Mental Exhaustion: If It’s Not Physical Then What Is It?

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I'll bet you thought that if you were mentally exhausted it was because of all the energy your brain just expended. Turns out it's probably not so; rather, what you believe makes it so. From Scientific American:

Unlike physical exercise, mental workouts probably do not demand significantly more energy than usual. Believing we have drained our brains, however, may be enough to induce weariness.

Let me place this in context. Atheistic materialism is committed to the theory that everything about our minds is explained by the physical activity in our brains. What we think has absolutely no effect on our physical selves; it's always the other way around.

It's an absurd theory on many levels, and this article reveals one more reason to reject it. It notes that difficult mental workouts are associated with stress in other bodily systems, which might also explain the weariness, and yet not all of it. Attitude matters:

Equally important to the duration of mental exertion is one's attitude toward it. Watching a thrilling biopic with a complex narrative excites many different brain regions for a good two hours, yet people typically do not shamble out of the theater complaining of mental fatigue. Some people regularly curl up with densely written novels that others might throw across the room in frustration….

Such fatigue seems much more likely to follow sustained mental effort that we do not seek for pleasure—such as the obligatory SAT—especially when we expect that the ordeal will drain our brains. If we think an exam or puzzle will be difficult, it often will be.

If materialists are right, and everything about the our mental states is explained by physical causes, then how is it that in this case our physical state is partly explained by our mental states? Why does belief affect our bodies?

I expect some will answer that the attitudes that cause mental weariness are themselves entirely the result of electrochemical activity in our brains. That doesn't resolve the issue. Either attitudes (beliefs, ideas, etc.) have effects or else they do not; and if they are entirely the product, the “epiphenomena,” of electrochemical activity, then it's only the electrochemical activity, not the attitudes or beliefs, that has any effect.

It's further evidence of materialism's multi-level absurdity.

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40 Responses to “ Mental Exhaustion: If It’s Not Physical Then What Is It? ”

  1. I don’t really know any atheists who think mental processes and thoughts are the one thing in the universe that cannot cause other things….

  2. Why does belief affect our bodies?

    I thank God that they do, especially around mile 23. 🙂 It’s the only thing that keeps my body from quitting.

  3. @SteveK
    Isn’t that the truth, eh? 🙂
    After 32km, it’s all grit and determination that makes me run that last 10K race.

  4. Hi Tom,

    I followed the link that you provided in your post, and it seems to me that you misread what the article is saying.

    In your second paragraph, you acknowledge that difficult mental workouts can stimulate the release of stress hormones which create a feeling of exhaustion. If you look closely at the article, you will see that this is the main point it’s making. According to the author,

    “Taking an exam that partially determines where one will spend the next four years is nerve-racking enough to send stress hormones swimming through the blood stream, induce sweating, quicken heart rates and encourage fidgeting and contorted body postures. The SAT and similar trials are not just mentally taxing—they are physically exhausting, too.”

    The author goes on to cite research in which college students who engaged in intellectually challenging activities had higher levels of the stress hormone cortisol in their blood than students who engaged in less challenging activities. However, instead of discussing these results, you say that stress explains only some of the weariness, “not all of it.” You proceed to quote the article, but the quote you give is taken out of context and does not support the statement that there’s anything other than stress to which we can attribute the feeling of mental exhaustion. The whole point of the article is that these feelings might be explained by the same physiological phenomena that cause us to feel stressed out.

  5. Robert, clearly the article said that those physiological phenomena contribute to that exhaustion. Clearly it said that beliefs contribute to it also, and to the very stress to which you refer here.

  6. Tom,

    I’m afraid I don’t understand what you’re saying here. It seems to me that attitudes and beliefs are the result of experiences which are recorded physically in our memories. For example, if I have a bad experience in a math course as a child, I may decide that I don’t like to do math. If later on I have to read a book with lots of equations, then I’m going to experience a feeling of mental exhaustion. The article is simply saying that this may be the result of my brain releasing the same hormones that cause stress.

    You seem to be talking about something different here. It sounds like you’re saying that belief is something nonphysical–something that cannot influence my body. Is that right?

  7. You’re right, I’m talking about something different.

    I’m not sure “decide” is the best word to describe what happens after a bad experience. I wish I could use it because my point would be easier to make; but sometimes we get imprinted with beliefs, expectations, and emotional reactions regardless of whether we decide to do so. So let’s say instead that having had a bad experience with math as a child, we end up, by whatever means, with a set of beliefs, expectations, and emotional associations connected with doing math as adults.

    Now, what are these beliefs, expectations, etc.? Reductive materialists say they are strictly and 100% the result of neurophysical events, and that these neurophysical events are 100% governed by natural law, all the way down to the level of subatomic particles. Some say that mental events are emergent properties that arise out of the complexity of these events, and some say they are epiphenomena, which are best described as passive passengers riding upon the physical events. Whichever you choose, you have one-way causation: the physical events drive the mental states, and there is no return ticket: mental states are caused by but do not cause physical events inside the brain or anywhere else.

    This article recognizes, as do I, that there is a physical component to all behavior including our thoughts. But it allows at least some causal efficacy to beliefs, which is problematic for atheistic/reductive materialists, because as I just outlined, beliefs as mental states shouldn’t be able to cause anything, if such materialism is true.

    My position is that mental states like beliefs, rational processing, decisions, etc. can have causal effects in the physical world. This is indeed something nonphysical, but obviously it can influence my body, otherwise I couldn’t do anything at all on account of deciding to do it. I couldn’t express a chosen opinion based on my prior beliefs. And so on.

  8. Regarding your notion of the “context”:

    Atheistic materialism is committed to the theory that everything about our minds is explained by the physical activity in our brains.

