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Domino Logic

Here are some really interesting videos in which dominos simulate logical reasoning and computing:


Non-physical thought processes

Image from the American Heart Association Blog

An argument for the non-physical intellect and the possibility that it can survive the death of the body (based on a recent Facebook discussion and also roughly on James F. Ross’s Immaterial Aspects of Thought)1:

D1) For all x, (x is a semantically determinate process ≝ there exists a y such that x contains y, and y is a set of operations that have a fixed and well-defined syntax and are semantically unique in their referents).
P1) For all x, (if x is a physical process, it is not the case that x is a semantically determinate process).
P2) There exists an x and there exists a y, such that {x is a formal thought process in my intellect, [x contains y, and (y = Modus Ponens)]}
P3) For all y, [ if (y = Modus Ponens), y is a set of operations that have a fixed and well-defined syntax and is semantically unique in its referents].
C1) There exists an x such that (x is a formal thought process in my intellect and it is not the case that x is a physical process). [From D1 and P1-P3]
P4) For all x, [if (x is a formal thought process in my intellect, and the mode of being of my intellect is physical), then x is a physical process].
P5) For all x, (if it is not the case that the mode of being of x is physical, then x is non-physical).
C2) My intellect is non-physical. [From C1, P4 and P5]
P6) For all x, if x is non-physical, then x cannot be physically destroyed.
P7) For all x and all y, if x cannot be physically destroyed and y can be physically destroyed, x can survive the physical destruction of y.
P8) My body can be physically destroyed.
C3) My intellect can survive the physical destruction of my body. [From C2 and P6-P8]

The point of the argument is essentially this: A physical process can be mapped onto a language, as we have computers do. But that physical process is only simulating the use of language and the way it computes symbols is only insofar as we tether symbols to physical states undergoing various processes. But the physical process itself does not fix the semantic content or the syntax, we do. And so we say that a computer might fail to “add” properly because of a hardware malfunction. But there is no telos intrinsic to the physical process that distinguishes functioning from malfunctioning, so it is merely our attempt to simulate adding that can, at times, be frustrated by a computer functioning in ways we did not anticipate or intend.

This is why no physical process can be semantically determinate. You can have a physical process that is given semantic content by a mind, and then it will be semantic, in a sense, but indeterminate in that the process doesn’t have to fix upon the syntax or semantics assigned to it.

However, a mental process like reasoning according to Modus Ponens is a syntactically well-defined operation that a mind can do. When the mind is doing this operation, it is preserving truth values. A mind cannot “do Modus Ponens” and “not do Modus Ponens” at the same time and in the same way. But a physical process “programmed” to track “Modus Ponens-like inferences” can run a program that makes “Modus Ponens-like inferences” while never actually doing Modus Ponens. It might be doing some other operation all together that is indistinguishable from Modus Ponens up to any given point in time, but in the next run of the program, the hardware catches on fire and it spits out on its display “if p, q/ p// not-q”. You can’t say that catching on fire and displaying an invalid argument on a screen was not part of the process, since the process just is however the hardware happens to function.

Given this, and given that the thing known is in the knower according to the mode of the knower, the rest follows from relatively uncontroversial premises.

Deduction: Let,
Px ≝ x is a physical process
Cxy ≝ x contains y
Ox ≝ x is a set of operations
Tx ≝ x has a well-defined syntax
Sx ≝ x is semantically unique in its referents
Fxy ≝ x is a formal thought process in y
Mx ≝ x has a mode of being that is physical
Nx ≝ x is non-physical
Rx ≝ x is physically destroyed
Vxy ≝ x survives the destruction of y
Dx ≝ (∃y){Cxy & [Oy & (Ty & Sy)]}
m ≝ Modus Ponens
i ≝ my intellect
b ≝ my body

