Preamble: although I believe in the LNC for Aristotelian/Quinean reasons and the argument from explosions to boot, and am not altogether adept at modal logic in general, much less counterpossible reasoning in particular, I am also enough of a logical pluralist to at least want to explore not only paraconsistent but outright dialethic options in philosophical analysis. My main hassle is trying to block the "inference" from, "Some contradictions are true," to, "Every contradiction could be true." If, "But that's inconsistent," is no longer sufficient to invalidate a claim, how would I gainsay anyone who wishes to start out from their preferred contradiction, to reach whatever relevant conclusion? My working "hypothesis" is to countenance contradictions derived from independent premises, but not quite contradictory premises themselves (at least, not on an "axiomatic" level). For example, general relativity and quantum field theory might be construed as individually consistent but jointly inconsistent, so I might be justified in inferring a scientific dialetheia from their juxtaposition. And I would hope to be able to perform a similar maneuver with respect to the question of free will.

Some definitions: in honor of the mathematical tradition of dividing descriptions into "strong" and "weak" forms, let us say that incompatibilist free will is strong free will. Now, a commonplace objection to strong free will is a claim that random and nonrandom determination exhaust the conceptual options, here, such that strong free will would amount to randomness, which is supposed to be "unfree" owing to considerations of intentionality. However, it seems possible that the family of concepts at issue subdivides into at least three categories: strict determination, chance, and randomness. But I see no absolute reason to stop at three subdivisions and would ask after the possibility that strong free will is actually a fourth sui generis such category. At any rate, for present purposes, I will waive the random-willings problem as illusory or shallow.

Question: suppose that there might be such things as dialethic machines, and so that quantum computers were a potential example of such machinery. Now, although quantum indeterminism does not strictly imply the precise form of indeterminism that plays into strong free will, nevertheless (and especially with respect to strong "consciousness causing collapse" interpretations of wave functions), there seems like there might be a sort of road from the one indeterminism to the other, at least if we're driving a certain vehicle down said road. Moreover, suppose that strong free will itself exists inconsistently: that is, it is dialethically true that (A) all macroscopic actions are rigidly caused by prior conditions and (B) some macroscopic actions are not rigidly caused by prior conditions. Perhaps the subcoherent essence of strong free will on one level is what makes it possible on another in the first place (as though subcoherent causes are what have subcoherent effects). My question, then, is as to how we might model a neuromorphic quantum computer, in terms of a dialethic quantum computer, so that we have an intentional (because neurological/mental) computation system that situates strong free will?

I doubt there's any detailed, established literature that attempts as of yet to answer to this question directly, but so I am at least asking after paraconsistent/dialethic approaches to the question of strong free will more broadly. EDITIf I remember correctly, Graham Priest has said somewhere that paraconsistency theory arguably allows for a more one-world/standpoint solution to the Kantian antinomies than Kant's solutions (as distributed over two worlds/standpoints). Seeing as the third such antinomy is the one concerning determinism and free will, it might follow that... Yet I don't know the details of Priest's proposal on this score, if he has gone into them anywhere (or, then, if he's just floated the idea)./EDIT

  • IMHO QM can't be a justification for free will however sophisticated the argument. A quantic event might not be entirely constrained by initial conditions (and consequently "free") but for it to express will, there must be a willing entity who decided the outcome of the event ("the particle will collapse to this state rather than another, so that I go left and not right"). Now we are back at square one: how was this decision taken? QM just push the problem further away but does not address it, because in the end it is still a "and then, a miracle happens" type of solution.
    – armand
    Jul 7, 2022 at 9:42
  • You might not see objects or events as causes, but hard free will is the idea that someone (whatever that is) is the efficient cause of an action. I don't think it makes sense either, but if you want to discuss the issue of hard (or libertarian) free will you have to do it under its paradigm, otherwise you are not addressing the idea you claim to be addressing. It's akin to bring up miracles in a physics discussion: the paradigm is methodological naturalism, so miracles have nothing to do there.
    – armand
    Jul 7, 2022 at 23:41
  • However you consider causation is irrelevant because libertarian free will is agnostic as to what exactly is causation. It just says that our decisions are not constrained by the natural flow of events. If we can't escape this flow, its compatibilism. Not agent causal free will is also just compatibilism. If the agents are not cause of their actions, they don't have libertarian free will. There is no concept of libertarian free will that is not supernatural, it would be self contradictory. Any natural concept of free will is compatibilist.
    – armand
    Jul 8, 2022 at 1:24
  • When I see non sense I just point it out. If agents are not the cause of their action it's not free will. Maybe you misunderstood the Sep article.
    – armand
    Jul 8, 2022 at 1:33
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    I have deleted my comments here because I realized that this subdebate is not being conducted in good faith. I was told that my account of free will was outside the incompatibilist paradigm; I proved that it was not; and then the responses switched to some other critique, one waived in the OP regardless. I see no point in helping people grind their own axes when I went out of my way to avoid dogmatism in the OP. Jul 8, 2022 at 14:28