    That’s an awkward paraphrase (“is explained by” is the wrong wording – “is attributable to” works better), but let’s call it close enough.

    What we think has absolutely no effect on our physical selves; it’s always the other way around.

    That’s a nonsensical strawman that comes perilously close to being “word salad.”

    If, by “what we think”, you are referring to “conscious thought”, this is understood to be a summary result of previous experience (including memories of previous internal reactions to external stimuli, as well as memories of the stimuli themselves). It is a reflection of how the brain (in its current state) has dealt with both external and internal sensation previously. As such, it most certainly does serve as a useful indicator of how an individual will respond the next time a particular stimulus (or internal sensation) occurs.

    In other words, “what we think” (including the notion of “attitude”) clearly does affect our response to the next physical event (whether external or internal), because “what we think” is itself a product of the particular brain state that produces the response.

    What people typically refer to as “free will” should actually be referred to as “inclination to learn.” You may “choose” (in the sense of “free will”) to continue to act as you have in the past with regard to particular events – this can (should) be understood to mean that you have not learned anything that would induce you to behave some other way. (Sometimes this is the appropriate response, because in fact nothing about those events has changed, so repetition of a previous response continues to “work” for you.)

    Alternately, you may “choose” to respond differently than in the past – this means you have either acquired more knowledge about the events, or are seeking to acquire more knowledge through experimentation using different responses.

    In terms of causation, a change in response could be triggered either by dissatisfaction with the results of a previous response to similar events, or by a sufficient degree of comfort that the consequences of possible failure from some novel response are tolerable.

    In any event, it’s a complicated business, and while understanding it in purely natural terms is hard, trying to maintain that a supernatural “explanation” leads to any better understanding is much harder.

  9. Tom,

    I agree that “decide” was a bad word to use. What I meant was something more along the lines of what you said.

    Now that you’ve clarified your position, I think we’re talking about something quite different from the article. I disagree that the article “allows at least some causal efficacy to beliefs, which is problematic for atheistic/reductive materialists”. The notion of “belief” that it is dealing with is something is something very physical in nature, consisting of emotional associations and expectations recorded by our brains. If we agree to use the words “attitude” and “belief” to refer to this sort of thing, then there’s no problem with the idea that our attitudes and beliefs influence our physical bodies.

  10. I’d also like to hear more of your thoughts about materialism. In your last post, you wrote

    “Reductive materialists say they are strictly and 100% the result of neurophysical events, and that these neurophysical events are 100% governed by natural law, all the way down to the level of subatomic particles.”

    If our brains do not obey the known laws of physics, it just means that our understanding of the nature is incomplete. The purpose of science is to understand and describe such things. In a hundred years, maybe we’ll know how the mind works and why we have consciousness. It’s conceivable that an understanding of the mind will require totally new laws of physics which are completely beyond our present knowledge.

    When you start to think about things in this way, it becomes clear that the notion “supernatural” doesn’t really make sense. If something happens in nature, then it is natural by definition. What would it mean to say that something was above or beyond nature? Even if God does exist, couldn’t we just regard him as a part of nature? Couldn’t we just regard miracles as rare natural events which can in principle be studied using methods of science?

    For these reasons, I don’t think that “materialism” is really an assumption about the world. In science we study things that are “natural” and “material” because it’s not clear that the alternative makes any sense.

  11. “Atheistic materialism is committed to the theory that everything about our minds is explained by the physical activity in our brains”

    no, it’s not “committed to the theory”, it’s simply the conclusion based on the evidence, all of which points to a materialistic picture of the Universe, and the human mind.
    Unfortunately for aspiring dualist of theistic bend, the overwhelming consensus in academia is not on your side here, Tom. So what is more likely: that the experts in this area– virtually all neuroscientists and the vast majority of philosophers of mind, have gotten it completely wrong and have misinterpreted the evidence, or that a layperson like yourself is dismissing the evidence in an attempt to hold on to his feel-good religious beliefs

    “materialism’s multi-level absurdity.”

    well, given that a materialistic view of human mind is the orthodoxy in academia, and is more or less considered to be as well established as the germ theory of disease, you have a lot of work to do before you convince us of the “absurdity” of materialism, and that long discredited “theories” such as substance dualism and the like, which currently lack any credibility whatsoever, should be proffered over what is essentially the reigning paradigm today. good luck with that :]

  12. @Robert Jones:

    If our brains do not obey the known laws of physics, it just means that our understanding of the nature is incomplete. The purpose of science is to understand and describe such things.

    No one doubts that our brains, being material bodies, obey the laws of physics.

    The claim is that the mind is not reducible to the brain, a purely philosophical claim by the way, needing no introduction of any God talk, at least not in any direct fashion.

    It’s conceivable that an understanding of the mind will require totally new laws of physics which are completely beyond our present knowledge.

    If that is conceivable, it is also conceivable that no naturalist explanation will be found for consciousness (e.g. the position of Colin Mcginn, a naturalist) or that naturalism cannot, not even in principle, explain consciousness which is the position of dualists of all stripes, with the help of arguments from lots and lots of naturalists — Searle, Chalmers, Nagel, Fodor, etc. (this is for the the ignorant idiots that invoke the “consensus of the academia”).

    If something happens in nature, then it is natural by definition. What would it mean to say that something was above or beyond nature? Even if God does exist, couldn’t we just regard him as a part of nature? Couldn’t we just regard miracles as rare natural events which can in principle be studied using methods of science?

    You are using the word “nature” equivocally, which is not really bad, because it is notoriously very difficult to define and separate the “natural” and the “supernatural”. But in fact, I think you are closer to the truth, in that I would say that supernatural only applies properly to God himself (for reasons I will not explain here).

    The rest is just the usual incoherent scientism. Such as:

    In science we study things that are “natural” and “material” because it’s not clear that the alternative makes any sense.