1. (∀x)(Px ⊃ ~Dx) (premise)
2. (∃x)(∃y){Fxi & [Cxy & (y = m)]} (premise)
3. (∀y){(y = m) ⊃ [Oy & (Ty & Sy)]} (premise)
4. (∀x)[(Fxi & Mi) ⊃ Px] (premise)
5. (∀x)(~Mx ⊃ Nx) (premise)
6. (∀x)(Nx ⊃ ~◊Rx) (premise)
7. (∀x)(∀y)[(~◊Rx & ◊Ry) ⊃ ◊Vxy] (premise)
8. ◊Rb (premise)
9. (∃y){Fμi & [Cμy & (y = m)]} (2 EI)
10. Fμi & [Cμν & (ν = m)] (9 EI)
11. (ν = m) ⊃ [Oν & (Tν & Sν)] (3 UI)
12. Cμν & (ν = m) (10 Simp)
13.(ν = m) (12 Simp)
14. Oν & (Tν & Sν) (11,13 MP)
15. Cμν (12 Simp)
16. Cμν & [Oν & (Tν & Sν)] (14,15 Conj)
17. (∃y){Cμy & [Oy & (Ty & Sy)]} (16 EG)
18. Dμ (17 Def “Dx”)
19. ~~Dμ (18 DN)
20. Pμ ⊃ ~Dμ (1 UI)
21. ~Pμ (19,20 MT)
22. (Fμi & Mi) ⊃ Pμ (4 UI)
23. ~(Fμi & Mi) (21,22 MT)
24. ~Fμi ∨ ~Mi (23 DeM)
25. Fμi (10 Simp)
26. ~~Fμi (25 DN)
27. ~Mi (24,26 DS)
28. ~Mi ⊃ Ni (5 UI)
29. Ni (27,28 MP)
30. Ni ⊃ ~◊Ri (6 UI)
31. ~◊Ri (29,30 MP)
32. (∀y)[(~◊Ri & ◊Ry) ⊃ ◊Viy] (7 UI)
33. (~◊Ri & ◊Rb) ⊃ ◊Vib (32 UI)
34. ~◊Ri & ◊Rb (8,31 Conj)
35. ◊Vib (33,34 MP)
36. Fμi & ~Pμ (21,25 Conj)
37. (∃x)(Fxi & ~Px) (36 EG)
38. (∃x)(Fxi & ~Px) & Ni (29,37 Conj)
39.[(∃x)(Fxi & ~Px) & Ni] & ◊Vib (35,38 Conj, which is C1-C3)

J.F. Ross. 1992. “Immaterial Aspects of Thought.” In The Journal of Philosophy. Vol. 89. No. 3. 136-150
I. Niiniluto. 1987. “Verisimilitude with Indefinite Truth.” What is Closer-to-the-truth: A Parade of Approaches to Truthlikeness. Ed. T.A.F. Kuipers. Amsterdam: Rodopi. pp. 187-188
(P4) is based upon the principle that a thing known is in the knower according to the mode of the knower. See, for example, Thomas Aquinas Summa Theologiae I.14.1.

The Imperative Mood and Immateriality

I think James Ross’s Immaterial Aspect of Thought offers one of the most powerful counter-arguments to physicalism. That said, the argument is difficult to grasp. Edward Feser has an article that unpacks the argument a bit more, and some blog posts on the argument, which can be found here. Also, I think this post by Rocket Philosophy does a good job explaining the relevance of Kripkenstein’s quus to Ross’s argument.

Part of the reason that this argument is difficult is because we have to be clear on what terms like “determinate” and “formal” mean. When I’ve tried to explain this argument to others, I’ve emphasized the ways in which formal thinking is truth-preserving in all relevant cases. But my interlocutors often counter with the fact that we can malfunction in our calculations just like calculators, and more often than not we do! They take this to be evidence that we, like the calculator, simulate adding as best we can with the hardware we have, i.e. the brain. My objection to this is that a simulation cannot properly assess when a malfunction has occurred, but we often catch our own mistakes. Furthermore, we are capable of recognizing when a calculator fails to preserve the truth of some function in a relevant case, i.e. when it malfunctions. But a calculator could not recognize that its processes cohere with quadding rather than adding. Should two calculators take in the same input and provide different output, neither calculator could adjudicate over the matter. They could only disagree over what physical processes cohere with adding and which with quadding.

I think there may be a more straightforward proof of the immaterial aspect of thought, and it involves the is/ought dichotomy. The argument is as follows:

P1. No physical processes are processes that contain stages literally expressible in the imperative mood.
P2. Some mental processes are processes that contain that stages literally expressible in the imperative mood.
C1. Some mental processes are not physical processes.

A justification of the premises:

P1: All physical processes are matters of fact, and all matters of fact are about what is the case, and so must be expressed by the indicative mood. I say “literally expressible” to avoid the possible objection that one might use the imperative mood in a metaphorical sense, as in saying something like, “the sun ought to rise.” A computer programmer might object by saying that imperative programming is commonplace and computer programs are physical processes containing stages expressible in the imperative. At best, those stages involve the mental processes of the computer programmer who thinks, “if the program receives this input, it should provide that output”. The programmer then utilizes her knowledge of causal relationship between the software and the hardware, and the hardware with itself, so that it behaves according to the way she thinks it ought to behave, that is, given the ends the programmer has in mind. The computer program itself is fully described and explained according to descriptive physical laws, without reference to the normative logical laws or the practical reasoning employed by the programmer. When we think that a program issues and follows commands, we are speaking metaphorically. The program isn’t literally “oughting” its way through the command lines.

