Does logical pluralism imply conceptual pluralism?

Question

By "conceptual pluralism," I mean something like, "Multiple conceptual analyses of the same concept are true." The example for the sake of which this question occurred to me is the concept of free will: if there are multiple "correct" logics of action and modality, say, does this imply that there are multiple "correct" definitions of free will, ranging from some stripe of compatibilism all the way to some of the more fantastical versions of libertarianism (not the most outlandish, of course, if such there be; to fend off retorsion problems, we eschew unrestricted pluralism in whichever direction)?

But we could also ask, then, if there are multiple "correct" analyses of lexical concepts like SUBSTANCE, PROPERTIES, GOOD, RIGHT, FACTS, EVIDENCE, etc. All the way, I suppose, to CONCEPTS or even CONCEPTUAL ANALYSIS itself. For example, John Rawls seems to prefer a method of analysis-unto-replacement, i.e. he seeks to replace an unclear concept of rightness with a much clearer concept of "according to the principles of the original position." But we could also accept, then, as pluralists, that Russellian or Fregean analysis are justifiable, as are Socratic or Wittgensteinian alternatives, etc.

Can conceptual pluralism in general be justified by logical pluralism "beforehand," or is the former justified regardless of the justification of the latter?

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EDIT: apparently this phrase "conceptual pluralism" is not at all new (who'd have thought! well, I should have thought that it wasn't new...). Here's a screenshot of a Google search with results for precisely the juxtaposition I am asking about:

Also Levy[22] appears to be a recent approach by a computer scientist/mathematician to mathematical pluralism, with some emphasis on negative caveats in this connection, though adapting his analysis to my question would take some effort, so far as I have been able to tell at this point.

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CLARIFICATION:

I'm envisioning an argument, here, with an air of paradox to it:

1. Logical pluralism implies pluralism about the lexical concept CONCEPTS.
2. Pluralism about CONCEPTS implies conceptual pluralism.
3. Therefore, logical pluralism implies conceptual pluralism.

However, if logical pluralism allows that the word "implies" can sustain multiple "correct" meanings even so, then is there not a version of "implies" according to which (1) through (3) is not valid?

Answer 1

You ask:

Does logical pluralism imply conceptual pluralism?

A resounding yes. Logical pluralism is a type of conceptual pluralism. Logic and concept are not orthogonal to each other because logic is a both type of concept and is also meta-conceptual when it is used in a meta-language to generate an object language. Let us assume a concept is ideation-adjacent-to-language and logic is a series of constraints about ideation. This is best explained by example.

Logical Pluralism as a Constraint on Conceptualization

The sorites paradox is a problem for the Ancient Greeks. Why? Because there is a logic built into the scenario: the law of the excluded middle. Either a thing is a heap or it is not a heap. Of course today, the resolution is simple, even if our intuitions are not entirely satisfied: graded membership. We can simply say that a grain of sand is a heap of one grain, and that the degree we have a heap is simply indicated by the number of grains. If we have a domain of discourse of 100 grains, then a heap has a measure from 1 to 100. The contradiction goes away, though we are left with the counterintuitive stipulation of apparent surd beings like a no-heap (heap₀), a grain is a heap (heap₁), un-heap-like heaps (heap₁, heap₂, ...), and fuzzy limits of heap (a true heap is visually detected between heap_m to heap_n).

The lesson is that if I accept only the LEM, then I have only the paradox. But if I accept classical AND fuzzy logic (now, I'm a logical pluralist), then I have the problem AND the dissolution. But something extra comes with admitting the two systems of logic into my logical ontology. I now have two theories or concepts of paradox itself! (Now, I'm a conceptual pluralist with two metaphysical positions.)

In the first notion case, the case of the Ancient Greeks, it was a perplexing challenge to reality itself! There are heaps without boundaries! But heaps visually have boundaries, so how can we not use words to capture their essence? Perhaps reality is broken! This of course is characteristic of Ancient Greek scientific ignorance when held up to our modern naturalized epistemology. Another example are Zeno's paradoxes which threatened the existence of motion.

In the second case, let us call the post-modern case, we are no longer perplexed by moving through a door with an infinite number of halfway points. Turns out that an infinite number of something need not itself have an infinite measure. That's a tough sell before Leibniz and Newton, but standard high school mathematics these days. And so too with categorization with heaps. We simply admit that we have multiple models of logic, and then we can make boundaries simple by admitting that boundaries on concepts are normative in some sense. We can even implement fuzzy logic on computers: the Japanese created a revolution in appliances by doing so. A fuzzy logic controller decides when water is dirty and not, which is the same as deciding when grains of sands are heaps or not. Vague predicates can be articulated.

This question is a pons asinorum if you think about it. There are a number of regular contributors on this site who reject logical pluralism and don't learn the lesson that Russell and others teach. They stick to their position. There's one true reality with one true logic and one true set of concepts and one true sets of senses and references. And then there are regular contributors who understand the normativity inherent in logic, and that normativity infects language and concept and theory.

The logical positivists were of the first sort trying to defend objectivity of logic and observation, and they ran right into the wall of theory-laddeness and underdetermination with their programme. Later thinkers like Brouwer (math), Quine (logic), Kuhn (history), and Sellars (epistemology) see the writing on the wall. That allowing for logical pluralism to inhere to natural language, one is no longer trying to find THE theory, but trying to find a BEST theory. Thus, we move from a simple correspondent notion of the construction of language and theory to a series of methodologies for constructing various languages and theories whose adequacy must be determined.

This is, of course, is unsettling to dogmatists of all stripes because what it says is that realism has limits, and those limits are circumscriptions of incompleteness, underdetermination, non-determinism, induction, and pragmatism. These are the hallmarks of fallibilism, and you can take what you will from the psychological implications of living uncertainly in an uncertain world and use it to impute motives of others.

Answer 2

Does logical pluralism imply conceptual pluralism?

What could "imply" possibly mean in the context of logical pluralism?

What concept of "imply" should a logical pluralist have in mind?

The idea of logical pluralism is logically inconsistent.

I guess you have your answer.

Answer 3

Sometimes there are multiple ways to understand a concept and sometimes there is only one. Also sometime a concept is understood as analog and sometimes it is digital. For example consciousness can be defined in multiple ways. One or more factors involving feelings , perceptions , choices , verbal communications with no physical attribute etc can constitute consciousness. You can approach consciousness from feelings point of view. Those with good , bad or neutral feelings can be called conscious. Or you can approach consciousness from choices point of view. Or you can approach consciousness from perceptions point of view.

Reality as a concept can also be approached from various point of views. A fish or crocodile has a different view of reality than a lion or a pig. Their conceptual understanding will be different.