I just read a book on philosophical logic and it states that one cannot deny the LNC. To do so would be to claim it isn't TRUE or that it is FALSE but not both, thereby affirming the LNC.
This claim by the author seems to rest on self-reference. Applying the denial of LNC to LNC itself results in self-refutation.
Perhaps rejecting the LNC shouldn't apply to the LNC i.e. we ignore the self-reference and continue.
Can anyone clarify? Thanks. — TheMadFool
As I see it, the "law" isn't a law, but rather an earnest (in the sense of "a token of something to come; a promise or assurance.").
IOW, like the apriori generally, it simply reflects our intent to use language consistently.
We posit consistent natures for things, proceed as if things have those natures (belief=trust, expectation), and then subsequent experience of them, or of things causally connected to them, either conforms to that posited nature - or not. If experience pans out as expected, well and good, we continue to use the term consistently; if experience answers in the negative, we think up another kind of nature or essence, or modify the original, and continue.
Now it so happens that the "middle-sized furniture of the world" amidst which we've evolved has things that do in fact have consistent natures or essences through time. But we've already seen how that breaks down at the micro-level and macro-level (although we can still draw conclusions that fit the logic-obeying middle-world we live in, in terms of scientific meter readings and dial readings on equipment that's causally connected to the bizarre goings-on). — gurugeorge
I think you're barking up the wrong tree. — MindForged
The negation of "no statement is both true and false" isn't "all statements are both true and false". If at least one statement is both true and false then the law of noncontradiction is false (and only false). — Michael
And ironically, according the semantics of standard dialetheic paraconsistent logics, the LNC is a dialetheia, it's both true and false. — MindForged
Does this "middle-world" you speak of violate the LNC? — TheMadFool
↪gurugeorge I hold similar views. Logic, at least in its useful form, must conform with experience. Does this "middle-world" you speak of violate the LNC? It does not and how do we actually go about rejecting the LNC? Please read below.
That's a good point. Rejecting the LNC doesn't require that ALL statements are both true and false. Finding just one statement that is both is a good enough counterexample to the LNC. So, in a sense, rejecting LNC shouldn't be self-referential. Thank you very much.
And ironically, according the semantics of standard dialetheic paraconsistent logics, the LNC is a dialetheia, it's both true and false.
— MindForged
Can you explain that a bit. I didn't understand. Thank you.
Nothing in the microscopic world has even been suggested to have an inconsistent nature. — MindForged
Well, if you're using an explosive logic (i.e. every type of logic besides Paraconsistent logic), rejecting the LNC does require that all proposition are true and false. It's provably so. — MindForged
Another way of putting the above: it's related to what they call "interpretation" in maths. When we say "1+1=2" whether that's true or false depends on what "+" means, what "=" means and what the natures of the objects we're talking about are. — gurugeorge
Can you show me how that is implied? How do you prove it?
I don't fully understand you. However, your thoughts on ''interpretation'' make sense but doesn't really refute the LNC. If A and B both interpret ''dead'' identically then the statement ''the cat is both dead and not dead'' is a contradiction. — TheMadFool
Can you explain what Wittgenstein means by ''language game''? — TheMadFool
I don't think you can refute the LNC, because it's not a "law," it's not a thing for refuting; it's a reflection of our commitment to speak consistently (e.g. to interpret "dead" identically for A and B). What would be the sense in refuting our own commitment? How do you refute a commitment? It doesn't make sense.
That we wish to remain consistent does not entail that we can remain consistent. It's not [merely] a commitment. — MindForged
You can refute an example of inconsistency, but how do you "refute" the very commitment to remain consistent that defines reason?
(Not trying to be flip here, this is really how I see it. The LNC is on a different level from things that use the LNC. The form of it makes it look like an object-language statement - which could be consistent or inconsistent - but I think it's really a statement of intent.)
I don't think you can refute the LNC, because it's not a "law," it's not a thing for refuting; it's a reflection of our commitment to speak consistently (e.g. to interpret "dead" identically for A and B). What would be the sense in refuting our own commitment? How do you refute a commitment? It doesn't make sense. — gurugeorge
But this is also why Wittgenstein didn't entirely repudiate philosophical theory either; it's just that he thought that whereas philosophers previously had believed they were making discoveries about a deep, hidden structure to language, what they were actually doing was creating artificial, simplified language games that give insight into use, just as he does with the simple language game examples in the PI.) — gurugeorge
It's an axiom — MindForged
So Wittgenstein isn't that injurious to philosophy as I supposed. One member, I think it was Banno, said that everything is a game. I wonder if philosophical truths are more about the game rather than anything substantive. The question itself is part of the game I suppose? — TheMadFool
No it's not, that's the thing. An axiom would be something presupposed as true, or assumed as true, or necessarily implied as true. But the LNC is not a presupposition or assumption or a necessary implication of anything, it just has the form of such, which is what's misleading. But because it's not a truth claim, it's not for refuting.
For example "A = A" (which is the root of the others, which are just "corollaries" IMHO, although even saying that could be misleading) looks like you're making a truth claim about reality, like this is an assumed fact, or a discovery about reality or the world. But it's actually just setting out the rules of the game: "We will use "A" consistently."
What on earth would it mean to say that "a thing is identical with itself"? Is that an informative statement
It could perhaps be referring to the proposition 'x=x' where x is a variable symbol. Some axiomatisations of first-order predicate logic contain an axiom schema which is of that form.What on earth would it mean to say that "a thing is identical with itself"? Is that an informative statement? — gurugeorge
That is a necessary but not sufficient condition for identity, assuming that identity means the same thing as '='. All equivalence relations are reflexive, transitive and symmetric. For example 'is the same age as' is an equivalence relation. But Arjun being the same age as Helga does not make them the same person.A better definition is that identity is a reflexive, transitive and symmetric relation. — MindForged
Well I didn't say these had to be assertions about reality. These can be understood purely formally and syntactically. — MindForged
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