p-zombies are inconceivable. With notes on the idea of metaphysical possibility.

zombiesby Massimo Pigliucci

Philosophy of mind and the nature of consciousness are fascinating topics, which recur both here at Scientia Salon [1] and at my former writing outlet, Rationally Speaking [2]. And of course we can hardly talk about consciousness for long before running into one of the most famous (and, in my mind, pernicious) thought experiments in philosophy of mind: the philosophical zombie! [3] (Now you should hear ominously sounding music in the background…)

In this essay I propose to do the following: we are first going to take a look at Chalmers’ zombie argument (one of a number of instances of zombification in philosophy of mind) to see exactly what it says and why I find it utterly unconvincing. Next, we’ll use p-zombies to broaden the discussion to parse the differences among different types of possibilities, especially logical, metaphysical and physical/nomological (with a nod toward two other types: epistemic and temporal/historical/contingent). Finally, we’ll use whatever we think we have learned in the process to talk even more broadly about the very nature of philosophical inquiry — or at the least the sort of analytic-type [4] metaphysics that Chalmers and his supporters indulge in.

What, if anything, are p-zombies?

The first thing to be aware of when we talk about p-zombies is that the concept has a long history and has been used in different ways for different purposes. It can be traced back to Saul Kripke’s arguments in the 1970s against type-identity theory in philosophy of mind as presented in his Naming and Necessity [5]. Versions of it were elaborated upon during the same decade by both Thomas Nagel and Robert Kirk. But we won’t go into any of that, focusing instead on the more famous Chalmers’ version of 1996.

Also to keep in mind is the fact that p-zombies have been deployed against different targets, the most important of which are behaviorism [6] and physicalism [7], though they have also been used to argue for the existence of an epistemic gap in our understanding of consciousness (the so-called “hard problem” [8], very much related to the issue of physicalism). Anti-behaviorism p-zombies are not particularly interesting, in my mind, because they beat a dead horse: while behaviorism survives as a useful practice in psychology, it has gone the way of the dodo as a theory of mind decades ago. Besides, it seems to me trivially true that one could face a being that behaves like a human and yet is internally constructed very differently from a human. So what?

As for the epistemic problem concerning consciousness, if by that one simply means that we don’t yet fully (or even very partially!) understand how consciousness can be produced in a physical system, that is obviously the case. But such observation licenses precisely nothing about the future likelihood, or even the in-principle possibility, of such knowledge. Accordingly, we will set this one aside as well.

Instead, I’ll tackle the best known deployment of p-zombies, by Chalmers, whose target was physicalism itself. Here is his argument, formalized:

  1. According to physicalism, all that exists in our world, including consciousness, is physical.
  2. Thus, if physicalism is true, a metaphysically possible world in which all physical facts are the same as those of the actual world must contain everything that exists in our actual world, including conscious experience.
  3. We can conceive of a world physically indistinguishable from our world but in which there is no conscious experience. It follows that such a world is metaphysically possible.
  4. Therefore, physicalism is false. (Because 4 follows from 2 and 3 by modus tollens.)

As plenty of commentators have noted, Chalmers’ argument is deductively valid, i.e., if its premises are true, then the conclusion must logically follow. You would think so. Any philosopher caught putting forth an invalid argument should have his license revoked (well, philosophers don’t really have licenses, but you get my drift).

Which means that we need to focus on (1), (2) and (3) above, from which (4) is allegedly derived. (1) is a fair statement of the metaphysical notion of physicalism, so no problem there. (2) is also true, pending further elucidation of what one means by the tricky term “metaphysically possible.” (3) is where Chalmers hits what will turn out to be an insurmountable brick wall.

Let’s look at it more closely, highlighting the potentially problematic bits: we can conceive of a world physically indistinguishable from our world but in which there is no conscious experience. It follows that such a world is metaphysically possible.

What does it mean to be able to “conceive” such world, in this case? And what, exactly, is metaphysical possibility?

The pertinent dictionary definition of “conceiving” is: to form a mental representation of [something]; to imagine. Well, in that sense, I can certainly conceive of a p-zombie, and of a lot of other nonsensical objects as well. Heck, I can fool myself that I can even conceive of a squared circle, which is mathematically impossible. Clearly, something more rigorous has to be in play here for the argument to go through.

One thing that is not in play is physical possibility. Chalmers himself clearly stated: “Zombies are probably not naturally possible: they probably cannot exist in our world, with its laws of nature.” [9] He also wrote: “it certainly seems that a coherent situation is described; I can discern no contradiction in the description” [10] by which I assume he means no logical contradiction. And finally: “From the conceivability of zombies, proponents of the argument infer their metaphysical possibility” [11].

Keep the above distinction among logical, physical and metaphysical possibilities in the back of your mind for a bit, it will turn out to be crucial.

There are, of course, a number of standard responses to Chalmers’ argument. Dan Dennett famously thinks that Chalmers is simply confused about the notion of conceivability: p-zombies are not actually conceivable, because when examined more closely they embed hidden contradictions, just like many other imaginary objects that we are free to conjure up in our mind when we impose few if any constraints. The better response, in this case, came from AI researcher Marvin Minsky, who pointed out that Chalmers’ argument begs the question: in order to work, it has to assume that some characteristics of human beings, namely consciousness, are not produced by physical processes, which is precisely what the argument allegedly sets out to prove. In formal terms, there is a hidden premise in the argument, lurking somewhere between (2) and (3) above. Once this premise is brought to light, the argument is actually shown to be circular (though still logically valid, mind you!).

What is metaphysical possibility?

Which brings us back to the pesky idea of metaphysical possibility. What is it, exactly, and how is it distinct from logical and physical possibility? This is critical, because Chalmers’ whole gambit relies on the proposition that metaphysical possibility is, in fact, distinct from the other two forms, and doesn’t collapse into one or the other. As we shall see, this assumption may be hard to defend.