    Why don’t you go tell that to mathematicians? I am sure they would love to hear that their work makes no sense.

  13. G. Rodrigues,

    You write

    “it is also conceivable that no naturalist explanation will be found for consciousness (e.g. the position of Colin Mcginn, a naturalist) or that naturalism cannot, not even in principle, explain consciousness”

    Can you give me an example of a phenomenon that would contradict naturalism or provide evidence for the supernatural? What does it mean to say that naturalism cannot, even in principle, explain consciousness?

    You go on:

    “Why don’t you go tell that to mathematicians? I am sure they would love to hear that their work makes no sense.”

    I happen to be a mathematician, and I was not talking about mathematics when I mentioned the “alternative” to materialism. I was referring to theories in which the world has a “nonmaterial” or “nonphysical” aspect. I don’t think that mathematics is relevant here because in mathematics we do not study reality in the sense that scientists do.

  14. @Robert Jones:

    Can you give me an example of a phenomenon that would contradict naturalism or provide evidence for the supernatural?

    First, slash “supernatural” because the argument is not, and cannot be, naturalism is false therefore God. Second, let us get clear on the meaning of naturalism. By it I mean, metaphysical naturalism, a philosophical position, *NOT* science.

    As for examples, intentionality, qualia, consciousness, first-person subjective view, personal identity, reason, etc. These are all phenomena exhibited by the mind around which arguments against metaphysical naturalism can be constructed, and positively, construct arguments for *some* sort of dualism.

    What does it mean to say that naturalism cannot, even in principle, explain consciousness?

    What is misteryous about the claim? Metaphysical naturalism does not have the resources to explain consciousness, so a consistent naturalist has to deny the very existence of consciousness as traditionally conceived, and cash out the phenomena in some other terms, which by the way is a position advocated by eliminative materialists like the Churchlands or Rosenberg.

    Maybe I should have said “cannot explain” by “explain away”, but since frew naturalists take the eliminative road (because it is patently incoherent, but I would argue, unavoidable for a consistent naturalist) such conflation is harmless.

    I happen to be a mathematician, and I was not talking about mathematics when I mentioned the “alternative” to materialism. I was referring to theories in which the world has a “nonmaterial” or “nonphysical” aspect.

    First, there is sizeable portion of Platonist mathematicians. There are variations within the Platonist camp, but in general, if mathematical Platonism is true, reality has “nonmaterial” or “nonphysical” aspects.

    But you make a fair point: you meant the modern empirical sciences and the material world. But then you should drop “I don’t think that “materialism” is really an assumption about the world”; of course it is, it is a very definite metaphysical claim about the whole of reality — either that or you are using the word “materialism” in a completely different sense. You should also realize that “In science we study things that are “natural” and “material” because it’s not clear that the alternative makes any sense” is then either false or a tautology, depending on how you construe “science”, “natural” and “material”, the last two being particularly hard to define, so much so, that it almost seems that you intended to make “natural” an all-encompassing word.

  15. G. Rodrigues,

    First of all, I think the word “supernatural” means something different to you than it means to me. You said in one of your posts that only God himself can really be called supernatural. When I asked you about evidence for the supernatural, I was not asking you to argue for the existence of God. I was just asking if there is any observable phenomenon that you would consider to be “separate” from nature, or somehow “above” or “beyond” the natural world.

    The examples that you gave were

    “intentionality, qualia, consciousness, first-person subjective view, personal identity, reason, etc.”

    Obviously nobody understands why we experience consciousness, but I see no reason why we cannot continue to attack the problem scientifically. Maybe someday we’ll understand consciousness, or maybe we won’t. But I think the fact that it’s part of our experience makes it automatically a part of the natural world. I don’t think there’s any sensible way to define the word “natural” other than to say that it’s what we experience.

    You also made the following comment about mathematics:

    “First, there is sizeable portion of Platonist mathematicians. There are variations within the Platonist camp, but in general, if mathematical Platonism is true, reality has ‘nonmaterial’ or ‘nonphysical’ aspects.”

    One interesting thing about mathematics is that there’s very little disagreement or debate among mathematicians. Since mathematics is all about logically deducing things from clearly stated assumptions, there’s little room for disagreement about results of mathematics. The same is true, I think, about philosophical questions in mathematics. It’s true that some mathematicians are more outwardly Platonist, but I think most mathematicians would agree that there is a sense in which mathematics is real and also a sense in which it’s not. It all depends what you mean by “reality”.

    Mathematics is real in the sense that two independent people starting with the same axioms would be able to prove the same theorems. This has nothing to do with the empirical reality that we’re talking about. I think it’s perfectly fair to say that materialism is not an assumption about the world. The fact that I’m excluding mathematical “reality” from the equation is irrelevant unless you’re claiming that our mental states live in the Platonic world of mathematical concepts.

  16. @Robert Jones:

    I think you are right and we are indeed talking past each other, at least up to a point. So let me try to clarify the pertinent points.

    Obviously nobody understands why we experience consciousness, but I see no reason why we cannot continue to attack the problem scientifically. Maybe someday we’ll understand consciousness, or maybe we won’t. But I think the fact that it’s part of our experience makes it automatically a part of the natural world. I don’t think there’s any sensible way to define the word “natural” other than to say that it’s what we experience.

