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So let's say I'm not a physicalist and my worldview is that there are two worlds one with the physical stuff and the other where mental events happen. One can use math to model both these worlds.

An explicit kind of example would be: Experience as an initial value problem?

Question

Is it possible for the mental world to have one set of axioms and the physical world to have another. Do these axioms need to be consistent?

Like they exist in different spaces I don't see why they can't be governed by contradictory axioms even? For example, in the world of mental events maybe not of not of x isn't x while in the physical world not of not of x is x

Mauro ALLEGRANZA
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More Anonymous
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  • If your goal is consistency, then you have reason to try to make the different sets of axioms fit together. Or you could go a semi-Kantian route and make their coherence a sort of non-issue (or another more-Kantian route where you try to find bridge principles). The more the separation, the less the specific contradiction between the sets, though. – Kristian Berry Jun 27 '23 at 02:28
  • What are "the axioms of the physical"? There axioms of the physical theories: Relativity, QM... And what those of "the mental"? – Mauro ALLEGRANZA Jun 27 '23 at 06:42
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    An example would be you can only have one experience at one moment. – More Anonymous Jun 27 '23 at 06:53
  • Can your computer be made of transistors and still run Microsoft Word? Yes. Can Word fight against the transistors? No. Can the transistors refuse to let Word run? No. – Scott Rowe Jun 27 '23 at 13:51
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    What is the goal? If the goal is to have a true Theory of Everything, then the axioms have to be consistent to be true. If the goal is to solve individual problems, then it's not clear why you would even need all physical axioms in all problem approaches to be consistent. – David Gudeman Jun 27 '23 at 14:58

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There's really-full blooded platonism which says "every mathematical theory—consistent and inconsistent alike— truly describes some part of the mathematical realm". So, abstract mathematical objects could be literally inconsistent with each other but that doesn't necessarily mean the physical and mental worlds can be inconsistent with each other, only the math we attach to them is (within RFBP). https://entailments.net/papers/fbplatonism.pdf. Maybe its just more pragmatic to have two inconsistent mathematical theories, one for the mental and one for the physical. To have the physical and mental consistent or inconsistent with each other seems more empirical and not something we are ready to rule on.

Ex, There's stuff like is the apparent mental flow of time physically objective. If there is no objective physical flow of time, then these would be good candidates for inconsistent mental-physical theories or axioms. But again this seems empirical and beyond our current grasp. Block universe proponents seem open to this idea at least.

J Kusin
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In fact, we can view most work in philosophy of mind as the byproduct of a desire to reconcile the "axiom sets".

The typical desiderata for a theory of the mental is an explanation of (a) intentionality and (b) qualia. Suppose that we conflate the axioms for a picture of the mental with these desiderata (this is not too bad, since any reasonable axiom system must take these desiderata into account). Arguments for and against physicalism can then be viewed as arguments against the consistency of (a), (b) with the physical. For example Quine 1960 claims that talk of (a) cannot be reconciled with talk about the physical and then argues that this presents the naturalist with a dilemma. Likewise Jackson 1982 purports to show that (b) is not physical then concludes with some form of dualism.

The more general thought is this: many philosophers have thought us both mental and physical beings, further that our mental states and physical environments are intimately connected. As such, a proper explanation of mind must take into account both the physical and mental, and this amounts to a consistency of both "axiom systems".

emesupap
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Is it possible for the mental world to have one set of axioms and the physical world to have another.

Not only possible, but necessary. The axioms ruling the mental realm (for example, metaphysics) are evidently different than those of the empirical realm (for example, physics). The mental realm does not need to address time and space, and the physical realm does not need to address synthetic a priori knowledge.

Do these axioms need to be consistent?

Evidently, otherwise they are isolated, and you deal with two completely separate systems of truth. At least one logical connection, providing logical consistency between both hierarchies of truth is necessary.

Like they exist in different spaces I don't see why they can't be governed by contradictory axioms even? For example, in the world of mental events maybe not of not of x isn't x while in the physical world not of not of x is x

Here, you are talking about alternative logical systems, not alternative axiomatic systems which are founded on natural Logic. When you speak about logical consistency, you imply natural/classical Logic. An statement like NOT(NOT(X)) != X implies not only a different and isolated axiomatic system, but a different and isolated system of logic.

RodolfoAP
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You don't even need to state whether you assume physicalism as your world view for this question.

Even a pure physicalist would be very used to modeling different parts of the world in different ways, with different axioms.

As an example: if a physicalist would model the behaviour of large groups of people - for example, a statistican working in an insurance company - they would work with certain models, axioms, rules and so on and forth which are tailored specifically to the domain. Even if they believe that humans can just be reduced to their atoms (nay, quarks...), they would never use the axioms ruling in the quantum world to calculate the finances of their firm. Granted, they would maybe not contradict real physical axioms, but they would be very separate; mostly having nothing much in common at all.

As a physicist (not physicalist), you would be very used to working with different models and outright contradicting axioms if you are looking at different scopes. For many areas of our daily life, the Newtonian classic mechanics are just fine, and enough to send rockets to the moon; even though we know that they are ultimately wrong. As a practical chemist, you can work and be successful all your life modeling atoms or molecules the old-fashioned Rutherford-Bohr way (which is still helpful for didactic purposes, but physically pretty much wrong), and completely ignore most if not all of quantum theory.

Modelling fluids and gasses is so utterly complicated that we don't even try - our best efforts are very very crude approximations. And still we build great vehicles that fly at many machs.

So, as even intra-physicalistically speaking it's perfectly valid or even necessary to have different axioms for the same areas of the world, very much the same must be true for your purported distinction between physical and mental; the very nature of the distinction enforces --some-- kind of difference, and that difference must lie in axioms (and rules and assumptions and so on and forth).

AnoE
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Sure

Mental objects can satisfy one set of axioms and physical ones another. There is no question of two sets of axioms being consistent with each other, if they refer to separate things.

For example there are axioms for Euclidean Geometry, which includes the parallel postulate, and axioms for elliptical geometry, which includes the negation of the very same postulate. These axioms seem to contradict each other. But on closer inspection it is revealed that all this supposed contradiction means, is that there is nothing that is simultaneously a Euclidean Geometry and a elliptical geometry.

Likewise for you. If your physical ad mental objects do not overlap, there is no risk of contradiction, no matter how different the mental and the physical axioms look from one another.

Daron
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