Does logical consistency require alignment with external reality?

Question

There are scientific theories that are pseudo-consistent. That is, they are internally logically consistent when taken on their own terms, but do not align with external reality. Socionics might be an example of one such theory.

Question: does logical consistency necessarily entail correspondence with reality? That is, can an intelligent pseudoscientist hypothetically create an internally consistent theory (say, ultra relativity) that is consistent in a way that lasts forever but just so happens to not comport with objective reality? By contrapositive, is it necessary that a liar be shown to eventually, at some point to have an internal inconsistency in his own web of lies?

Answer 1

See Jan Wolenski, Truth and Consistency (Axiomathes, 2010):

The concepts of truth and consistency are very often discussed together in the context of the coherence theory of truth, perhaps the most important among nonclassical aletheiological theories. A very simple, almost straightforward argument, going back to Russell, against truth-coherentism points out that truth cannot be identified with consistency, because one might formulate a consistent story, fantastic or even fairly empirical, which is notoriously false. Consequently, although consistency is a necessary condition of truth for truth, the former does not constitute a sufficient proviso for the latter.

Only in logic, consistency ensures that there is some sort of "reality" to which the consistent theory applies; see Model Existence Theorem.

Regarding the "ethics" tag, maybe relevant: Bernard Williams, Ethical consistency.

Answer 2

>Does logical consistency necessarily entail correspondence with reality?

Absolutely not.

Logic is purely syntactic, textual. Sentences are generated from other sentences using rules of inference.

If axioms (top-level assertions) are true, then leaves on the deductive tree will be true. That's why logic was invented. But It's a subfield of mathematics. Physical reality is not the purview of logic; that's science.

Answer 3

Logical consistency has nothing to do with reality, and not much to do with truth. In logic, a theory is consistent just in case there is no proposition P such that you can infer both P and ~P from the theory. A theory can be consistent even though every one of its premises is obviously false. There are many lies that are consistent, so consistency is not a very good test to know if a theory is true or someone is telling the truth.

Answer 4

Logical consistency and alignment with reality are two different pairs of shoes. A theory which aligns with reality has to be logical consistent. But logical consistency is no proof for alignment with reality.

So, logical consistency is necessary but not sufficient for alignment with reality.

1. The number of possibilities is always much bigger than the number of facts: There are fairy tales, different myths about the basic laws of our world, science fiction, variants of virtual reality, etc.

   A simple example shows the difference between formal sciences and sciences of reality: The different axiomatized theories of Euclidean and non-Euclidean geometry. And the final application of generalized Riemannian differential geometry in the theory of general relativity.

2. Even a short survey of the different sciences shows a variety of methods. Methods which scientists have established to investigate and to check the results of their theories. In their attempt to explain the phenomena of reality.

I do not know to which degree socionics is established as a social science. Different methods apply to convict a liar of their lies, e.g., at court.

Answer 5

"Logic" is a broad enough topic that it is reasonable to talk about "logics" (such as, but hardly limited to propositional or modal). Given this enormous scope, it is actually somewhat difficult to address your question comprehensively.

Still, most logical systems are, foundationally, designed to allow us to synthesize existing knowledge and also to distill simple and general knowledge from complex aggregates of knowledge. For example, it is widely accepted that knowledge of:

((p∧q)∨(p∧¬q))∨((p∧r)∨(p∧¬r))

for (nearly) arbitrary "knowables" p, q and r is not distinct from knowledge of simply "p".

However, while logic empowers us to synthesize and distill knowledge, it does not generally provide any "starting knowledge" with which to kick off the process. We have to input this knowledge in order for logic to work, and logic is not super picky about whether this "starting knowledge" is right or not. In other words, we could invent an entire fantasy world, and logic could easily allow us to "build out" properties of our fantasy world that are consistent with the fantasy world. One example where you might want this is when writing a script for a movie: it's not important that the movie characters perfectly reflect the "real world", but it is generally important that the world and the plot be logically consistent.