Let us begin with a little classificatory scheme of possibilities (and, equally, impossibilities):

  • Logical: typically thought of as the broader kind of possibility (and, conversely, the strictest kind of impossibility). “My friend Phil is a married bachelor” is an example of logical impossibility, as the word bachelor is defined as an unmarried man. More intriguingly, it turns out that something called Noether’s theorem [12] mathematically proves that if the laws of physics are invariant through time then the principle of conservation of energy has to hold true. That is, it is logically impossible for a universe to have both time-invariant laws and violations of conservation of energy. (Naturally, it also follows that it is not logically contradictory, as far as we can tell, to imagine a universe whose laws change over time and where the conservation principle does not hold.)
  • Metaphysical: this is the pesky one. It is commonly thought to be either co-extensive with logical possibility, or to be a subset of it. Perhaps the best known example of metaphysical necessity (which is, of course, stronger than mere possibility) is Kripke’s statement that “water is H2O” is metaphysically but not logically necessary. The idea is that there is no logical contradiction is thinking that water might not be H2O (so this doesn’t rise to the level of logical necessity), and yet it seems physically impossible for that to be the case. Hold this particular thought in place while we turn to the next level.
  • Physical (or nomological, i.e., law-mandated): this means that something is possible (or impossible, or necessary) under the laws of physics of our universe. For instance, for me to jump out the window and start levitating is logically possible (i.e., the idea involves no apparent contradiction of any principle of logic), and yet it is physically impossible. Philosophically, what is interesting here is that ever since Hume, many philosophers have treated the laws of physics as metaphysically contingent, in the sense that they could have been otherwise. Indeed, if the concept of the multiverse [13] holds water, this is likely the case. Some philosophers, however, like Sydney Shoemaker [14], think that the laws of physics couldn’t be otherwise, in which case physical and metaphysical possibility would turn out to be the same.

As I mentioned above, there are two other types of possibilities that occasionally enter into these discussions: epistemic and temporal/historical/contingent. Let’s examine them briefly before setting them aside and going back to the all-important concept of metaphysical possibility.

Temporal (or historical, or contingent) possibility simply means that things could have been otherwise not only logically, but also physically (i.e., without contradiction of either logical principles or physical laws). For instance, I could be writing this essay in my office at CUNY’s Graduate Center, rather than at home, as in fact I am. While contingency plays a crucial role in pretty much all the so-called “special” sciences (i.e., anything but fundamental physics), it doesn’t really concern us here. [15]

As for epistemic possibility, this is marginally relevant to our discussion, as hinted at above. For instance, at the moment at least, we do not know whether Goldbach’s conjecture [16] in mathematics is true or not. But, presumably, there is a fact of the matter as to whether it is or it isn’t, regardless of whether we will or will not ever be able to find out.

Back to metaphysics, then. First off, remember that metaphysical possibility lies somewhere between logical and physical possibility. But here is a new question: which logic, and which physics?

The question is not facetious, and indeed I suspect may lead us to a pretty solid conclusion of our quest, which will imply the rejection of Chalmers’ argument above, among other things.

As any above-introductory level student of logic knows, there are many types of logics out there [17], so that, strictly speaking it makes no sense to say that something is logically possible/impossible unless one also specifies which type of logic applies. For instance, in classical Aristotelian logic, the principle of non-contradiction applies: either A is B, or A is not B, but definitely not both [18]. But if one adopts dialethic logic [19] it turns out that certain propositions (typically, those involving logical paradoxes under classical logic) can be both true and not true. (That said, unlike my colleague Graham Priest, I don’t actually buy this, but it will do for the sake of illustration here.)

Analogously, we need to be clear on which set of laws of physics we are operating. The obvious one is the set that applies to our universe, but one could imagine situations applicable to other parts of the multiverse (if it exists) that are governed by different laws. Indeed, some physicists have even proposed that the laws of our universe change over time [20], which means that we would have to specify not just which universe we are talking about, but also when (again, personally not buying it, but it’s out there). Consider again Kripke’s assertion that “water is H2O” is not logically, but metaphysically, necessary, because it cannot physically be otherwise. Well, that’s true for our laws, in this particular period of the universe’s evolution. But if one or more physical constants were different, then it would be perfectly (physically) possible for a substance to have the chemical constitution H2O and yet for its behavior to be different from what we call “water.”

The bottom line is that I think that when people talk about metaphysical possibility/impossibility/necessity they can do so coherently, and position metaphysical space in between logical and nomological spaces, only because they are not careful enough to specify which logic and physics they are contemplating. I suggest further that if we are more precise and fix a particular logic and a particular nomology, then metaphysics space collapses into either one or the other (i.e., some metaphysical possibilities/impossibilities/necessities will turn out to be logical, and other, physical).

So, what about analytic metaphysics, then?

All of the above would seem to bode badly for the whole idea of doing anything like analytic metaphysics, the sort of thing Chalmers engages in [21]. Indeed, one could use the above analysis to question the point of philosophical inquiry itself, at least conducted in the above fashion.

Except, of course, that what you just read is an essay in philosophy — not science, not logic, not mathematics, not literary criticism. What we did was to begin with a startling claim, which was apparently presented in a logically solid framework; we parsed it, unpacked it, poked into it, until we found one or two weak points; we then proceeded to explore just how weak those points were and why; and we finally reached some conclusion, which of course is going to be tentative and open to the very same process, which I’m sure my readers will launch into with gusto as soon as this is published. That’s philosophy, folks!

What about metaphysics and metaphysical possibility, however? If it is true, as I’ve argued above, that metaphysical possibility/necessity/impossibility collapse into either their logical or physical counterparts, depending on the particular statement being made and on which logic and physics one considers while making it, what is left to do for metaphysicians?

Here I endorse (with some caution) the now famous approach to metaphysics articulated in a number of fori by James Ladyman, Don Ross, and colleagues [22]. Although these authors refer to what they do as “scientific” or “naturalized” metaphysics, and they openly disdain the Chalmers brand, labeling it as “neo-Scholasticism,” in reality, I hope, they are all doing the same thing (though some better than others). What they are doing is positioning metaphysics at the interface between logic and science, from which it naturally follows that metaphysicians will arrive at conclusions that are constrained by either the principles of logic or the laws of physics, depending on which side of that spectrum of possibilities they happen to be focusing. P-zombies, as it turns out, are physically, and therefore metaphysically, impossible (in this universe), though not logically so. But the fact that they are logically possible is no argument against physicalism at all, since physicalism itself isn’t a logical necessity, it just happens to be the best (in the specific sense of most fecund) metaphysical approach to understanding the world.

_____

Massimo Pigliucci is a biologist and philosopher at the City University of New York. His main interests are in the philosophy of science and pseudoscience. He is the editor-in-chief of Scientia Salon, and his latest book (co-edited with Maarten Boudry) is Philosophy of Pseudoscience: Reconsidering the Demarcation Problem (Chicago Press).

[1] Is quantum mechanics relevant to the philosophy of mind (and the other way around)?, by Quentin Ruyant, SciSal, 21 July 2014; The Turing test doesn’t matter, by Massimo Pigliucci, SciSal, 12 June 2014; Information is the new Aristotelianism (and Dawkins is a hylomorphist), by John Wilkins, SciSal, 1 May 2014.

[2] Three and a half thought experiments in philosophy of mind, by Massimo Pigliucci, Rationally Speaking, 6 September 2013; Computation, Church-Turing, and all that jazz, by Massimo Pigliucci, Rationally Speaking, 5 August 2013; Philosophy not in the business of producing theories: the case of the computational “theory” of mind, by Massimo Pigliucci, Rationally Speaking, 29 July 2013; The zombification of philosophy (of mind), by Massimo Pigliucci, Rationally Speaking, 29 July 2008.

