Sunday, March 18, 2018

Mental States are Causally Irrelevant on Naturalism (p. 4)

Home > Philosophy > Metaphysics
  1. Problems for Naturalism
  2. Why Mental States are Causally Irrelevant on Naturalism
  3. The Symbolic Logic
  4. Proving It
  5. The Argument is Sound, but So What?

Proving It



Some propositional variables I will use in the proof:

I = The initial physical conditions hold.
O = The physical outcome will occur.
L = In the absence of supernatural intervention, given the initial conditions I, outcome O will occur.
N = Naturalism is true (and thus there is no supernatural intervention).


L, I, and O are merely placeholders, but to illustrate what the symbols mean, our laws L and initial physical conditions I might be such that the universe contains only two human beings (whom we can name Alice and Bob) and the laws dictate that the physical properties of this universe are such that Alice and Bob will go get a drink of water (in the absence of supernatural intervention), in which case O will include the state of affairs Alice and Bob will go get a drink of water.

By definition, the laws L say that given the initial physical conditions I physical outcome O will occur in the absence of supernatural intervention—and naturalism by definition says there is no supernatural intervention. Thus, N ∧ L ∧ I being true with O being false is as self-contradictory as a married bachelor. N ∧ L ∧ I entails O. In symbolic logic:
  1. □((N ∧ L ∧ I) → O)
Certain mental state associations to the physical world that sound crazy are nonetheless logically possible. For example, it is not self-contradictory that mental states are associated with individual electrons. We can conceive of a world with physical properties and physical laws identical to our own but with wildly different mental state associations; e.g. the only things that have mental states are individual electrons and nothing else. Let M2 be a placeholder for some set of mental state associations one wouldn’t naturally expect for our universe; e.g. Alice and Bob’s mental states yielding the belief that they don’t want to drink water, or only individual electrons having mental states. The mental state associations in M2 doesn’t have to be something that could actually happen (in the sense of being metaphysically possible), just logically possible. We can symbolize, “On naturalism, it is logically possible for the physical state L ∧ I to have a different set of mental states in M2 associated with that state” as this:
  1. ◊(M2 ∧ N ∧ L ∧ I)
The proof will show that the following is a deductively valid argument:
  1. □((N ∧ L ∧ I) → O)
  2. ◊(M2 ∧ N ∧ L ∧ I)

  1. Therefore, (M2 ∧ N ∧ L ∧ I) □→ O
Since M2 is merely a placeholder for some different set of mental states associated with the physical state, we can plug-in all sorts of different mental state association sets into M2, and the conclusion becomes tantamount to “On naturalism, the following is true: If a physical state had any different set of mental states associated with it, the same outcome in the physical world (e.g. one’s behavior) would result.”[5] Thus, on naturalism mental states would be causally irrelevant if premises (1) and (2) are true.

Because the type of possibility used in premise (2) is logical possibility this deflates some would-be objections. One objection is that it’s metaphysically impossible for a given brain state to have a different mental state. If I were a naturalist, while I would believe that there’s some kind of quasi-physical necessity in brain states determining mental states, to me it seems too easy to imagine the arrangement and movement of particles in the brain giving a different mental state, and the claim that there is no metaphysically possible world in which brain states determine different mental states seems no more plausible than it being metaphysically impossible to have different physical laws. Even so, it doesn’t really matter for our argument; even if it were metaphysically impossible to have different mental state associations, it is still conceivable for different mental states to be associated with the same brain state, and so premise (2) remains true. We can still reasonably imagine what would happen if the same physical state had a different set of mental states associated with it.

Another objection is that mental states just are brain states; in philosophical parlance, one would say that mental states are identical to brain states. Even if I were a naturalist I would not find this plausible; it would seem more likely to me that mental states are an emergent property of brain states rather than being identical to them (think of how wetness emerges from water molecules even though no individual water molecule is wet), at least in part because it’s too easy to imagine a different mental state emerging from the arrangement and movement of particles in the brain. Even so, it doesn’t matter for our argument. Even if brain states were identical to mental states, it is nonetheless conceivable for brain states to be identical to different mental states; even if metaphysically impossible, there’s no self-contradiction, just as there is no self-contradiction in only individual electrons having mental states. So premise (2) remains true.