OTOH, if your "starting knowledge" DOES "align with external reality", then it is generally expected that correct application of the rules of logic(s) will permit you to synthesize and distill that knowledge into "new" statements that ALSO "align with external reality". However, it turns out that which "starting knowledge" "aligns with external reality" is often subject to much debate. It may also be the case that the logic to synthesize some knowledge is too complex, and it is more convenient to simply inject more "starting knowledge" into the process. This is the case, for example, bridging the gap between physics and chemistry - in theory all of chemistry could be logically/mathematically reduced to physics, but this logical reduction is frequently more difficult than simply directly observing the chemistry and moving forward logically/mathematically from there.

tl;dr; yes and no. Logic is garbage-in garbage-out, so it all depends on what statements you adopt as premises.

Answer 6

Not at all. There are strictly more truths than proofs. Even if a system containing an unprovable truth couldn’t be constructed, it should still be trivial to make one that can’t be proved within the lifetime of our universe.

Answer 7

Question: does logical consistency necessarily entail correspondence with reality?

@Conifold's comment expresses the common sense, generally accepted answer:

Logical consistency not only does not entail correspondence with reality, necessarily or otherwise, it has nothing to do with it. Logical consistency only requires not deriving contradictions by a handful of abstract rules, that is a trifle compared to what corresponding to reality demands. An empty theory is trivially "consistent in a way that lasts forever", but reality is not empty and so does not correspond to it.

However, this answer trivializes the question and seems unsatisfactory to me. Strictly speaking, it's not entirely correct since logical consistency does not mean that so far we didn't happen to derive a contradiction, but that no contradiction can ever be derived. Given any actual, serious (so, non-empty) theory this is less easy to demonstrate (if it is possible to demonstrate it at all). Even in a non-empirical science like mathematics, in number theory, it turns out that the question "how to formalize the demand (or assertion) of consistency" has led to some disagreements between mathematicians, and to disagreement (again among mathematicians) about the philosophical interpretation of Hilbert's question and Gödel's second incompleteness proof. (See the discussion about Artemovs recent papers at mathoverflow.)

The OPs question seems to be "Given a consistent (empirical) theory -- that is, given a theory that we assume to be and remain consistent --, could this theory yet be false, could some false statement yet be derived from the theory?" In one interpretation this is a trivial question -- we all know theories that led to false predictions, even though in the application of the theory no logical errors were made. [You have to ask here: Is the application of a theory part of the theory? How or to what extent does a theory compel a particular application of it? -- Wittgenstein's rule-following paradox seems relevant here. Pierce's concept of indexical signs also.] But the more interesting interpretation seems to me: "If we assume that all premisses of the theory are true, and assume that no logical errors will be made in applying the theory (making predictions, deriving unknown facts), could the theory still be false or lead to false predictions?"

Someone may again see that question as trivial and answer: "No, of course not! That's what consistency means! If it's consistent, you cannot get a falsehood!"

But what if we interpret the deeper question as "Ok. But what is it -- in reality or what is it about reality -- that makes logical truths true? Why do we regard some logical truths as true, in particular the law of non-contradiction (LNC): A proposition (p) and its negation (¬p) cannot both be true? Why do we feel compelled to accept this?" [You could also ask, from a more pragmatic/pragmatist point of view: "Why do we or why should we care about consistency? Because we cannot not care? 'Cannot' in what sense? 'Logically cannot'? Doesn't that again lead in a circle?"]

Doesn't that law state something (anything) about reality? (It uses the predicate "true".) Or does it "only" state a "law of thought", a limitation of our thinking? Or is it both? Or perhaps, it's "merely" a linguistic relation that underlies it, stating something about the meaning of 'true' and 'assertion' and 'negation' -- it's just that we happen to use those words in those ways? (That seems to beg the question since we want to explain why we feel we cannot use those words in any other way.)

Clearly, this law involves idealizations. For example, we do accept that a man might be both not bald and bald (he still has a few hairs on his head). He is almost bald, almost ready to throw away his comb. But "almost" is a vague, ill-defined, indeterminate concept; we want to ignore those kind of concepts. (Which should make us worry a bit: What if our logical concepts also are vague? How do we know they're not?)