[3] The Conscious Mind: In Search of a Fundamental Theory, by David J. Chalmers, Oxford University Press, 1996.

[4] Is there (still) a continental-analytic divide in philosophy?, by Massimo Pigliucci, SciSal, 17 July 2014.

[5] Naming and Necessity, by Saul A. Kripke, Wiley-Blackwell, 1972.

[6] Behaviorism, by George Graham, Stanford Encyclopedia of Philosophy.

[7] Physicalism, by Daniel Stoljar, Stanford Encyclopedia of Philosophy.

[8] What hard problem?, by Massimo Pigliucci, Philosophy Now, 2013.

[9] Consciousness and Its Place in Nature, by David J. Chalmers, in: The Blackwell Guide to the Philosophy of Mind, edited by S. Stich and F. Warfield, Blackwell, 2003, p. 5.

[10] The Conscious Mind, p. 96.

[11] Consciousness and Its Place in Nature, p. 5.

[12] Noether’s Theorem.

[13] The multiverse as a scientific concept, by Coel Hellier, SciSal, 3 June 2014 & 5 June 2014.

[14] Time Without Change, by Sidney Shoemaker, Journal of Philosophy, 1969, 66:363–381.

[15] Of course, if metaphysically you are a reductive determinist then temporal possibility reduces to physical possibility, because nothing could have happened differently, and our sense that there are stochastic events in the universe is the result of limited epistemic access to reality.

[16] Goldbach Conjecture.

[17] Logics, by John Nolt, Cengage Learning, 1996.

[18] Aristotle on Non-contradiction, by Paula Gottlieb, Stanford Encyclopedia of Philosophy.

[19] Beyond true and false, by Graham Priest, Aeon magazine, 5 May 2014.

[20] Time, laws, and the future of cosmology, by Lee Smolin, Physics Today, 2014, 67:38-43.

[21] Metametaphysics: New Essays on the Foundations of Ontology, ed. by David Chalmers, David Manley and Ryan Wasserman, Oxford University Press, 2009.

[22] Scientific Metaphysics, ed. by Don Ross, James Ladyman and Harold Kincaid, Oxford University Press, 2013.

148 thoughts on “p-zombies are inconceivable. With notes on the idea of metaphysical possibility.

  1. I found this very helpful and clear, and it seems to do away with much clutter, but would not see it as quite the end of the story, The claim that zombies are logically possible would need a proof. I would judge them to be logically, physically, nomically, metaphysically and conceptually impossible, and see no reason here to change my mind. I would also reject Chalmers’ third step as given above, for the reasons given, but would see this as away of making his argument work. It seems that there is one opinion per person on zombies.

    How would show that zombies are logically possible?

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  2. Hi Massimo,

    I’m surprised though pleased that you’re returning to this topic. I thought you’d had enough of it! I hope we can find a way to take the conversation in new directions without rehashing old arguments fruitlessly.

    Firstly, I must say that though I have been on record defending Chalmers and p-zombies, I agree that his argument against physicalism fails. I think p-zombies are a useful contribution to the literature as a thought experiment to elicit and discuss intuitions about consciousness, not as a proof of anything.

    Incidentally, I’m not sure even Chalmers thinks it is a proof against physicalism. I think he’s quite open to the idea that there’s something wrong with the premises. He has always struck me as a philosopher who remains open minded and is more interested in exploring the possibilities and how different ideas seem to support or contradict each other than someone convinced he has the right solution.

    Even so, I don’t quite agree with your analysis of why the argument fails. Indeed, your analysis seems a little inconsistent.

    Chalmers’ whole gambit relies on the proposition that metaphysical possibility is, in fact, distinct from the other two forms, and doesn’t collapse into one or the other.

    In my view, this is completely wrong. In fact, his syllogism is completely reliant on the assumption that logical and metaphysical possibility are one and the same. He derives the fact that philosophical zombies are metaphysically possible from the fact that they are logically possible. Arguing that metaphysical possibility may collapse to logical possibility (and I believe it does) actually supports his case.

    Yet I think Chalmers’ argument fails, and for precisely the reason Dennett gives and you alluded to with reference to the conceivability of square circles. The fact that Chalmers cannot perceive a logical contradiction does not mean that there is no logical contradiction. Lacking an account of what consciousness is, he cannot assume that the same physical reality can exist without giving rise to consciousness. Indeed, on my view (computationalism), p-zombies would not be logically possible. If computationalism is correct, p-zombies would in fact be inconceivable.

    I think Dennett’s argument is actually equivalent to (or at least complementary to) Minsky’s argument, because Chalmers’ intuition that there is no logical contradiction is predicated on the assumption that computationalism, biological naturalism and so on are incorrect, so he’s smuggling something into the premises making the whole thing circular.

    P-zombies, as it turns out, are physically, and therefore metaphysically, impossible (in this universe), though not logically so.

    Chalmers’ whole argument is about other universes (or other possible worlds), not this one. In agreeing with Chalmers that p-zombies are logically possible, and in your inclusion of that parenthetical “(in this universe)” you concede the argument.

    PS: I just want to reaffirm that even though I disagree with Chalmers’ syllogism, I am not actually a physicalist (though I am a naturalist). I think mathematical objects exist, and I think the mind is a mathematical object not unlike software. From a physical perspective, there is no mind and only the brain exists. The brain is a physical implementation or instantiation of that abstract object.

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  3. There is something very wrong with the idea that there is any necessity to the fact that water is H2O. Firstly, it is at best contingently true, given our laws of nature, that there exists a compound with this formula, but under different laws of nature this would not have been the case. Secondly, it is not even strictly true. As I’m sure Massimo realises, water is actually a mixture of H2O, small amounts of HDO, and very small amounts of D2O, together with (at least in the liquid form) 0.1 micromoles/L of H9O4+ and OH-.

    But I think that in any case, Massimo slew the dragon very early on. If we knew whether, in any conceivable universe, p-zombies were possible, we would know whether the complexity of observable behaviour that we associate with persons is possible without consciousness, and we will not know this as long as the hard problem of consciousness remains unsolved. As to what we can conceive (or even firmly believe in the existence of), that must relate to our psychology and our state of knowledge. The ancient Greeks, famously, did not know, as we now know, that it was logically (not merely physically) impossible to trisect an angle using straight edge and compass only. Was it then, and is it now, metaphysically possible to perform this feat? If someone could explain this to me, I would have a much clearer idea of what is meant by “metaphysical possibility”.

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  4. “How would show that zombies are logically possible?”

