and in the instances.List,For me it is not clear, what exactly is claimed to justify intuitionistic logic. Is it the not yet done proof, is it the weak negation, or is it habout handling concepts?If it is the not yet achieved proof, I think, that is nominalism, isnt it? And it can easily, by induction, be refuted: Nature has worked due to natural laws based on mathematic laws before these laws have been proved by humans or aliens, yet at a time before there were stars and possibility of life of e.g. mathematicians concerned with proofs. You can see that with a telescope.If it is the weak negation, I think it can be shown, that the weak negation applies to e.g. belief or knowledge, but not to existence or nonexistence, that is truth or falsity. What is true, is true throughout the whole universe, and what is not true, is false. "I don´t believe that A exists" (weak negation) is not the same as "I believe, that A does not exist" (strong negation). But there is no difference between "A is not true" and "A is false".If it is about handling concepts, the justification of intuitionstic logic would be a misunderstanding due to inaccurate language: "For atheists, God does not exist" is inaccurate. It means: "For atheists, it seems, that God does not exist". This is not existence, but belief. "For cows, the concept of the colour red does not exist" means: "Cows do not share the concept of the colour red", or "Cows don´t know the concept of the colour red". This does not mean, that the shape of a cow has got the ability to punch a hole out of the colour-concept´s existence domain, which is the universe. This example too is not about existence, but in this case about knowledge.The example I earlier gave, about somebody talking about a concept in another universe, is absurd, because information cannot travel between universes.So I wonder, what justifies intuitionistic logic.Best, Helmut
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