Platonism/Realism is sometimes described as the point of view that mathematical objects, or abstract objects (like numbers, the empty set, the set of all natural numbers, etc, including facts about them) are also real, real in a kind of separate realm. I believe that is a misleading description. The correct description is that Platonism believes that so-called abstract, idealized objects are the reality - that that is what is real. [Anything else, anything revealed by sensory perception for instance, is at most almost real, as it were.] Anyway, from a platonist/realist point of view, LNC is true because it states a fact about the world, independent of our cognition, and we discover this fact (by thinking, not by empirical investigations). We discover it either as "self-evident" -- which suggests there is no further 'why' to it -- or perhaps by reflecting back on the fact that we're thinking, and then arguing (for instance) that denying LNC would imply that everything becomes provable, so either inference or truth or both become meaningless, or by arguing (for instance) that we cannot consistently deny LNC (though this seems a circular argument). [Those arguments don't necessarily presuppose a platonist point of view, of course. Do they have more force in platonism?]

If someone adopts any view of LNC that accepts it as a somehow meaningful truth, rather than an "empty" tautology --, doesn't this imply that LNC says something about the world (including the empirical world, if we consider that world as "real")? -- In Ayer's logical positivist view it would merely be an empty tautology, true by linguistic convention, not saying anything about 'the world' (the empirical world). Wittgenstein in the Tractatus also posited logical 'truths' as mere tautologies, statements that don't say anything about 'the world'. But according to Wittgenstein tautologies (and contradictions) show something about both language (and thinking) and the world: they show the "logical form" that language (thought) and the world "must" have in common for any meaning and truth to be possible (knowable). Wittgenstein's distinction between saying and showing seems marginally better than appealing to self-evidence, but is hard to grasp. If something can only be shown, it still needs to be seen. And if seen, but unsayable, how does it really differ from an appeal to being 'self-evident' (which practically means 'showing it self as such or so')?

I realize I haven't yet answered the initial question, only raised more questions. To cut this short -- my answer so far is: "Consistency" seems to be a tricky beast. I don't know. Part of what we mean by "logical", I think, is "compelling". In philosophy we should try to dig into the meaning of what is it that makes an inference (or a truth) compelling. (And we cannot say that it's the fact that it's logical - since that's what we're trying to explain and dig into.)

Answer 8

Him's answer correctly points out that there is more than one "logic"; I put the word in quotes here because you probably meant the classic binary logic in which propositions are either true or false.

With this logic it is obvious (to me) that one can build systems of propositions, based on arbitrary axioms, — theories, if you want — which are consistent but are not "aligned" with reality. The propositions may be very abstract, unverifiable or simply "false" with respect to the reality we perceive; nonetheless, we can play a "what if" game and build a consistent theory on top of them. Modern-ish mathematics seems to be a field which falls in the category of "very abstract" axioms which do not have a strong relation to the material world.

But there is a more fundamental issue with classic, binary logic: It is heavily influenced by — indeed is an abstraction of — the world we perceive. There is a chair in this room or not; somebody is dead or alive; I'm in Berlin or I'm in America; something happened before or after something else.¹ Notably, this "intuitive" logic has emerged as an abstraction of the rules we observe in the macroscopic world. You guess what's coming: This is not the entire picture, or rather fundamentally mistaken, if one looks closely at the microscopic level. Things can be there and at the same time somewhere else; the cat can be dead and at the same time alive, etc. This "logic" about which you are inquiring is contingent; it is a choice. There are other, different "logics" which would lead to very different theories.² For example, a logic based on quantum theory would not be binary but would be based on probabilities.

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_{¹ More diligent scrutiny will find that most trivial-sounding propositions have at least a natural language problem (U.S. or the continent? Where does this room end?) and often a reality problem (dying is a gradual process with a grey zone during which it is impossible to draw a finite line). Whether the reality problem is in fact a language problem which can be solved by speaking more exactly ("I mean brain dead") is not clear; I think not.}

_{² I like the premise of the book and movie Arrival in this respect; the idea that there may be an entire different "angle" of looking at the world.}