    Isn’t it up to the person who says “I can imagine a square circle” to convince the others, rather than for others to prove to the imaginer that he is not really imagining?

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  5. Hi Massimo,
    That’s a nice and clear exposition, and I agree with your argument and conclusion. Just a few minor comments:

    Regarding “logically possible” versus “physically” possible. From my scientismistic stance, “physical laws” are descriptions of how the world is, while “logical laws” are descriptions of how the world is; the only difference being that the latter are a sub-set of the former. Thus the difference between “logically possible” and “physically possible” is only a matter of which rules we are testing compatibility against.

    From there it follows that there is no such thing as “metaphysically possible” in between “logically possible” and “physically possible”. In that case the question of whether a p-zombie is “possible” can only mean whether a p-zombie is possible in our world, with the logic, physics and biology of our world, and asserting that it is is indeed begging the whole question.

    That arrives at the same conclusion as you but by a slightly different path.

    … one could imagine situations applicable to other parts of the multiverse (if it exists) that are governed by different [physical] laws. Indeed, some physicists have even proposed that the laws of our universe change over time …

    This really comes down to whether descriptive statements are universal, or local and contingent. For example, the value of the electron mass is (as far as we know) universal, whereas things like orbital distances of planets are local and contingent. A multiverse scenario doesn’t change that basic distinction, it just envisages a far bigger canvas, with some properties that we had previously assumed to be universal instead being local.

    As for the “laws of our universe” changing over time, well our universe does change with time, and it is entirely meaningful to say that we are 13.7 Gyr after the Big Bang, and the consequences of that fact are clear and observable. In a genuinely static universe it would either not make sense to specify a time after some beginning, or there would be no way of discerning that time.

    So really the discussion of whether the “laws of physics” change over time in our universe is really a matter of asking which aspects of physics have changed and which have not. There are (as far as we know) lots of things in both categories.

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  6. That is not the Chalmers argument I have seen. Chalmers has said that the move from conceivability to possibility is only valid via his 2 dimensional semantics and so his argument is couched in terms from 2d semantics, like primary and secondary conceivability and primary and secondary possibility.

    The 2d version of the argument might be newer than this.

    Not that 2d semantics makes a lot of sense to me.

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  7. I think you are being picky pointing out tha water contains other compounds.

    But if our laws of nature were different would there be H2O? I can’t see your reasoning there.

    Is it really valid to call something which behaves differently from a hydrogen atom a hydrogen atom?

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  8. Was it then, and is it now, metaphysically possible to perform this feat? If someone could explain this to me, I would have a much clearer idea of what is meant by “metaphysical possibility”.

    No, you’re confused with epistemic possibility. It was epistemically possible that the Greeks could have performed such a trisection, which just means that it was possible as far as they knew (i.e. they did not know it was impossible).

    It never has been metaphysically possible because metaphysical possibility is a subset of (or perhaps equivalent to) logical possibility.

    A metaphysical possibility is something that can happen in some possible world. Perhaps not in this universe but in some other.

    Another way of looking at it is that metaphysical possibility considers ways the world might have been different. After all, it seems implausible that the way the universe actually is is the only way it might have been.

    My own view is that metaphysical possibility and logical possibility are the same thing. That is, there is no reason why a logically consistent universe cannot exist. This is different from the claim that all logically consistent universes do actually exist in fact (although I also believe this).

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  9. Eric. Pardon the missing word in the question.

    I don’t know how to prove what can be imagined, but for me where an idea requires a logical contradiction or impossibility it would be (in a full sense) unimaginable. When we think we can imagine a creature that behaves like a human being but is not conscious I think we are kidding ourselves. The idea is nonsensical. But then, some folk would argue that they can imagine nonsensical things, and it’s hard to show that they’re wrong. I suppose we could argue that they are not imagining it conscientiously.

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  10. Hi Massimo,

    But if one or more physical constants were different, then it would be perfectly (physically) possible for a substance to have the chemical constitution H2O and yet for its behavior to be different from what we call “water.”

    If you have something which behaves differently to the way a hydrogen atom behaves, is it really meaningful to call it a hydrogen atom?

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  11. Hi Coel,

    From my scientismistic stance, “physical laws” are descriptions of how the world is, while “logical laws” are descriptions of how the world is; the only difference being that the latter are a sub-set of the former.

    I think you should realise that you are bending terms beyond recognition when you make statements like this, to the point that they become meaningless.

    You can argue that we derive logic from interaction with the physical world, but this does not mean that logical laws are a subset of the former. We can after all imagine other logically consistent universes. One way to do this is to tweak the physical laws of this universe, e.g. by messing with the constants.

    It would seem that it is logically possible that the ratio of the masses of the top quark to the charmed quark could be other than it is. This simply means that we cannot derive its value from the armchair, and that its having other values does not imply any contradictions. However, if it is a physical law that it has the value that it has, then it is not physically possible for it to have other values, meaning that no experiment could take place or physical circumstance arise in this universe whereby this ratio would be other than it is.

    As such, the distinction between logical possibility and physical possibility is a sound one unless it so happens that it is logically impossible for the laws of physics to be otherwise (which would seem to be untrue).

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  12. Hi Robin,

    If you have something which behaves differently to the way a hydrogen atom behaves, is it really meaningful to call it a hydrogen atom?

    Yes, in the sense that deuterium is hydrogen (a form of hydrogen). Terms such as “hydrogen” really refer to an envelope of allowable behaviour, and if the “something different” is within that envelope then it still merits the label.

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  13. Exactly. I do not believe that anyone can imagine a square circle, and that anyone who claims to is falling into a use-mention fallacy.

    The idea of a square circle is something that we can mention, but unlike the p-zombie, it is not something which we can use to point to a conceivable referent. We can conceive of concepts which don’t make sense, but that is not the same thing as being able to conceive of how they would make sense experientially. I can say the words “square circle” but I cannot imagine holding or beholding an object which is exclusively square and exclusively circular. This is what Chalmers would call Metaphysically Impossible. By contrast There is no problem in conceiving of a machine which performs human like functions but is not human, just as there is no problem conceiving of a Mill or a Chinese room which has nothing but the presence of physical parts without any additional mind animating them.

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  14. Thanks a lot for your work here.

    Excellent overview of the literature, really lays out the big-picture. The devil, however, is in the details. One risk might be that we reject the conceivability of zombies on the conditions Chalmers himself lays out: that in the act of conceiving of zombies we reveal a contradiction. His response to these is usually that for things to be properly conceivable, they need to be conceivable upon ideal rational reflection, and only then does their conceivability (positively) entail their possibility. He calls this Weak Modal Rationalism (WMR) and roughly speaking, it is the doctrine that the right kind of conceivability entails the right kind of possibility.