    First, there is a definition of metaphysical naturalism, which is the one I have been using throughout (probably dropping metaphysical here and there). You on the other hand, do not seem to have a precise definition of “natural”. What we experience? Some people report that they experience God, so should we count God as natural? That certainly will not do, on yours or my world views. If you cannot define what is “natural” then it is meaningless to say that we will understand (or not) consciousness in “naturalistic” terms. It also makes it a tad difficult to comply to your request of “observable phenomenon that you would consider to be “separate” from nature, or somehow “above” or “beyond” the natural world.” What are you asking for exactly? Does saying that I am a Christian help somehow? Obviously intentionality, qualia, reason, etc. are phenomena and they are natural, insofar as they are part of the whole created order. But you missed the crucial follow up, so I will quote myself:

    These are all phenomena exhibited by the mind around which arguments against metaphysical naturalism can be constructed, and positively, construct arguments for *some* sort of dualism.

    For the arguments, check the relevant literature.

    It seems to me that you think in order to vindicate dualism (of any stripe), we must have a very certain specific set of evidence (e.g. “supernatural” empirical phenomenon amenable to the scientific inquiry), but that is a scientistic claim that I completely reject.

    Second, you say you “see no reason why we cannot continue to attack the problem scientifically”. But what are the questions that the modern empirical sciences can legitimately be expected to answer? Certainly *some* questions can be attacked by the empirical sciences, but not *all* questions can. The success of the modern empirical sciences is directly proportional to the delimitation of their field of study, in a nutshell, the metric quantifiable properties of material bodies. In fact modern empirical science rests on some metaphysical assumptions; these are not only more fundamental than the whole edifice of science since they support it, but they are more certain, since conclusions are only as certain as their assumptions.

    The same is true, I think, about philosophical questions in mathematics.

    In my admittedly little experience, most mathematicians care little and rarely worry about philosophical, foundational questions in mathematics. But I believe your claim is simply false. Besides, mathematical Platonism makes a definite ontological claim about the nature of reality, so I cannot make heads or tails of your sentence “It all depends what you mean by “reality””.

    Mathematics is real in the sense that two independent people starting with the same axioms would be able to prove the same theorems. This has nothing to do with the empirical reality that we’re talking about. I think it’s perfectly fair to say that materialism is not an assumption about the world.

    Correct in the first two sentences, but honestly, I do not know why you are even bringing this up. What I said was *if* Platonism is true, then metaphysical naturalism is false, at least in its common garden variety. I suppose you could still pull Quine-Putnam’s indispensability hypothesis… The last sentence is incorrect, insofar as materialism is a metaphysical claim about the nature of reality.

    note: I am *not* arguing for Platonism, in fact I reject it. I am just making a point about what arguments *for* metaphysical naturalism, and materialist monism in particular, must achieve.

    The fact that I’m excluding mathematical “reality” from the equation is irrelevant unless you’re claiming that our mental states live in the Platonic world of mathematical concepts.

    I was not pursuing this avenue, but no it is not irrelevant, since the ontological status of abstract concepts plays an important role in arguments for dualism (of all stripes). Look, *if* Platonism is true, and our minds are capable of conducting mathematical reasoning, then it is clear that there is something fishy about a wholly naturalistic account of our minds.

  17. Robert,

    First, I want to thank you for the good discussion. I really appreciate it.

    The distinction you draw between natural and supernatural needs a further look, though. You say, “I think the fact that it’s part of our experience makes it automatically a part of the natural world.” But consider how that works if miracles happen. If they happen, they are part of their participants’ experience and happen within the context of the natural world. Does that make them natural rather than supernatural? I think not.

    You might say that qualia, consciousness, intentionality, etc. are part of everyone’s experience and are therefore natural, but it seems to me that the principle, “it’s part of experience therefore it’s natural,” fails whether it’s a few, as in the case of miracles, or whether it’s many. You can’t define “natural” simply in terms of it being a part of experience.

    You also draw a strange distinction when you say, “I see no reason why we cannot continue to attack the problem scientifically.” Consciousness, qualia, and so on certainly have scientifically-addressable aspects to them, and no theist would deny that. The question is not whether they have natural facets to them, it’s whether they are entirely natural.

    And I think for our purposes here the more useful definition of “natural” is something along these lines: to be natural (as used here) is to be part of an uninterrupted chain of natural cause and effect, where that chain is best described in terms of impersonal and non-intentional natural law (known or yet to be discovered), and where each event is therefore the necessary and unavoidable effect of its antecedent causes. That’s the sense of the term that seems most relevant for this discussion.

    Any event that occurs as an exception to that impersonal and non-intentional causal flow as described by natural law, is therefore something other than natural. I don’t want to label every such event as “supernatural,” for reasons I’ll get to in a moment, but each such event (if such events occur) is certainly not “natural,” in the relevant sense of the term.

    Now, if those definitions are at all accurate, then any act of personal decision-making is arguably not natural. Either humans decide or we do not. If we decide, then either our decisions are the end product of unbreakable, unbendable, natural necessity, or they are not. If the former, then it seems strange to call that “deciding.” There’s no decision going on at all: there’s only neurophysical reactions going on and producing their inevitable and unavoidable outcome. Any sense we have of choosing is illusory.

    Now, science is the study of what regularly happens according to natural law. If human decision-making is real, then it happens at least partly outside the domain of natural necessity, and therefore it will always have an aspect to it that is at least partly outside the reach of science.

    Similarly for intentionality, also termed “aboutness:” either humans have thoughts about things or we do not. But natural entities, forces, effects, etc. are never “about” anything. A rock is not “about” the slope it is sliding down, or “about” gravity, and gravity is not “about” the sliding rock. They have no “aboutness” relation to one another. Science can obviously study rocks and slopes and gravity, but science qua science knows nothing of that “aboutness” relationship. And given what science claims to know about human origins, it’s very difficult to imagine where we got to the place where the topic of “aboutness” would even arise for discussion.

    So while there are scientifically addressable aspects to all these facets of experience, they retain some non-natural mystery. To call it “supernatural” is to conflate it with the controversial domains of God, angels, etc.; but clearly there is something going on in human experience that isn’t entirely natural (in the currently relevant sense of “natural”).