Without further ado, here’s the proof:
  1. □((N ∧ L ∧ I) → O)
  2. ◊(M2 ∧ N ∧ L ∧ I)

    1. (N ∧ L ∧ I) → O 1, T-reiteration
    2. M2 ∧ N ∧ L ∧ I conditional proof assumption
      1. N ∧ L ∧ I 4, simplification
      2. O 3, 5 modus ponens
    1. (M2 ∧ N ∧ L ∧ I) → O 4-6, conditional proof
  1. □((M2 ∧ N ∧ L ∧ I) → O) 3-7, necessity introduction
  2. (M2 ∧ N ∧ L ∧ I) □→ O 2, 8, non-vacuous counterfactual introduction
If the symbolic logic argument is sound (i.e. valid with all true premises), mental states are causally irrelevant on naturalism in the way I described: on naturalism (N), if the physical state (L ∧ I) had any other conceivable set of mental states associated with that physical state (M2), the physical outcome would have been the same (O).

Still, one can accept that the argument is sound and still have other objections; e.g. am I simply using an idiosyncratic definition of “causal irrelevance”? Does mental states being causally irrelevant on naturalism in the way the symbolic logic describes pose any real problem for naturalism?

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[5] To simplify things I didn’t make this point explicit in the symbolic logic, but I could have using something called predicate logic. So consider this a bonus section for those who want to see a predicate logic version of the proof.

To give an example of predicate logic, consider the following symbolization key:

Bx = x is a Bachelor.
Ux = x is Unmarried.


The letters B and M in these examples are predicates which say something about the element they are predicating. The symbol; ∀ means “For All” or “For Any” such that the following basically means “All bachelors are unmarried:”

universal quantification
 
In English In Symbolic Logic
For any x: [if x is B, then x is U] ∀x[Bx → Ux]


The domain of discourse is the set of things we’re talking about when we make statements like ∀x[Bx → Ux], such that the “∀x” means “For any x in the domain of discourse (i.e. set of things we’re talking about here).” We can let an individual lowercase letter signify a specific element in our domain of discourse; e.g. c can signify a guy named “Charles” and we can let Bc to signify c is B (i.e. Charles is a bachelor).

A rule of predicate logic called Universal Instantiation allows us to instantiate a universal quantification (a ∀x[...] statement) for a specific individual, like so:
  1. ∀x[Bx → Ux]
  2. Bc

  1. Bc → Uc 1, universal instantiation
  2. Uc 2, 3, modus ponens
There’s a somewhat complicated rule called universal generalization (also called universal introduction) to get a universal quantification statement. Roughly, the idea is that if a statement contains some variable that is a placeholder for anything in the domain of discourse, we can generalize this to get “For any x, such-and-such holds true.” Part of the reason I went for a simplified version of the proof was that the universal generalization rule is fairly complicated (you can only use it under certain specified conditions) and the symbolic logic explanation page was getting a bit long already. At any rate, here’s the predicate logic version of the proof and the symbolization used:

I = The initial physical conditions hold.
O = The physical outcome will occur.
L = In the absence of supernatural intervention, given the initial conditions I, outcome O will occur.
N = Naturalism is true (and thus there is no supernatural intervention).
Mx = x is a conceivable set of mental state associations that obtains. A set of mental state associations is essentially a function that maps things in the physical world to (a) a mental state associated to that thing (e.g. a brain); or (b) there being no mental state associated with that thing.

  1. □((N ∧ L ∧ I) → O)
  2. ∀x[◊(Mx ∧ N ∧ L ∧ I)]

    1. (N ∧ L ∧ I) → O 1, T-reiteration
    2. Mt ∧ N ∧ L ∧ I conditional proof assumption
      1. N ∧ L ∧ I 4, simplification
      2. O 3, 5 modus ponens
    1. (Mt ∧ N ∧ L ∧ I) → O 4-6, conditional proof
  1. □((Mt ∧ N ∧ L ∧ I) → O) 3-7, necessity introduction
  2. ◊(Mt ∧ N ∧ L ∧ I) 2, universal instantiation
  3. (Mt ∧ N ∧ L ∧ I) □→ O 8, 9, non-vacuous counterfactual introduction
  4. ∀x[(Mx ∧ N ∧ L ∧ I) □→ O] 10, universal generalization
Line (11) says that on naturalism (N), if the physical state (L ∧ I) had any other conceivable set of mental states associated with that physical state (Mx), the physical outcome would have been the same (O).

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