    This conceiving business strikes me as philosophically suspect. For a start, Chalmers needs qualia to be genuine entities in order for the argument to make any sense at all. The “qualitative character of experience” is nowhere more seen than in an act of pure imagination (even if that act is very rigorous, as Chalmers demands it to be). However, there is no reason to expect our conceiving capacities to be suitable to determining the space of possibilities. One reductio offered by Mizrahi and Morrow (2014) takes Chalmers’ requirements for conceivability and argues that the possibility of WMR being false fits the bill with regards to the conditions laid out by Chalmers. They outline a story of a possible world inhabited by creatures just like us, but with consistent modal illusions. On this account, WMR (by its own standards) is not a valid form of determining possibility.

    More than that, however, I find suspect the notion that some particular “quail” can settle the issue as to the ontological status of qualia. The kinds of arguments Chalmers defers to when it comes to this issue (other than his own p-zombies) is Mary’s Room and Bats. These are all stories where the (minimally logical) possibility is entailed by the conceivability of some state of affairs, and disagreements tend to end on a note of “oh well, I guess you just don’t share my intuition on this matter”. This is a sad state of affairs.

    As a result, I suggest we give up on trying to show the positive possibility of anything. Rather, we can be quite safe in determining contradictions, and having contradictions entail impossibility (or confusion). In everyday life, we will appeal to conceivability (“I just can’t see how that’s possible”) in cases where we see a good reason something couldn’t be the case, and I suggest we extend that practice into our arguments about metaphysics.

    All the best,
    Petar

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  15. Hi DM,

    We can after all imagine other logically consistent universes.

    Just as we can imagine other physically consistent universes. As I said, the real distinction here is between universal descriptions (ones that apply to everything) and non-universal descriptions (local, contingent descriptions). What, to you, is the difference between a logical universal description and a physical universal description?

    However, if it is a physical law that it has the value that it has, then it is not physically possible for it to have other values/

    Physical laws are descriptions of how things are. Thus your sentence can be translated as “If it is the case that the value is always the same, then it will never be different”, which has the merit of being true but doesn’t actually say anything.

    You can say exactly the same about logic. If we can envisage different and incompatible logical systems, then our logic is just as contingent as our physics (might be). On the other hand it might be that logic is universal, but then it might well be the case that some of what we label “physics” is universal.

    the distinction between logical possibility and physical possibility is a sound one

    I’m still not getting it. The meaningful distinction seems to me between “things that could be different” and “things that are always the same”.

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  16. [Thanks, Disagreeable. You confirm my perplexity. I understand logical impossibility, and that if something is not logically impossible, there could be a world in which it is so, but I still do not understand what is meant by the claim that there is a category, metaphysical impossibility, distinct from either physical or logical impossibility.] Regarding H2O, one can imagine a universe in which the proton/electron mass ratio was much smaller than in our own, but things were otherwise quite similar. It could then be the case that hydrogen and oxygen atoms would still form, and bond to make H2O molecules, but the zero point vibrational energy of such a molecule inside liquid water would be greater than the intermolecular binding energy. Under such conditions, liquid water would not exist. So, even within the set of possible universes where H2O would exist, its actual properties are contingent on the local physical laws.

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  17. PeterJ,

    I don’t know how to prove what can be imagined, but for me where an idea requires a logical contradiction or impossibility it would be (in a full sense) unimaginable.

    A comment on “imagining”, “conceiving” and being “possible”.

    Take a bright teenager who is good at school maths, but who has never studied prime numbers. Explain to him what prime numbers are, and then discuss with him whether there is a largest prime number. From the way the frequency of prime numbers gets smaller and smaller, it is “intuitive” that they might peter out and that there is a largest prime number. I would have thought that such a teenager could readily “imagine” and “conceive of” a largest prime number.

    Then give that teenager Euclid’s proof that there is no largest prime (which is simple enough for such a boy to follow). Would we then have destroyed his conception of a largest prime? Would he now be in the state of being unable to conceive of a largest prime, since if he tried he would immediately think of the logical contradiction that that led to?

    My conclusion from thinking about this is that what a human can imagine and conceive of are not actually a good guide to what is possible without contradiction. And without that link the p-zombie argument gets nowhere.

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  18. Hi Coel,

    Just as we can imagine other physically consistent universes.

    What does physically consistent mean? You mean universes which share our laws of physics but differ in initial conditions or how quantum events panned out? OK. But there remains a distinction to be drawn between those which do share our physics and those which do not. The physically-consistent universes are a subset of the logically-consistent ones.

    What, to you, is the difference between a logical universal description and a physical universal description?

    I don’t know. I don’t even know what you mean. A description of a universe is logically consistent if it entails no contradiction. Physical possibility is not about consistency but about whether some scenario could be realised in our universe.

    Physical laws are descriptions of how things are. Thus your sentence can be translated as “If it is the case that the value is always the same, then it will never be different”, which has the merit of being true but doesn’t actually say anything.

    That X is a physical law is just the proposition that the value is always the same, that it can never be different. This proposition could be true or false. We don’t usually know which is why we need experiments to find out, and even then we could be wrong (e.g. if what we think are physical laws actually change over time).

    That X is a logical necessity is the proposition that for the value to be otherwise would entail a logical contradiction. The negation of the proposition is therefore incoherent and so the proposition must be true. We don’t need to do experiments to find out, although it may be no harm just to double check that we haven’t made some mistake in our reasoning.

    You can say exactly the same about logic. If we can envisage different and incompatible logical systems, then our logic is just as contingent as our physics (might be).

    Or a plurality of logical systems are possible.

    On the other hand it might be that logic is universal, but then it might well be the case that some of what we label “physics” is universal.

    Well, some of what you label “physics” is universal. If you want to speak the same language as the rest of us, call that part “logic” and call the rest “physics”.

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  19. An excellent essay! I agree that p-zombies, at least any interesting version of them, are nonsense.

    I’m always a bit suspicious when people start talking about things being logically possible but not possible with our current natural laws, and yet proceed to try to make meaningful conclusions based on that logical possibility. Many things are logically possible given inaccurate premises. It’s logically possible for water to not be H2O, but only if my premises are wrong or incomplete or if I’m using an uncommon definition of “water”.

    It’s not clear to me that even invoking the multiverse rescues this endeavor. We have no guarantee that logic as we understand it would have any traction outside of our universe. An assertion that logic necessarily transcends our universe strikes me as a statement of faith.

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  20. Hi DM,

    But there remains a distinction to be drawn between those [universes] which do share our physics and those which do not.

    Just as there is a distinction between those universes which share our logic and those which do not.

    The physically-consistent universes are a subset of the logically-consistent ones.

