Verbal disputes over logic
Generally speaking, differences in logic are taken to reflect differences in metaphysics, yet they can just as easily be verbal- based on differences in exactly what we mean by the predicate “true” and other terms.
Dialetheia - true (or true*) contradictions
Let me start with the somewhat less convincing example of the pair I have in mind. Can we have a meaningful logic, that appears to be about the sort of things we talk about every day, in which sentences can be both true and false?
Generally, in logic, we work by assigning truth or falsity to fully interpreted sentences. Suppose we didn’t do that. Suppose we assigned truth and/or falsity to partially interpreted sentences. Why would we want to do this? Well, one reason is that it’s rare that sentences in natural language are fully disambiguated. Plausibly, not only do we not know exactly what a speaker meant, but there simply is no fact of the matter to decide one way or the other.
What would assigning truth values to partially interpreted sentences look like?
A statement is true* if there is a correspondence between a relevant meaning of a sentence and the world and false* if at least one of its relevant meanings fails to correspond.
Where the notion of relevance is something like "a meaning the speaker could plausibly be disambiguated as having intended on the basis of all facts”. Since some relevant meanings can correspond while others don’t, on this logic it will be possible for sentences to be both true* and false*.
Let’s use a tweaked version of one of Graham Priest’s examples- the doorway. Suppose I say: "Bob has left the room" and it just so happens that Bob is in the exact middle of the doorway. In one relevant sense of "left the room" [everything up to and including halfway through the doorway] this is true. In another relevant sense [everything up to but not including halfway through the doorway] this is false. Hence on this concept, truth*, we have a dialetheia- a statement that is both true and false- or at least true* and false*. The logic appropriate to the property truth* will thus surely need to be a paraconsistent logic- a logic in which things can be both true and false without everything becoming true and false.
Nor do I think this concept of truth is wholly artificial. This is perhaps what people mean when they say "Well it's both true and false" in ordinary conversation- ordinary people don't necessarily think in terms of fully interpreted sentences. Also, as already mentioned, it’s really hard to get fully interpreted sentences- for everyday sorts of propositions it may be impossible in practice. It wouldn’t surprise me if giving a totally complete exposition of the meaning of '‘she’s left the room’ wouldn’t be finished before being rudely interrupted by the heat death of the universe.
Footnote: Graham Priest has bought it to my attention that David Lewis makes a similar (basically the same) suggestion re: partially interpreted sentences in section three of his paper Logic for Equivocators. I am certainly not the first philosopher in history to have been beaten to an idea by David Lewis;
Fuzzy logic
Okay, so the above example depends on using partially interpreted sentences- which I think is not unreasonable for the reasons I outlined, but can we get different logics without partially interpreted sentences? I reckon so.
Something can be very red, a little red, almost red and so on. Other concepts are binary. A number is even, or it is not. Logicians usually define truth to be binary. Many logicians though have noted that you can have a perfectly respectable logic in which things can be partly true- and this might be useful for cases like a heap. You take one grain away and it’s not plausible that something suddenly ceases to be a heap, yet perhaps it is plausible that the statement “this is a heap” becomes a bit less true- a truth value of 0.74 instead of 0.75.
You can take binary concepts and make them non-binary, and you can take non-binary concepts and make them binary. For example, I can make the concept “even” subject to degrees by saying that powers of two are extra even, numbers that are multiples of 4 as well as 2 are extra even etc. I can make the concept of red binary by saying that anything between 620 to 750 nm in length is completely red, and anything outside that is completely non-red. These are just different ways of defining the terms in question, and if we encountered populations that used these terms this way, we wouldn’t necessarily say they were wrong, just that they meant something different by their words to us.
I want to suggest that the dispute over whether truth is fuzzy (non-binary) or binary is purely verbal it literally just depends on what you mean by truth. Surely for example I can define a predicate true! which is binary and a predicate true# which is fuzzy and comes in degrees. Now I guess there’s a semantic debate to be had over whether true! or true# best captures the folk concept of “truth” and there’s a debate to be had over whether true! or true# will help us get along better in understanding the world and discovering its secrets. However, debates about which account of truth is ‘right’ miss the point- each of them describes a different, perfectly real property of sentences- the property of truth# and the property of truth! Any ‘debate’ between truth# and truth! is verbal. You can choose to use either in your language at your leisure.
I’m not sure whether this position would be seen as radical or mundane by philosophers working in the area, but I think it would be a surprise to a lot of philosophers outside of it. Most philosophers seem to think something very fundamental is at stake in the debate over the law of the excluded middle and so on and so forth. If what I’ve written here is right, there isn’t. Like so many philosophical disputes, it just depends on what you mean by your terms.
Of course, there’s no ‘magic relativism’ going on here. For every notion of truth, and for every sentence (fully or partially specified as appropriate), there’s a fact of the matter about whether a statement is true, false, partly true, both true and false, neither true nor false, or something else.
Interesting. Sounds a bit like what I've read from Husserl. Of course you may think not and I could be incorrect as my knowledge is mostly passages inserted by other writers quoting Husserl. But my interpretation from such limited knowledge, is that he reflects on not so much what the literal words are, but about how the words can be interpreted, or differently interpreted. Of course Husserl wrote in German and for the life of me I find it difficult to interpret anyone I've read in German from Kant to Schleiermacher to Hegel into "logical" English. I find it extremely difficult sometimes making sense of English other than strictly literal which is probably a lack in me. I guess that's why I am partial to "inventing" adjective and adverbial forms or using existing ones in uncommon formulations because English (for me to comprehend) needs extreme preciseness. At least I need it to be precise, and my experience is that I easily misinterpret "half-sentences, etc." To tell the truth I generally write my outlines in koine (greek). I don't know quite know why, since English is my birth tongue but many an argument that I've ever witnessed is because people are actually meaning the same thing and arguing over their own imprecise interpretations that they do have substantive to argue. For instance; "Jimmy Carter had no understanding of how to make his policies understood by the American people." "Jimmy Carter was a terrible president." The first was trying to say why he thought Carter failed, but doesn't actually state a preference one way or the other for the policies. The latter stated his preference but not the why. But both agreed that Carter failed. I witnessed one shooting at the other simply out of miscomprehension of lazy and imprecise. usage of the language I, personally, am very wary of attempting to understand such impreciseness by English speakers because too often I've seen conflict arise when the interpreter of a statement may not interpret the speaker the way the speaker meant or the speaker may not interpret the interpreter's meaning of his own comment.
This may not create conflicts to the same degree in philosophical discussions of linguistics, but I can't tell you how many broken friendships I've witnessed over misinterpreting incomplete thoughts. English simply has too few inflections to be interpreted unless thoughts and statements are complete and leave as little as possible to being interpreted other than in the manner the speaker intended.
And I would think speakers would want to be precise to not be misinterpreted.
So to your illustration the man has left the room (but he's halfway in the doorway) I would be incapable of making sense of the statement he's left the room if he's halfway in the doorway. But I could make sense of man is half way through the doorway and is leaving the room.
Of course there is another way to interpret my reply---you could interpret my whine to mean that I'm on the lower end of language development skills, i.e. I'm too dumb to properly assume what they mean like all normal English speakers do.