  18. AOR21, you say, quoting me first,

    “Atheistic materialism is committed to the theory that everything about our minds is explained by the physical activity in our brains”

    no, it’s not “committed to the theory”, it’s simply the conclusion based on the evidence, all of which points to a materialistic picture of the Universe, and the human mind.

    “The evidence,” you say. But the evidence you have to point to is that which is produced by science, which has no capacity to find anything but materialistic pictures. You think that because a carefully delimited discipline cannot find anything outside its careful delimited scope, therefore nothing exists outside that scope.

    I have two words to describe that: closed-minded and irrational.

    I am aware of the overwhelming consensus of academia. I am also aware of the sociological pressures within academia toward that conclusion. I am also very aware of how inept neuroscientists tend to be on this issue. And I know that philosophers of mind are not in absolute agreement on this issue, and that any philosopher of mind worth his or her salt would say that the argument from authority or from numbers is no argument at all.

    I am further aware that psychologizing my conclusions as “holding on to feel-good religious beliefs” is a game that could be played back and forth all day—you’re holding on to your feel-good atheism, right?—and all we would gain is a deeper sense of embittered entrenchment against each other, which makes the whole approach rather useless and childish.

    I am also aware that a materialist view of mind is not as well established as the germ theory of disease, which means that I can point to a simple error of fact in your argument, which doesn’t do your position much credit.

    Finally, as for “reigning paradigms,” thank you for that vote in favor of never changing our minds. Think of the once-regnant paradigms as the inherent inferiority of the African races, the geosynclinal theory for the earth’s dynamics, the wisdom of eugenics, … I’m not much impressed by the “reigning paradigm” argument, and I can’t imagine why you would be.

  19. G. Rodrigues,

    Let me start with this:

    “What we experience? Some people report that they experience God, so should we count God as natural?”

    I think you have to be careful here. Obviously there are many people who believe that they have experienced God. I would say that those experiences are real and deserve to be taken very seriously. I would also argue that such experiences are caused by something in nature, but the cause isn’t necessarily God.

    I also want to say a few words about this:

    “Look, *if* Platonism is true, and our minds are capable of conducting mathematical reasoning, then it is clear that there is something fishy about a wholly naturalistic account of our minds.”

    Perhaps I don’t know what “Platonism” is exactly. I always assumed it meant that mathematical concepts have a sort of “reality” which exists in some objective sense regardless of who’s doing the calculations. In my last post, I explained very precisely the sense in which mathematical concepts are “real”. If we take this as our definition of Platonism, then our ability to do mathematics does not imply anything fishy about the way our minds work. Doing mathematics is just manipulating symbols according to very precise rules.

  20. Tom,

    The definition of “natural” that you gave is the following:

    “And I think for our purposes here the more useful definition of “natural” is something along these lines: to be natural (as used here) is to be part of an uninterrupted chain of natural cause and effect, where that chain is best described in terms of impersonal and non-intentional natural law (known or yet to be discovered), and where each event is therefore the necessary and unavoidable effect of its antecedent causes. That’s the sense of the term that seems most relevant for this discussion.”

    I see a couple of problems with this definition. For one thing, it’s circular because you used the word natural twice in the definition.

    Even more seriously, I think that you display a huge amount of prejudice when you use words like “uninterrupted chain”, “cause and effect”, “impersonal and non-intentional”, “event”, “unavoidable effect”, “antecedent cause”, and so on. When you use these words, you’re assuming all sorts of things about the nature of time, causality, and determinism. You realize that in the twentieth century, science gave us radically new insights into all of these basic concepts, right? When you define nature, you don’t get to give it whatever attributes you like. Nature is the thing that we’re trying to understand, and we don’t want to confuse our prejudices about how nature ought to work with our understanding of how it really is.

    Looking over your post, it seems that you chose this definition precisely so you could claim that free will is nonmaterial and not amenable to a scientific treatment. I don’t think you are at all justified in making this claim. After all the things that science has taught us, how can you possibly say that we won’t ever understand free will?

  21. Robert, you are right about my overuse of “natural.” Just delete those two occurrences and it should solve the problem.

    Usually when I define philosophical naturalism I include chance in the scope of the definition. That should probably also be included in what I wrote here.

    So the revised version would go like this:

    to be natural (as used here) is (a) to be part of an uninterrupted chain of cause and effect, where that chain is best described in terms of impersonal and non-intentional necessity (commonly called “natural law,” including that which is known or yet to be discovered), and where each event is therefore the necessary and unavoidable effect of its antecedent causes; and/or (b) to be strictly an occurrence of chance.

    (b) is disputed by those who disagree with the Copenhagen interpretation of QM, but I don’t mind including it as a disjunct. Allowing (b) as an option does nothing to give nature (so defined) any intentionality or aboutness. It does nothing to permit human decision-making or personality. The problems I stated earlier remain.

    It seems you think there might be more to reality than this. What might that more be?

    (Caution: you seem to think science will take us there, but to make that assumption is to commit the science-of-the-gaps fallacy.)

  22. Tom,

    I think you’re missing the point here. I wasn’t saying that you could explain any of the mysteries of the mind by including chance in your definition of nature. I’m saying there’s some much more fundamentally wrong with what you’re trying to do.

