It's about the number of correct logics (i.e. logics that ensure true conclusions follow from true premises). In general, it's a position about applied logic, which is why monists and pluralists often justify their demarcation of correct logic(s) in terms of natural language, scientific discourse, etc. Nihlism would, by contrast, say there are no correct logics (and also no incorrect ones). This is not to say that reasoning is entirely arbitrary, presumably there are some standards for what constitutes appropriate reasoning. But there is no logical consequence relationship that is appropriate or correct for any particular topic. So, for instance, the intuitionist and his rival in mathematics are both wrong in that neither are "right." — Count Timothy von Icarus
I'm not sure I'd go as far as to say "correct" in describing a logic. What would it possibly mean for a logic to be correct in a non-question begging way? "Correct" seems to already presume some standards of coherency, and I'd say validity is a species of coherency.
That is, we'd be presuming some logic in setting out the correct logic. Now if there were only one logic that would at least be consistent, but then we get to the part on begging the question -- which, I think, is why the puzzle is interesting: Either answer can be made self-consistent (monism or pluralism), but in what sense can the two camps speak to one another?
You could think of this as similar to how there are very many geometries, and unfathomably many possible ones. One can identify what "follows" from their axioms according to whatever logical consequence relationship one cares to use, but this doesn't necessitate that the geometry of the physical world is infinitely variable or that it lacks any "correct" geometries. We tend to think that there would be just one geometry for physics (at least physicists normally do), or that, if there were many, there would be morphisms between them. The claims of the monist in particular are roughly analagous to the claims of the physicist re geometry. For instance, when Gisin recommends intuitionist mathematics for quantum mechanics, he does not mean to suggest that this is merely interesting or useful, but that it in some way better conforms to physics itself in ens reale, not just ens rationis.
[/quote]
Can you fill out this analogy?
Geometry:Physics :: Logic:D
What takes the place of "D" here? I understand the relation between geometry and physics, but also by the time we're talking geometry and physics it seems a logic, an epistemology, an ontology are already in play for the purposes of producing knowledge -- Also I'm not sure that the analogy serves the monist very well because geometers do geometry outside of the bounds of physics, and so we'd presume the same would hold for the logicians?
Normally it gets framed in terms of the entailment relationship. This avoids unhelpful "counterexamples," like competing geometries that use some different axioms, but nonetheless have the same underlying entailment relationship. These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions." This is why monists might also allow for multiple logics that are "correct," the "correct logic" being more a "weakest true logic." — Count Timothy von Icarus
I'm not sure the entailment relationship ends up being any more stable than the LNC or the principle of explosion. Pick your hinge and flip it!
When you say
These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions."
There's a quibble I feel that may indicate some miscommunication (or not, we'll see).
The question for logic, IMO, is
not "How does one move from true premises to true conclusions?" -- I'd say that's a question for epistemology more broadly -- but rather logic is the study of validity. The big difference here from even introductory logic books is that the truth of the premises aren't relevant, which I'm sure you know already -- the moon being made of green cheese and all that.
So we don't care if the premises are true or not. We only care that
if they are true, due to the form of inferences, that the conclusion
must be true.
Do you see a difference between the questions?
I'd say your question asks for evidence or rationation, whereas the study of validity will depend upon how we define our logic.\
I don't think Hegel is really a good example here because the Absolute is the whole process of its coming into being, in which contradiction is resolved, and contradictions contain their own resolution. It's examples of contradiction, being's collapse into nothing, etc. are very much unlike the standard examples meant to define dialetheism. — Count Timothy von Icarus
Just to be clear, and I have not been so sorry, I'm not presenting Hegel as a dialetheist, but rather as a philosopher that uses contradiction in his reasoning -- since the conclusion to a contradiction is not "Meaningless" or "simply false" it strikes me as different from the older assumption of the LNC.
Also, you've mentioned it but, what makes Hegel an interesting case is his simultaneous acceptance and modification to the LNC. He accepts the LNC in its own context (i.e. outside of time), but when time gets involved he introduces a new inference -- sublation -- to manage the contradictions of becoming.
This isn't to say that he's a pluralist, either. I agree that if Hegel were anything that "monist" makes sense. It's only to say that in order for us to make sense of Hegel we have to be able to evaluate contradictions without rejecting them out of hand, and so at least the logic which makes sense of Hegel must reject the LNC.