Which is not surprising, as the Logic Of All And Only Universal Principles would need to have its laws apply in complete generality, and thus talk about every other logical apparatus in existence.
Logical Monism holds that there is only one correct or true logic, meaning that a single set of logical rules or principles governs valid reasoning universally. Proponents believe that this one logic captures the essence of valid inference across all contexts. [Note, books making the case for monism I have seen generally focus on applied logic as the target for their argument. The analogy here would be the difference between trying to identify the physical geometry of the world versus the purely mathematical consideration of very many geometries.]
Logical Pluralism asserts that more than one logic can be correct, depending on the context or purpose. Different logical systems may be valid for different kinds of reasoning (e.g., classical logic for everyday reasoning, but other logics like intuitionistic or relevance logic in specialized cases). [The most common historical example here I can think of is the claim, arguably in Aristotle, that the Law of the Excluded Middle does not apply to statements about the future].
Logical Nihilism denies that there is any objective or true logic at all. It suggests that no logical system accurately captures reasoning or inference, and that the concept of "correct" logic may be meaningless or arbitrary. [Or, one way to put this more specifically, as Russell points out in a footnote, is idea that the logical consequence relationship in natural language (and so arguably scientific discourse as well) is actually empty. Of course, the nihilist may also recommended other ways to retrieve the concept of a "correct logic" as well.]
That's on the mark. appears to think this amounts to nihilism. It doesn't. Nihilism would have it that there are no laws of logic, that logic is at best a rhetorical device. That is not what Russell, or I think, @Clearbury, is claiming.So, if it turns out that all proposed logical laws have exceptions, it doesn’t mean there are no laws of logic—only that they are more specific than we once thought. — Clearbury
Indeed, any logician will be aware that there are various logical systems.
Yes, which maybe should make you question if you have any clue what the debate is about. — Count Timothy von Icarus
However I do remember someone asking whether there were any logical laws that applied to all forms of logic. How about validity and consistency? Or which is basically the same as far as I can tell—the law of non-contradiction? — Janus
I'm a defender of dialetheism, thus far.
Which rules out the LNC. — Moliere
My point was that within any valid logical argument of whatever stripe there must be consistency between the premises and the conclusion. If a premise contradicts another premise or the conclusion then the argument cannot be valid. That sort of thing. — Janus
Can you explain how dialetheism rules out the LNC? — Janus
A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true. If falsity is assumed to be the truth of negation, a dialetheia is a sentence which is both true and false.
A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true. If falsity is assumed to be the truth of negation, a dialetheia is a sentence which is both true and false.
Can you think of any examples of a sentence wherein both A and not-A are true in the same sense or context? For example I could be said to be both old or tall and not old or tall but not in the same senses or contexts. — Janus
M'kay. Then my example would not convince you of dialetheism, and at this point in the debate I'd ask -- if dialetheism were somehow justified would that then justify logical pluralism? — Moliere
Then presumably you conclude that paraconsistent logic is not logic proper? And isn’t the liar in ordinary language? — Banno
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.