    The problem is that you’re trying to define what nature is based on your own understanding of reality. This is not right. Nature is what it is. It’s the world around us, which we understand through our experiences and our senses. The purpose of science is to learn more about it, to understand it a little better by investigating it empirically. Therefore when you write

    “to be natural (as used here) is (a) to be part of an uninterrupted chain of cause and effect, where that chain is best described in terms of impersonal and non-intentional necessity (commonly called “natural law,” including that which is known or yet to be discovered), and where each event is therefore the necessary and unavoidable effect of its antecedent causes; and/or (b) to be strictly an occurrence of chance.”

    you’re saying all sorts of things that may turn out to be wrong. You’re viewing time as a sort of smooth continuum of cause and effect, for example, and I can easily imagine that that’s not how the universe is fundamentally. Perhaps space and time emerge from some more primitive building blocks which obey very abstract rules which are not causal in the usual sense. Perhaps the fabric of our universe does not consist of pointlike events as your definition implies. Perhaps the usual notions of probability are not the right way of thinking about quantum mechanics, and we’ll find out that physical necessity and chance are not the only options.

    Now you could try to change your definition to allow for all of these possibilities, but you would be making the same mistake all over again. My point is that you don’t know what nature is fundamentally. Nobody does. It’s best to think of science as a process of exploration and discovery. We’re just looking at the world around us to learn as much as we can. Of course there is a self-imposed rule which says we can only make falsifiable explanations, but we don’t make any assumptions about how nature works, not even metaphysical ones.

    And just to be clear, I make no assumptions about what science will teach us. It’s possible that eventually we’ll be able to understand things like consciousness and free will, or they may remain permanently out of reach of science.

  23. Robert, I agree that everything you say here is a possibility. It’s also highly speculative. Based on what we know of the world now, there is no natural explanation for the phenomena G. Rodrigues brought up, including intentionality, identity, reason, consciousness, and I would add free will. There is nothing even on the horizon to suggest that we might find natural explanations.

    Your science-of-the-gaps is evident when you say things like,

    If our brains do not obey the known laws of physics, it just means that our understanding of the nature is incomplete. The purpose of science is to understand and describe such things. In a hundred years, maybe we’ll know how the mind works and why we have consciousness. It’s conceivable that an understanding of the mind will require totally new laws of physics which are completely beyond our present knowledge.

    Remember that the trail we are on is toward a definition of nature. Such a definition is crucial so that we have some way, at least conceptually, to denote what is within nature and what is not. My point in this article was to say that beliefs and especially the act of believing are not explainable within the bounds of nature alone. Whether that’s true or not depends on whether there are definable (at least in theory) bounds to what is natural.

    Your approach seems to be that nature is whatever exists: “Even if God does exist, couldn’t we just regard him as part of nature?”

    If nature is everything that exists, then of course I am wrong. To define it that way, however, begs the question against theism, which takes it that God created nature, and that God’s person (not the effects of his actions, but his person) is far beyond the reach of scientific analysis.

    What I was pointing to originally here is that human believing is similarly beyond the reach of scientific analysis—not completely, but partially. The discussion has expanded to include the other phenomena in question. I am bold enough to say that I am just about absolutely sure that no science will ever explain the aboutness relationship, for nothing in nature as science understands it exhibits anything resembling aboutness. As a corollary to that, science will never find a fully physical explanation for the words “true” and “false,” for truth and falsehood are either true or false about some proposition. Further, therefore—and here we come back to where we started—science will never explain beliefs, for beliefs are beliefs that p is true or false.

    These are things of which I am quite sure: that science will never accomplish these things. I think they are pointers to a reality beyond the reach of science, a reality greater than physicalists and materialists will allow exists but which nevertheless does.

    Some think science will someday overturn my convictions on this, I would say they are persons of great faith in that which has no evidence for it. The only evidence they have going for them is the historic progress of science; but that progress has only been toward discovering absolute necessity or else absolute chance. It has done absolutely nothing toward solving these other kinds of problems.

  24. I understand, by the way, that you claim no such faith: that you say these things might remain forever out of the reach of science.

    What then do we do with that which is neither necessity nor chance? What do we do with that which is personal, with that which holds beliefs, with the aboutness relationship? I say they point to something beyond nature as I have defined nature. If you don’t like my definition of nature, perhaps you can at least agree that if one were to take nature to mean what I have said here, then these things point beyond nature, so defined.

    And if so, what is it that they point toward?

  25. @Robert Jones:

    I think you have to be careful here. Obviously there are many people who believe that they have experienced God. I would say that those experiences are real and deserve to be taken very seriously. I would also argue that such experiences are caused by something in nature, but the cause isn’t necessarily God.

    Now, I hope you see why your definition is not a good one. For if you say that what is “natural” is what we experience, then on what *a priori* grounds should we dismiss the reports of people that have experienced God? Certainly, some of them would be false, in that there were perfectly natural (there is that sneaky word again) causes for these experiences. But to rule out God *a priori* is just question-begging, but since it is clear that neither you nor I will want to class God in the “natural”, it seems that your definition simply will not do.

    Perhaps I don’t know what “Platonism” is exactly. I always assumed it meant that mathematical concepts have a sort of “reality” which exists in some objective sense regardless of who’s doing the calculations.

    Correct. One of the main theses, possibly the characterizing one, of mathematical Platonism is the *objective* existence of abstract, mathematical objects.

    But why it is *objective*? Precisely because, according to the Platonist, mathematical objects are real existent beings and are the truth-makers of mathematical propositions, so that mathematical truth is just a variety of the correspondence, realist account of what Truth (just like that, with a capital T) consists of.

    If we take this as our definition of Platonism, then our ability to do mathematics does not imply anything fishy about the way our minds work. Doing mathematics is just manipulating symbols according to very precise rules.