1 Answer 1


SUMMARY -- I don't have references for you for whether a dialethic quantum computer could model, approximate, emulate, or achieve free will

What I can offer is a reasoning path that brings rationalism and analyticity into doubt, and which endorses pragmatism. And notes how pragmatism allows for accepting incompatible causation and free will models simultaneously, through tolerance for cognitive dissonance.

Whether cognitive dissonance can be coded through using features of a dialethic quantum computer -- that will have to be further research.

Pluralism breaks rationalism

The first hint I had that rationalism is a doomed project was when I explored alternative ethics thinking to utilitarianism. Utilitarians face an apparently insurmountable calculation challenge -- future effects are impossible to predict, and spin-off effects can be VERY significant, plus the challenge of weighting welfare, and summing over the future vs the present, and for communities vs individuals, lead to no unique "utilitarian calculus", and all being impossible to ever perform.

But Rights ethics presented even worse problems. And this, I realized, was because rights were plural. Multiple rights lead intrinsically to conflicts between rights, and the need to make rights less than absolute -- which produces an indeterminate problem even worse than that faced by utilitarians. By extension -- the legal code, which is constantly growing as individual judges try to reconcile conflicting laws -- is likewise in a situation of congenital indeterminacy, and always subject to logic explosion.

I believe this is intrinsic to a pluralist reference base. As you note, physical reduction itself is subject to logic problems, due to the incompatibility of QM and relativity. And not all of physics is even reducible to those two subjects, as several aspects of solid state physics appear to be emergent, not reducible. Which leads to further pluralist reference logic problems.

Note also, the SEP article on scientific reduction admits taht philosophers of science have abandoned strong reduction, and "the unity of sciences" as a program, basically at the turn of the millennia. See section 5. https://plato.stanford.edu/entries/scientific-reduction/ So -- physics is pluralist, and science is pluralist, and both can reach different conclusions in the same circumstance, when starting reasoning from different starting reference points. And sometimes one reference is wrong when they are tested against each other, and sometimes the other.

Plus, almost everyone in academia at least has abandoned scientism -- the view that science is the only way to gain valid knowledge. So there are valid NON-scientific ways to gain knowledge of our world. Pluralism, and logical incoherence, seem to be intrinsic to our world model -- and by the indirect realist inference that is central to science -- to our world.

Additionally -- logic itself is plural. My first realization of this was when I realized that methodological naturalism reasoning operates off a four state logic not the two state of classical logic (sufficiently supported to be taken as valid, sufficiently refuted to be taken as not valid, still indeterminate, and incoherent/irresolvable and therefore "not even wrong" question). Logicians have, also with the turn of the millennia, now wholesale abandoned the belief in a "one true logic", in favor of logical pluralism. https://www.cambridge.org/core/journals/think/article/abs/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877 Without "one true logic" and in the face of pluralism, rationalism as a knowledge method looks to be unsustainable.

Along the way, I also realized analyticity -- the use of careful definition-based reasoning to solve philosophic problems, was also invalid. The first key insights was in Quine's "Two Dogmas of Empiricism", where he showed that NO language can ever have sufficiently precise shared definitions to support analytic reasoning. The other was in Popper's detailing of the scientific method, in which exploration, idea development, and guided exploration precede even the first hypothesis forming, and his treatment of definitions as hypotheses. IE definitions FOLLOW the first several stages of science. Popper also locates philosophy as the parent of sciences, hence philosophy is in the stage where even subjects of inquiry are in dispute conceptually -- it is therefore even more inappropriate to start with definitions in philosophy than it is in the early stages of science.

Pragmatism as path forward

Pragmatism offers an alternative philosophic framework to rationalism, and supports pluralist reality. The key feature of pragmatism is its abandonment of "truth" as something that is singular. Sciences, and in even more so engineering, are VERY pragmatic. There are alternative methods of calculating most problems in engineering, but some are more useful in one domain than another. So good engineers work with a sute of potential starting points, and when one isn't sure which is more valid for a problem -- the solution is to design to satisfy ALL of them!

Cognitive dissonance is the human skill of maintaining incompatible reference frameworks simultaneously. I note in this PhilSE answer, how cognitive dissonance relative to free will v. determinism, is successfully maintained even among Illusionist advocates: If Free Will Is Proven Illusory, Is There a Case for Suppressing the Finding?