P2: Some mental processes contain stages that are normative. For instance, formal thinking is normative in that it appeals to rules so as to preserve truth. Likewise, moral reasoning involves an appeal to normative rules that preserve goodness. So a certain stage in a mental process could be literally expressed in the imperative mood. A person might express a certain stage in a mental process as “I shall conclude with the consequent of this conditional, since I have affirmed the antecedent” and so engage in the formal processes of modus ponens, or he might think “I ought to stop that mugging from happening” as part of a mental processes whereby his mind resolves to apprehend some villain and restore justice. A physicalist could object that one might be able to express all mental processes in the indicative, that is, with the appropriate adjustments, say, by burying all imperative verbs in noun-phrases, e.g. “the thought that I ought to stop the mugging from happening is occurring in my mind.” But the ability to avoid the imperative isn’t sufficient to avoid the conclusion. My argument runs not only if certain mental processes contain stages that can only be expressed in the imperative, but if such processes are possibly expressed in the imperative. Put simply, it isn’t possible to express physical processes in the imperative, at least if the expression is literal.

Implications for freedom of the will: The physicalist might be tempted to think that mental processes can only be metaphorically stated in the imperative, but the thought process itself should be literally expressed in the indicative, even if the content of those thoughts are expressed in the imperative mood. This naturally leads to the sort of determinism that causes the libertarian to recoil in horror. And the libertarian can hardly be blamed for such a reaction! For the determinist treats the normative content of thoughts as a mere epiphenomenal feature of the thought. The thought processes themselves are extrinsically determined by all of the physical facts involved. The libertarian, on the other hand, believes that the agent contributes uniquely to the causal nexus by willing to adhere to certain normative principles, that is, by allowing her apprehension that she ought to follow those principles to be part of the causal process by which she acts. I would suggest that agent causation can be understood best if one accepts that certain stages of the mental process can be expressed in the imperative mood. This is because mental processes can have genuine normative features, while physical processes cannot. If a mental process includes the apprehension of normative principles such that the apprehension is an actual part of the process (and not an epiphenomenon of the process), then an agent genuinely reason validly, i.e. with formal processes that preserve truth in all relevant contexts. For, to reason validly is not merely to accidentally accord with the formal process of a valid deduction. A process that is “accidentally valid” is just a simulation of validity, since the process of a valid deduction doesn’t just happen to be truth preserving by some coincidence of the physical laws. So to deny that we really reason validly is to undercut any sound argument in favor of determinism. Hence determinism is viewed as self-defeating. Why should I follow the reasoning of someone who concedes that his reasoning process is no more truth-preserving than the processes by which my Mr. Coffee brews my morning cup. The process that Mr. Coffee undergoes has nothing to do with truth preservation. Even if we decide to the coffee grounds stand for “1”, the water for “2” and the coffee that drips out of the machine as “3”, we can’t say that the coffee machine genuinely adds. It merely undergoes processes that we anticipate through induction. We can assign values to the physical components that the coffee-maker predictably modifies, declare by fiat that the modification is some function, and then use the coffee maker as a rudimentary calculator to help us track our own thinking processes (we just have to remember that grounds are a symbol like “1,” water is a symbol like “2,” and coffee is a symbol like “3”).

Daniel Dennett famously argues that religious beliefs originate in our HADD (hyperactive agency detection device). That is, we are evolved to attribute agency to any given phenomenon, whether it is the wind blowing a branch, or a thunder-clap. Ironically, I think it is physicalism that is a result of HADD. But it happens in three stages: 1) the physicalist falsely detects agency in a calculator, 2) the physicalist realizes that the calculator can be completely explained through physical processes, 3) the physicalist concludes by analogy that his own agency can be completely explained through physical processes. Calculators don’t have libertarian freedom, but they can add just like the physicalist without the need of such mystical freedom, or so the physicalist presumes.

If the determinist is correct, the processes by which she arrived at the conclusion contained no normative principles. However, this is why the libertarian says that the determinist abandons morality. The alternative view suggested here is that agent-causation occurs when a mental process becomes normative, which is to say that the normative aspects of thought feature as a genuine part of a mental process. But then agent-causation is not reducible to a physically determined process. To return to an earlier point, when I correctly perform a mathematical operation, I sense my own freedom and ability to take a truth-preserving function and choose to have that function preside over my thoughts. When I make a mistake in mathematics, I realize that my freedom is limited and constrained at times. I think about how I must have failed to remember the proper rules, or forgot which numbers I was dealing with, or lost focus about what I was doing, and so on. But that works well with my own theory of mind arising out of hylomorphism, for I do think that memories are located in the brain, and that there is two-way causation between the physical aspects of the mind and the immaterial intellect. The ability to be free is not a guarantee that I will always act freely, nor is the ability to reason in truth-functional ways a guarantee that we will always think validly. We can make mistakes. But it is our ability to recognize and learn from our mistakes along with our desire to avoid them that makes us more than just physical.