    I am loathe to correct a mathematician on its field of expertise but saying that “mathematics is just manipulating symbols according to very precise rules” is a itself a typical formalist claim (riffed from Hilbert?) that a Platonist would reject. Not only that; it is simply false to the very experience of doing mathematics. When a mathematician concocts a proof he is gaining *understanding* of what, for lack of a better word, I will call the mathematical universe (no implied Platonic adherence in this expression), *NOT* doing symbol pushing; we have computers to do that now. Once again, *if* Platonism is true, how can a purely material object, the brain, gain insight into the abstract immaterial realm of mathematics? This is just a simplified gloss; there are very powerful versions of these arguments, and in my own judgment conclusive, that purport to show that the mind *cannot* be identified or reduced to the brain, like J. Ross’s under-determination arguments.

    note: As the saying goes, one man’s modus ponens is another man’s modus tollens. In all fairness, my last (rhetorical) question can be turned into an argument *against* Platonism, the so-called epistemological argument. A modern exposition can be found in one of Benacerraf’s articles (the name escapes me right now, but I can dig it up if you want me to). Insofar as I understand it, I think the argument fails against mathematical realism; in fact it is even a non-starter because it relies on metaphysical assumptions that are highly dubious and that I reject.

    I will also butt in in your discussion with Tom Gilson (with my apologies), and just make two points. You say and I quote:

    You’re saying all sorts of things that may turn out to be wrong. You’re viewing time as a sort of smooth continuum of cause and effect, for example, and I can easily imagine that that’s not how the universe is fundamentally. Perhaps space and time emerge from some more primitive building blocks which obey very abstract rules which are not causal in the usual sense. Perhaps the fabric of our universe does not consist of pointlike events as your definition implies. Perhaps the usual notions of probability are not the right way of thinking about quantum mechanics, and we’ll find out that physical necessity and chance are not the only options.

    Besides what Tom said, I think this betrays a crucial misunderstanding of the arguments, which runs parallel to the continuous scientistic streak you (unwittingly?) display — more on this, below. The way you describe things, it is as if the arguments are gap arguments, but that is patently false. They are metaphysical proofs, much like a mathematical proof (minus the strict formalization aspect), some in the reductio form, taking as premises either what metaphysical naturalism claims or certain other metaphysical premises. Saying that the universe can be like this or that, is, besides a complete speculation, also besides the point, because the arguments do not rely on the specific details of how the universe works or on the specific details of our best current scientific theories, but rather on general philosophical grounds, grounds which science itself must presuppose to do its job. They maybe wrong on further evaluation, but your wild speculations does nothing to refute them.

    My point is that you don’t know what nature is fundamentally. Nobody does. It’s best to think of science as a process of exploration and discovery. We’re just looking at the world around us to learn as much as we can. Of course there is a self-imposed rule which says we can only make falsifiable explanations, but we don’t make any assumptions about how nature works, not even metaphysical ones.

    And here it is, scientism in all its glory: the problem is essentially philosophical not a scientific one. Of course empirical science can give input by its discoveries and even raise new questions, but it is not in its job description to give the *ultimate* answers. I am sorry, but you are wrong as wrong can be, because even to get science off the ground you have to make a ton of metaphysical assumptions (the universe is orderly, our senses are in general reliable, our reasoning capacity is in general sound, etc. and etc. and etc.). And what is the fundamental *postulate* of special relativity that the speed of light is the maximum possible speed if not an assumption? And what is the fundamental *postulate* of classical Newtonian mechanics that space-time is a four-dimensional affine space with a degenerate metric, the Galilean metric, which is euclidean in the spatial component, and where there is a special class of frames, called inertial frames, if not a whole procession of assumptions? I could continue with examples, but these two will have to suffice. You, a mathematician of all people, should know that the set of deductive entaiments of the empty set is just the empty set: ex nihilo nihil fit.

  26. Tom,

    I’m not sure how much more I can say about this without getting repetitive. I think you’re trying to make a very artificial distinction between the things things that you consider natural and everything else. You’re choosing your definition of the word “natural” specifically in order to label certain things as “nonmaterial” or “supernatural”.

  27. G. Rodrigues,

    “For if you say that what is ‘natural’ is what we experience, then on what *a priori* grounds should we dismiss the reports of people that have experienced God?”

    I didn’t say that we should dismiss their reports a priori. I am not trying, as you are, to exclude God from being part of nature. If God really exists and can intervene in the world that we experience, then it makes sense to consider him part of nature. Recall that, in one of my earlier comments, I wrote “Even if God does exist, couldn’t we just regard him as part of nature?”

    “I am loathe to correct a mathematician on its field of expertise but saying that ‘mathematics is just manipulating symbols according to very precise rules’ is a itself a typical formalist claim (riffed from Hilbert?) that a Platonist would reject. Not only that; it is simply false to the very experience of doing mathematics.”

    I’m afraid I have to disagree with you. Mathematics is a fascinatingly rich subject with many striking connections to science, but if you want to know literally what it means to do mathematics, I would say that it’s nothing more than working out the consequences of a set of precisely defined rules. I don’t think there’s anything mystical about it.

    “And what is the fundamental *postulate* of special relativity that the speed of light is the maximum possible speed if not an assumption? And what is the fundamental *postulate* of classical Newtonian mechanics that space-time is a four-dimensional affine space with a degenerate metric, the Galilean metric, which is euclidean in the spatial component, and where there is a special class of frames, called inertial frames, if not a whole procession of assumptions? I could continue with examples, but these two will have to suffice.”

    Maybe I should have been more clear. This is not what I meant at all. I recognize that all scientific theories are based on certain postulates. But I don’t think that all of the assumptions that you and Tom have been mentioning are really necessary for doing science. For example, you say we need to assume the world is orderly. Why would we need to assume that? If the world is not orderly, then all of our scientific theories will eventually be disproven, but that can’t stop us from trying to do science.

  28. I noticed you were getting repetitive, too, Robert, and I was already wondering when you would get on with the topic. Seriously.

    For I began, you see, and I have continued since then, by using a very standard definition of “natural.” That wasn’t good enough for you.