    And the logically-consistent ones are a subset of the meta-logically-consistent ones. What we have are nested sets of rules, with different degrees of universality.

    A description of a universe is logically consistent if it entails no contradiction. Physical possibility is not about consistency but about whether some scenario could be realised in our universe.

    “Logically consistent” means does not violate some rule about how things are. “Physically possible” means does not violate some rule about how things are. The only difference is that by “physical laws” we mean a superset of descriptions that includes the logical laws.

    That X is a physical law is just the proposition that the value is always the same, that it can never be different.

    Or, for example, that momentum is conserved, which is the rule that “conservation of momentum is never violated”.

    That X is a logical necessity is the proposition that for the value to be otherwise would entail a logical contradiction.

    In other words, that a logical law would be violated. (Call the logical “law” an “axiom” if you prefer.)

    The negation of the proposition is therefore incoherent and so the proposition must be true. We don’t need to do experiments to find out …

    What you mean is that *if* the logical axiom holds *then* it holds, and things following from it must be true. In the same way, *if* the law of conservation of momentum holds *then* it holds, and things following from it must be true.

    Well, some of what you label “physics” is universal. If you want to speak the same language as the rest of us, call that part “logic” and call the rest “physics”.

    OK, I’d go along with that. But note that’s the same distinction I made. And it would make ideas such as “conservation of momentum” logic rather than “physics”. (I’m ok with that, but then from my radical-scientismist persective logic and maths are part of physics.) Note, also, that whether or not something is universal is an empirical question, so we’ve again married logic and physics, and again that suits me fine!

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  21. Hi DM. I’m not sure what ‘valid’ would mean in this context. I cannot see any philosophical use for the Turing test.

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  22. multisensereralism – You state, ‘There is no problem in conceiving of a machine which performs human like functions but is not human’. This is true. I can conceive of a robot arm. I cannot, however, conceive of an insentient machine which becomes a Roman Catholic. The idea that consciousness is not required in order to replicate human behaviour is so weird that I cannot even conceive of a philosopher who might believe this.

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  23. I really like the idea of metaphysical possibility falling between logical and physical possibility (though I’d imagine this would be a point of attack) and the concept of it collapsing into one or the other.

    The analogy I like to use in discussions of p-zombies is to say, “imagine a universe exactly the same as ours in all physical respects, except that in this universe gasoline does not explode when you throw a lit match on it.” To me, this makes the problem with Chalmers’ intuition obvious, but judging by the discussion about H2O above, it seems this doesn’t work for everyone.

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  24. A child takes the garden hose and pours water into his father’s car’s gas tank, afterall he sees his father pour liquid into the car all of the time at the gas station. The father yells at the child that what he did is just plain wrong and stupid. The child grows up, wins a scholarship and studies chemistry and engineering, and invents an engine that runs on water. Because the father could not explain the chemical bonding properties of gasoline and water, his primary negative conceivability intuition seemed correct.

    Queue the zombie argument, human beings are biological mechanisms composed of smaller biological zombie mechanisms (cells) all the way down so the primary negative conceivability of consciousness or primary conceivability of zombies reveals either something is added or as Chalmers points out, the metaphysics of the ontological,epistemic,explanatory gap(s)……

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  25. Coel. Yes, I see your point. My response would be that Euclid proved that a highest prime is inconceivable, and that the teenager thought he could conceive of one only because his concept of a prime number was inadequate in the first place. Equivalently, a person who can conceive of a zombie would have an inadequate idea of what he is trying to conceive. We can conceive of anything at all if we do it badly, and we can use any word to name what we are conceiving. Many people can conceive of ex nihilo creation, or so they say, but nobody can make sense of the concept. Is that what counts as conceiving? I feel that if our concept of a phenomenon is incoherent, or not fully defined, then we are not conceiving of it in any meaningful sense.

    That is, I assume that for conceivability we must start with a clear definition of what we are conceiving and our conception must meet it in full. It is easy to poorly conceive of anything at all.

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  26. Hi PeterJ,

    Hi DM. I’m not sure what ‘valid’ would mean in this context. I cannot see any philosophical use for the Turing test.

    The Turing test is sometimes interpreted to be a test of consciousness based on behaviour. If a computer behaves indistinguishably from a human (as assessed by text-based conversation), then it is assumed to be conscious.

    I think that is a reasonably safe assumption, but this is a minority view. It is certainly rejected by Massimo. Your statement — “When we think we can imagine a creature that behaves like a human being but is not conscious I think we are kidding ourselves.” — implies that you ought to agree with me. If you have doubts about the Turing test, you should reconsider your statement.

    You might amend it as follows:

    “When we think we can imagine a creature that is physically and behaviourally like a human being but is not conscious I think we are kidding ourselves”.

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  27. Hi Coel,

    The only difference is that by “physical laws” we mean a superset of descriptions that includes the logical laws.

    I’m not sure there’s much purpose in continuing this conversation on this thread. I just wanted to point out that your usage of these terms is controversial if not entirely idiosyncratic and so you are likely to be misunderstood or engaged in endless talkings-past-each-other.

    Even if you think logic is derived from physics, just remember that what most people mean by logic is Aristotelian logic, while what most people mean by physics is that which is descriptive of the empirical behaviour of the universe at a low level (i.e. GR + QFT and other laws derived from them).

    For almost everybody, this excludes logic because most people do not think logic is empirically determined (although I recognise that you do). If you don’t want to make every discussion about physics and logic about this issue, I suggest that you use terms as others do.

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  28. Coel,

    You might like these two papers.

    How (from a physicalist’s perspective) logic and math is a particular part of the physical world:

    Mathematics in a Physical World

    Click to access szabo-math_in_physical-v2.pdf

    Mathematical facts in a physicalist ontology

    Click to access LESzabo-math_in_physical-preprint.pdf

    “mathematical and logical truths express objective facts of a particular part of the physical world, namely, the facts of the formal systems themselves”

    from http://phil.elte.hu/leszabo/publications.html

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  29. Hi DM,

    Even if you think logic is derived from physics, …

    I think it’s derived from experience of the universe (not derived from physics, though physics is also derived from experience of the universe).

    … just remember that what most people mean by logic is Aristotelian logic, while what most people mean by physics is that which is descriptive of the empirical behaviour of the universe at a low level …

    Are you suggesting that Aristotellian logic is *not* descriptive of the empirical behaviour of the universe? Does this logic not work when applied to the universe?

    … this excludes logic because most people do not think logic is empirically determined …

    OK, but how we arrived at logic is a different matter from your last point, whether logic *describes* the universe. As you say, I do consider that logic, maths and physics all derive from our experience of the universe.

    I’m not trying to make everything about this point, but as a comment on an article that carefully distinguishes between “logically possible”, “physically possible” and “metaphysically possible” it is relevant.