Your embrace of para-consistent logic is an embrace of pragmatism, and no "one truth".

Objections to your assumptions

BUT -- your continued search for "one true paraconsistent logic", and pursuit of logic itself -- are not consistent with the critiques of rationalism and universal pluralism above. Logic needs definitions, and definitions have failings noted above, plus A=A is not true of any object in our world (objects change logically over time).

Also, your example of a paraconsistent problem for free will and determinism uses two stage logic, and any science-consistent paraconsistent logic will have to be at least a 4 stage logic. Based on logical pluralism, if you want a universal paraconsistent logic, it will have to be an N-stage, universally generalizable logic. And my suspicion is that it will not be possible to make a consistent universal "one true" N-stage paraconsistent logic.

Meanwhile, you assume in your paraconsistent example problem that all macro scale events are deterministic. That this is not so is explained in this PhilSE answer: Is it the incorrect assumption of an "a priori determined universe", which creates the paradox of determinism versus free will? Our world is not determinist at the macro scale. Macro scale determinism is a useful APROXIMATION to the world, but is not logically universal.

Implicit in some of your discussion is the inference from causation, to determinism. This is a natural inference, and I consider it logically valid under the "one true" classical logic paradigm. However, I also note that causation suffers from definitional ambiguity. this was the central premise of a question I asked my philosophy cafe recently: https://www.meetup.com/philosophy-cafe-central-maryland/events/klgqtsydckbbc/ The indeterminacy of definition of free will has been a major objection to libertarian free will among rationalists, but causation suffers from the same problem, though to a lesser degree.

A final objection is that I have outlined multiple cases of logical indeterminacy in our world -- and quantum mechanics is only one of multiple such cases. There is no good reason to infer that free will and determinism are coupled with quantum indeterminacy. There are so many intrinsic logical indeterminacies to our universe, that it is far more reasonable to think that indeterminacy is intrinsic, and any coupling between indeterminacies is possible, but far from necessary.

Path Forward?

For me, I have just accepted pragmatism and pluralism. Causation is a super useful assumption, despite our definitional issues, and the indeterminacy of our world. And Free Will is also a super useful assumption, as it seems to be intrinsic to selfhood, agency, and consciousness.

Could you reconcile these two with paraconsistent logic? Possibly. It seems like an interesting, and possibly fruitful program of investigation in the logic field.

Could computers approximate, emulate, or instantiate free will if they do paraconsistent logic using dialethic quantum computing? I think the first two are likely, and the last is unlikely, but possible. I DO think that computing with paraconsistent logic has a lot of potential to be more applicable to our paraconsistent world, and that a logic system that can sustain cognitive dissonance will be essential to approximate human thinking. it seems like an interesting, and potentially fruitful project. But will it get to free willing, or to consciousness? Unlikely, but at least plausible.

  • I appreciate the effort that went into this answer, but it also seems to (ironically) present pluralism very dogmatically. In a MathOverflow question about deontic pluralism, I mentioned the logical peril of self-defeating pluralisms, which I locally tried to avoid by casting plural rationality as permission-based rather than obligation-based. But so case-in-point: as a logical pluralist, I accept 2-valued and higher-valued logics, to some extent. Jul 9, 2022 at 18:15
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    @KristianBerry — Thanks. I considered your question interesting enough to deserve a response. I tried to outline the reasoning and evidences that convinced me to embrace pluralism recently, after a lifetime of mostly being a tentavist Popperian. I was surprised you found that dogmatic.
    – Dcleve
    Jul 10, 2022 at 1:31
  • The content of your answer is strongly pluralistic; it's the syntax/style that presents more dogmatically. At any rate, the argument from general subcoherence to the possibility of strong free will is better than my mere evocation of quantum indeterminacy, so this answer is a good candidate (albeit the only one as yet) for acceptance. Jul 10, 2022 at 1:35
  • We humans have a strong tendency to leap to universalizing valid local observations. We also incline toward confirmation bias (dismiss evidences that conflict with a universal we want to be true), and worse, toward intellectual totalitarianism (disparage the narratives and their advocates based on the dismissed evidence). Accepting intrinsic pluralism helps inoculate against these inclinations. I see that as a tremendous good.
    – Dcleve
    Jul 10, 2022 at 13:31
  • @KristianBerry Plural and therefore in combination subcoherent valid reference frames IS my justification for accepting both causation and free will. I had not realized that your question was intended to probe for weaknesses in the quantum analogy justification. I consider the quantum analogy a dead end because probabilistic is as incompatible with “willed” as determined is.
    – Dcleve
    Jul 10, 2022 at 13:39

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