Privileged Access to Minds not Brains

Sometimes pop songs can be quite profound. Consider the following: “Unwritten” by Natasha Bedingfield

I am unwritten, can’t read my mind, I’m undefined
I’m just beginning, the pen’s in my hand, ending unplanned

Staring at the blank page before you
Open up the dirty window
Let the sun illuminate the words that you could not find

Reaching for something in the distance
So close you can almost taste it
Release your inhibitions
Feel the rain on your skin
No one else can feel it for you

Only you can let it in
No one else, no one else
Can speak the words on your lips
Drench yourself in words unspoken
Live your life with arms wide open
Today is where your book begins
The rest is still unwritten

This song always reminds me of a certain argument against the identity of minds with their physical correlates. Each of us has privileged access to our own mental lives. No one can feel the rain on your skin for you. No one can experience your pleasure, or your pain. Even if we could use behavioral analysis or scans of the brain to infer your thoughts, there is something special to the way you access your own thoughts. Whereas the former constitutes publicly accessible knowledge, the latter are intimately and uniquely known to the subject.

The philosopher Richard Swinburne argues that these sorts of mental events are evidence that the supposed identity between the mind and the brain fails.

Swinburne’s point is that it is not at all obvious that a full physical description would include a description of the event from the perspective of the one who actually experiences the mental event. Even if the physicalist were to insist that a full physical description would contain a perspectival description, the physicalist would be in no position to claim that one description logically entails the other. But if there is brain-mind identity, then mental states simply are identical to physical states. Since experiencing rain on one’s skin is a mental state, it would be identical to a brain state. But brain-states lack the sort of special access that mental states have. Even the subject who “feels the rain” on her skin would have to use the same sort of equipment as the neurologist to observe those brain states that occur simultaneously with the experience. That is, we don’t have privileged access to brains, even (or rather especially) the grey matter that is encased in our own skulls.  Likewise, the neurologist cannot use her equipment to have your experience.  At best, she can infer what that experience might be like by correlating physical states with mental states and extrapolating.  But her inference of what your inference is like is not your experience, it can’t be, it is her experience of the extrapolation of what your mental states might be like given physical states.

So the argument is a reductio that goes something like this:

1. Brain states are identical to mental states (Assumption).
2. Some mental states are states for which there is privileged access.
3. No brain states are states for which there is privileged access.
4. Some mental states are not brain states (From 2,3 Festino)

Given that 1 contradicts 4, we must reject the assumption. Therefore:
5. Brain states are not identical to mental states.

A Question about Naturalism, Mereology, and Individuating Persons

“If [Helen Joy] ‘is not,’ then she never was. I mistook a cloud of atoms for a person. There aren’t, and never were, any people. Death only reveals the vacuity that was always there. What we call the living are simply those who have not yet been unmasked. All equally bankrupt, but some not yet declared” (C.S. Lewis 1989, 41).

I think Lewis is basically right. To me, the soul is the formal principle of the body–necessary to explain a person’s identity and individuation despite spatio-temporal and material change. If souls do not exist, i.e. if there are ultimately no real formal causes to explain how the physical parts of a human body can constitute an organic whole conscious and living person, then what natural/physical facts or phenomena could be invoked to explain the fact that I am a whole person? If naturalism is true, and there are no souls, does it remain possible to show that mereological nihilism is false?


Lewis, C.S. 1989. A Grief Observed. New York: Harper Collins Publishers.

Can clouds love?

Following the death of his wife Helen Joy, C.S. Lewis wrote some reflections which were gathered up into A Grief Observed.  In one section he wrote,

If H. ‘is not,’ then she never was.  I mistook a cloud of atoms for a person.  There aren’t, and never were, any people.  Death only reveals the vacuity that was always there.  What we call the living are simply those who have not yet been unmasked.  All equally bankrupt, but some not yet declared.