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  30. All right, so, I guess we could put it this way. For most people, physics is empirically determined while logic is not. For you everything is empirically determined so there is not much to distinguish the two. Furthermore, you think that there could be universes which worked according to different logical principles. This is a controversial position and I think it is incorrect.

    It is not my intention to argue any of these points here but rather to encourage you to describe as physics that which is uncontroversially empirically determined and to describe as logic that which seems to most people not to depend on any empirical fact.

    However, I take your point that if you could show that logic and physics are the same thing, then it would seem that Chalmers’ argument would dissolve, so what you are saying may not be irrelevant, in which case I should probably drop it!

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  31. “Epistemic and temporal/historical/contingent” is indeed the most important issue for all disciplines. You have done an excellent job on showing that Chalmers’ four point logic is wrong. I would like to make only two supplemental points.

    One, the validity of the conclusion of any logic (induction, deduction or else) can always be verified ‘independently’, that is, outside of the logic framework. In this case, the physicalism is totally true because that we can show its ‘framework’ to be a solid reality. Of course, I will not show ‘that’ right now in this short comment.

    Two, the validity of the conclusion of any logic is always ‘conditional’, the validities of it preceding statements (including the ‘definition’ of the terms). You have showed that Chalmers’ statement [3] is not logically sound. I would like to go one step further. Chalmers’ using the term ‘consciousness’ is not a good scientific definition. It is about a human-like ‘consciousness’. With this one-tier definition, it automatically prevents it being a proper definition outside of this ‘tier’. Thus, it has no chance to go into other tiers, let alone to say that the physicalism is about the framework at the ‘lowest’ tier.

    In general, a definition must be ‘all’ encompassing. Thus, the un-consciousness can be defined as 0-consciousness. Low-consciousness can be defined as x-consciousness. I have given a scientific definition for consciousness.

    Consciousness = the ability of a ‘self’ to distinguish itself from ‘others’.

    This is a very precise definition, with only three key words.
    1. Ability to distinguish
    2. Self
    3. Others

    All these three really come down to only one issue, a ‘uniquely’ way of tagging all entities in this universe. In fact, when every ‘self’ is uniquely tagged, the ‘others’ are also defined. In human (or many animals) level, the ‘skin’ is a good divide for the self from the others. For the twin who share a same body, the ‘brain’ can be the unique tag. For proton or electron, they are definitely uniquely tagged per Pauli’s excluding principle. That is, they also have the ‘ability’ to distinguish itself from others. Thus, all fermions are ‘self’-conscious, which of course becomes the physicalism-base for the higher-tier consciousness. A rock is obviously having no consciousness on happiness and love, but it definitely has the ‘space’ consciousness, as it will not give up its space without putting up a fight. With a ‘proper’ definition, the stone-space-consciousness is not in conflict with the emotional-and- intelligent-human consciousness.

    “As plenty of commentators have noted, Chalmers’ argument is deductively valid, i.e., if its premises are true, then the conclusion must logically follow.”

    Now, we know that Chalmers’ argument is ‘not’ deductively valid, as he did not even give a ‘proper’ definition for ‘consciousness’.

    “Philosophically, what is interesting here is that ever since Hume, many philosophers have treated the laws of physics as metaphysically contingent, in the sense that they could have been otherwise.”

    This is another key issue. If physics law is made out of concrete, why can it be made of wood? Just having different strength. So, the whole issue is about ‘what is the physics law made out of?’

    If physics law is made out of ‘one thing’ which cannot be substituted by any other things, then it is unique and cannot be otherwise. This ‘one thing’ can have two types.
    A. There is no other thing can substitute this ‘one thing’.
    B. Everything which substitutes this ‘one thing’ turns out to be ‘identical’ to this ‘one thing’.

    Can we find such a ‘one thing’ in this universe? This is a big issue. Let me make a suggestion, the ‘nothing’.

    “Nothing” is in fact encompassing the both types. It cannot be substituted, and every substitution will definitely turn out to be itself. Yet, the key issue is that “Is ‘nothing’ a part of this universe?” This is a big issue, and I will not discuss it here. But, if it is and if it gives rise to physics laws, then physics laws must be ‘unique’ and cannot be otherwise.

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  32. Hi Disagreeable Me,

    “If a computer behaves indistinguishably from a human (as assessed by text-based conversation), then it is assumed to be conscious”

    If a computer behaves indistinguishably from a human (as assessed by text-based conversation), would you also consider it a reasonably safe assumption that it digests food? If you don’t, why then consciousness and not digestion?

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  33. “Logically consistent” means does not violate some rule about how things are.

    All men are women
    All women have green tentacles
    Therefore, all men have green tentacles

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  34. Hi Asher,

    That is logically consistent in that it doesn’t violate rules of logic. Thus there are *some* rules about how things are that are not violated. There are, though, other descriptions of the world that it does violate.

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  35. It’s embarrassing to admit, but I’m not sure I understand the actual proposition in #2, part of which seems to be stated in #3.

    Since it’s part of a modus tollens arguments, perhaps it would be better to try to be just a little more formal?

    If, and only if, there is a world we live in in which everything that exists, including consciousness, that is physical,
    then, there is a metaphysically possible world which contains only everything that exists, including consciousness, physically indistinguishable from our world.

    I don’t think I can rephrase this without omitting “contains.” Now so far as metaphysically existing in this possible world, if we think as, so many people do, that science is only the measurements and observations, then all the concepts and interpretive framework for the experimental results can be deemed products of reason, i.e., metaphysics, Metaphysically existing then is the logically possible, i.e., consistent or coherent, principles corresponding to the set of physical facts. In a Venn diagram, metaphysically possible is the intersection of two categories of true possibilities. One is all the physical facts possible, that correspond to reality. The other is all the logical possibilities, everything that is logically consistent or coherent. On a charitable reading, “metaphysically possible” and “contains” are intelligible.

    But is it logically necessary that there is a unique set of metaphysical possibilities that correspond to the physical facts? If so, the consequent above should be amended to read “contains only,” not just “contains.”
    If not, then Chalmers could be correct about the possibility of conceiving our universe without consciousness, yet since we can also conceive the one we actually have, the conclusion doesn’t follow.

    (Also, in the different context of critiques of materialism, it is denied that the universe can be logically demonstrated to be consistent. In which case, unless #1 is amended to assert this, we cannot accept the existence of any metaphysically possible worlds, with or without zombies. But this is a nitpick.)

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  36. Very nice, but I see some problems. I will single this one out: if the laws of physics are assumed to constrain the metaphysical modality, but we can assume that they could change or be rather different (when we are considering the metaphysical modality), then why zombies are “impossible (in this universe)”? Physicalism is no logical necessity, but it’s not a physical necessity either, and even if it were, it would be only relative to some prior specification of physical truths (and that seems like a regress waiting to happen). Something seems to be wrong here. No logical truth will tell you which physical truths are necessary, and no physical truths will tell you that either. Then, either you abandon matters of modality regarding physical truths (and then it’s pointless to argue against p-zombies or in favor of physicalism) or you will need metaphysical modality to be something prior to physical modality at least.

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  37. Hi Marc,

    If you don’t, why then consciousness and not digestion?

    Recall that I am replying to “When we think we can imagine a creature that behaves like a human being but is not conscious I think we are kidding ourselves.” This point was not about digestion.

    I don’t want to dodge your question, but I’m not trying to turn this into another debate on computationalism.

    I just find it strange that the same people who find the idea of a philosophical zombie incoherent when described in those terms find the idea of human behaviour without consciousness to be perfectly reasonable when we’re talking about computers.

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  38. Michael Weisberg, a philosophy professor at the University of Pennsylvania has a similar gripe about all this talk of “water being H20”.

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  39. Hey Massimo. Beautifully written, as always.

    You said P-zombies, as it turns out, are physically, and therefore metaphysically, impossible (in this universe), though not logically so.

    I’m not convinced that P-Zombies are logically possible, based on the following premises:

    1. Consciousness is necessarily an information process. (This is the premise most likely to be attacked, but I will start by saying I defy you to describe a conscious event that doesn’t involve a pattern recognition.)

    2. Information is a property of matter, and so, any information process requires matter. (You can describe an information process mathematically, but you cannot perform one without matter.)

    So is it logically possible that Consciousness is not an information process?

    James

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  40. Myself, I’m quite confused by the title “p-zombies are inconceivable”. You certainly havent argued for that, Massimo. To do that you would have to argue, Dennett style, that there is no coherent conception of such entities but you expressly find such arguments uncompelling. You have argued the p-zombies are not physically possible and that we should be skeptical of a space of metaphysical possibilities over and above physical possibilities. Yet, as you note, I can conceive of many impossible things, physically or otherwise: “Well, in that sense, I can certainly conceive of a p-zombie, and of a lot of other nonsensical objects as well. Heck, I can fool myself that I can even conceive of a squared circle, which is mathematically impossible.” At best you could say that p-zombies are inconceivable in this world given its laws of nature but thats a very strange use of “inconceivable”.

    A lot is contained in the promissory note to the effect that physicalism “just happens to be the best (in the specific sense of most fecund) metaphysical approach to understanding the world.” Chalmers could certainly contest this. You dont do a lot to motivate the view here but it seems to me to be the real center of the disagreement.

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  41. A few thoughts on possibility/conceivability. I take it that language is compositional and productive. By that I mean that in possessing a language I have at my disposal certain items, for instance words, and rules on how to put them together. “The cat sat on the mat” is following the rules properly while “cat sat mat on the the” is not. Neither is “The cat cat on the mat” because “cat” is not a verb. Statements are true when objects meet the conditions stipulated. Language is productive in the sense that given a few items we can combine them according to linguistic, grammatical procedure in infinitely various ways. I hold and want to defend the idea that any grammatical combination is therefore meaningful.

    One might be tempted to say that “The highest prime number is red” is a nonsensical statement. But why? And what sort of nonsense is it? Certainly not of the same sort as “Supercalifragilistic expialidocious Iggily biggily Gollygoops Ittly bittly” which does not start from meaningful linguistic items. Neither can it be of the sort which includes “cat sat mat on the the”. “The highest prime number is red” is a well formed, grammitical English sentence. Well you might argue, Wittgensteinian interlocutor of mine, that the notion “highest prime number” or the notion that numbers could bear colors is confused such that phrases like “the highest prime number” and sentences like “The highest prime number is red” are nonsense. I believe this is a mistake. When uttering “The highest prime number is red” we are in exactly the same business as when uttering “The cat sat on the mat.” In the first we claim there is some object, it is a prime number, it is higher than the other prime numbers and it is red. In the second we claim there is (or was) some object, it was a cat and it sat on a mat. Both are making claims about objects and what they are like. The former is more exotic in that we happen to know that no object can ever satisfy the description “highest prime number” because doing so would cause a contradiction in our mathematics. I say *cause* and not *be* a contradiction because the bare notion “There is a highest prime number” by itself does not contradict, but in combination with other mathematical notions it implies a contradiction or so I am told from mathematicians who seem honest enough to me. Yet we should not conclude from the fact that no object could ever satisfy a description that it is meaningless. After all when mathematicians were wondering whether or not there was a highest prime were they not asking a meaningful question? When we say “There is no highest prime number” is not that meaningful? Why then not “There is a highest prime number”?

    Its hard to always remember the way Russell and Quine showed us out of Plato’s beard. Its important to remember that when we talk about the actual the possible and the impossible we are not sorting out three kinds of objects in the world (or in all possible worlds) even though it can often feel that way. When I use a description like “the possible fat man in the door way” it seems like I’m referring to an object (a very exotic kind of object in that it is a possible one) in the same way I am referring to an object when I use the description “the computer I am typing on”. Yet this is mistaken and leads to contradiction (ie The possible fat man exists.) Its better to see three kinds of descriptions some of which are satisfied (actual) some not but could be (possible) and some which can never be satisfied (impossible). Its tempting to think that if a statement is meaningful it relates to some object (actual or possible) and if not then it is meaningless or nonsensical. This is where the dictionary definition of conceive: “to form a mental representation of [something]; to imagine.” leads us quite astray. Notice: some*thing*. I think this is what motivated Massimo to say “…in that sense, I can certainly conceive of a p-zombie, and of a lot of other *nonsensical* objects as well. Heck, I can *fool* myself that I can even conceive of a squared circle, which is mathematically impossible.” (emphasizes obviously mine) Well objects are not nonsensical, descriptions are, so what I think MP means here is that the description “a square circle” is nonsensical and presumably on the grounds that it can never be related to an object. I think that is false. It is a description that no object can ever satisfy but what of that? It is still meaningful. In fact we know no object can satisfy it *because* it is meaningful. Likewise there is no need to “fool” ourselves. I understand (let’s say..) what a square circle or highest prime is supposed to be. Is that conceiving? I think it is. Is it conceiving of some*thing*? Certainly not, but why should that be a problem?

    Well that got out of hand. Hope someone actually reads it. 🙂

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  42. Peter J,
    I think the student (or myself for that matter) conceives of it in the following way: there is some object, it is a prime number, it is higher than any other prime number. I challenge you to show me any conceiving which is more robust than this. I would likewise be gratified if you saw my (admittedly lengthy) comment below. 🙂

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