But this must be nonsense; vacuity revealed to whom?  Bankruptcy declared to whom?  To other boxes of fireworks or clouds of atoms?  I will never believe–more strictly I can’t believe–that one set of physical events could be, or make, a mistake about other sets (1989, 41)1

It seems to me that this is a powerful objection to a naturalistic worldview.  I do not understand how it could be that the physicalist accounts for the identity and individuation of persons.  In fact, I think that if physicalism is true, there could be no persons to know it is true.  I would argue as follows:

1.  If physicalism is true, then there are no objective criteria for individuating and identifying persons.

2.  If there are no objective criteria for individuating and identifying persons, then no persons exist.

3.  If no persons exist, then I cannot experience love for my wife.

4.  If I experience love for my wife, then there must be persons.

5. I experience love for my wife.

6.  Therefore, physicalism is false.

In other words, if the physicalist is to convince me that my experiences belie reality, they still must appeal to me and “my experiences”.  If my experiences are to be false and I am mistaken, then there must be criteria for individuating and identifying me from the rest of the physical universe.  These criteria cannot be subjective, arbitrary, and ad hoc.  Rather, they must be objective, essential, and real. But, I think we have good reason to think premise 1 is true.   Organisms constantly change in that which they are physically composed.  The physicalist might say that the pattern remains the same, but they really mean that patterns are similar.  Consider the physicalist who supposes that a transporter might copy a human, decompose the matter at one location and reproduce the pattern perfectly elsewhere.  The physicalist might say that the human has been transported like a faxed message.  But if the original is not destroyed when the copy is produced, the physicalist struggles to explain what has happened.  Are both the copy and the original the same person?  The struggle reveals the point that even if all physical facts of a person are copied and reproduced in matter elsewhere, there is still something non-physical through which a person is identified and individuated as the self-same person. So, I would challenge the physicalist to supply these objectively real criteria.  For, without such an account, I could hardly be faulted for thinking that these real and objective criteria are found in non-physical realities–in what the supernaturalist calls the “soul”.

1C.S. Lewis. (1961). A Grief Observed. New York: Harper Collins Publishers.

Am I My Body?

Aside from the fact that Dr. Plantinga isn’t quite sure how many legs a beetle has–come on, eight, really?!?–I think he presents a really good argument against physicalism.

The argument runs something like this:

1.  If I am my Body, then anything possible with regard to me is also possible with regard to my body.

2.  It is possible that I exist when my body does not exist.

3.  It is not possible that my body exists when my body does not exist.

4.  Thus, “I exist without my body” is something possible with regard to me that is not possible with regard to my body.

5.  Therefore, I am not my body.

The argument demonstrates a discernible difference between the body and the self.  But does it matter that we are talking about mere possibilities here?  Plantinga’s point is that there is no possible world where a body exists without itself.  Yet, it does not seem logically impossible to imagine a possible world where the self exists without its body.  We take such stories to be supernatural, fantastical, or fictional, but not logically incoherent.  So, it seems reasonable to suppose the logical possibility of a disembodied self.

This means that proving an identity relationship between the self and the body requires a lot more than empirically proving a causal relationship between physical states and mental states.  One must also prove that it is logically incoherent to suppose that there are any possible worlds where the self is disembodied.  So it seems that while this burden is heavily placed upon the physicalist, the supernaturalist can merrily go along believing that she is her soul.  Right?

Not so fast, my friend Shaun Miller has pointed out to me that this argument, if anything, proves too much (Shaun was inspired by Shelly Kagan, ff about 43 min in for the appropriate part).  Kagan points out that we could imagine that the same body is possessed by different souls. His point is not that we are not our soul, but that our soul doesn’t seem sufficient to establish personal identity.  As far as I can tell, Shaun’s response to Plantinga is original, and quite difficult to overcome.  He points out that we could substitute just about anything in the argument, including the soul, and prove it to be non-identical with the self.  Does this mean that I am not my soul?!? My initial reaction to this was, “Well, it’s just not possible that I exist without my soul, since I am my soul.”  But now I’m guilty of special pleading.  This fallacious soul-ution is to stipulate that “soul” is simply defined as “self”.  But then we have just stipulated our way to victory, which is not very satisfying.  What would prevent the physicalist from stipulating “body” as “self”?  We’re back to square one.

Upon further reflection, I think the argument achieves something.  It proves that unless we have good reason to think that it’s not possible for X to exist when Y doesn’t exist, then we don’t have good reason to think X and Y are identical.   I have no good reason to think I am my body, because I think it is at least logically possible to be disembodied and survive.  But then I should be willing to bite the bullet and concede that I have no good reason to think I am my soul.  So be it.  I have no good reason to think I am my soul either.  As I said before, we could substitute just about anything for body–just about.  However, I cannot substitute “self”.  Whatever “self” is, it cannot both exist and not exist, at the same time, and in the same possible world!  So I do have good reason to think at least this…  I am myself.

But is this an adequate response?  Are there other problems with the argument that I am not mentioning here?