    So upon your objections, I turned it into what philosophers call a technical definition, one which may or may not be the ordinary usage of the word but which is useful in relevant ways for the current context. In other words, I tacitly granted you that “natural” may or may not normally be defined the way I have done here. Whether it is or not, my claim has been that the way I have defined it here is relevant for the current discussion. That was a concession I made to you, not because I thought it was strictly called for, but because I thought it would be better than fighting over what might or might not be the universally correct definition of “nature.”

    I have done that, for example, when I have said things like “for our purposes here,” or “the sense that’s most relevant for our discussion,” or “in the relevant sense of the term,” or “in the currently relevant sense of ‘natural,'” or “nature, so defined.”

    Meanwhile you give every evidence of wanting to define nature as being whatever is, known or unknown. That’s very idiosyncratic of you. It’s also hopelessly useless. You make the word mean everything, and as a result you make it mean nothing, for it denotes no distinctions.

    Furthermore you keep missing the point: you keep telling me that I am using the word “nature” incorrectly, while missing the shift I made toward using it as a technical term with a definition clearly delineated for use in this context. The more useful objection for you to make at that point would have been either (1) there is a better term than “nature” that I should have used to express what is contained in the definition I gave in this context, or (2) the topic or concept which I was thereby expressing is irrelevant to this context. You have done neither.

    Anyway, if it would make you feel any better I could quit using the word “nature” and use “glickmorj” instead, as the term expressing what I have up until now tried to express through the word “nature.” Then you couldn’t complain I was misusing it. I would go ahead and define it in exactly the same I was defining nature, we could have our conversation about “glickmorj,” and we might get somewhere.

    Either that or else we could talk about that which I have defined for these purposes, for this context by using a term that is quite commonly and generally used for that which that definition denotes, that word being “nature.” We could quite fairly treat it as a technical use of the word, and when we have finished having our discussion, then we could ask whether it was the right word for the purpose.

    Would you care to do that? Or would you prefer to use “glickmorj”?

  29. You say,

    For example, you say we need to assume the world is orderly. Why would we need to assume that? If the world is not orderly, then all of our scientific theories will eventually be disproven, but that can’t stop us from trying to do science.

    What is science if not the search for order? Who searches for what one does not believe exists?

  30. @Robert Jones:

    If God really exists and can intervene in the world that we experience, then it makes sense to consider him part of nature.

    Ok, then for you “natural” is a vacuous word as everything is natural. Fine, maybe you should just avoid using the word as you will only confuse people. Stick to the more or less standard definition of metaphysical naturalism then.

    I would say that it’s nothing more than working out the consequences of a set of precisely defined rules. I don’t think there’s anything mystical about it.

    I did not say that there was anything mystical, unless understanding the proper subject of mathematics is mystical to you, a very bizarre notion of mystical. But for the second time, no mathematics is “nothing more than working out the consequences of a set of precisely defined rules”. If it were that, we would program a computer to churn out the theorems entailed by a class of axioms. You could say that the method is not practical, but that is missing the point, the point is that mathematics is the attaining of *understanding* not symbol pushing. If it were “working out the consequences of a set of precisely defined rules” then there would be no valuation in mathematical results as they would all have the same value. The solution of the Riemann hypothesis or of a Diophantine equation with 79 variables would be on par.

    For example, you say we need to assume the world is orderly. Why would we need to assume that? If the world is not orderly, then all of our scientific theories will eventually be disproven, but that can’t stop us from trying to do science.

    Right. Inductive inference? Out the window. Extrapolation to the past? Sorry, Robert Jones has closed that path. Astronomy and cosmology? Down the drain, for the universe may not be orderly and for all we know little magical elves may be calling all the shots down there in Andromeda. You have just made science impossible.

  31. @Tom Gilson:

    The display of a new posted comment appears in the “Further Information” menu right after clicking Post Comment and reloading the page, but it does nort appear on the page itself.

    Also, it seems I have posted twice my last post. Delete the first one, if you please.

  32. @Tom Gilson:

    The first option. It is something I noticed happening recently — not a big deal.

  33. I noticed the same thing late last night when Tom posted 2 comments. I saw the comments on the “recent comments” page but not on the actual page when I clicked through.

  34. For example, you say we need to assume the world is orderly. Why would we need to assume that? If the world is not orderly, then all of our scientific theories will eventually be disproven, but that can’t stop us from trying to do science.

    C’mon, really??? Do you think any of us, as professional physicists, would take you seriously after a canard like that?

    How could you even empirically prove or disprove anything if there is no inherent and consistent order to the universe? At least Biblical Christian Theism affirms that the Creation is inherently orderly, based on the character and purposes of its Creator, Who is neither irrational nor capricious.

  35. Hi guys,

    In this post, I’m going to try to respond to all of the main points you’ve been making. I’ve enjoyed talking about these issues with both of you, but unfortunately I don’t have a lot of time to devote to this discussion, and I think this will have to be my last comment. I hope you understand. I would love to discuss these matters further, maybe next time they come up on this blog, but I simply don’t have the time to respond thoughtfully to all of the points you’re making.

    I’ll start by addressing some of the criticisms that both of you have made, and then I’ll talk about some of your individual points.

    Both of you have criticized my definition of natural for including too much, for denoting everything that exists, known or unknown. I don’t think that’s a completely fair characterization of what I’ve done. I think I made it pretty clear that when I talk about nature, I’m talking about things that have some observable manifestation, things that we can experience through our senses. That’s very different from saying “nature is everything” and not making any distinctions at all. I’m essentially using the word as a synonym for “observable universe”, and I don’t think that this usage is all that uncommon. I know many scientists who use the word to mean roughly this.

    Of course if you use this definition, many things which were traditionally labeled as “supernatural” suddenly become natural. For example, if God exists and has some physical manifestations, then he could also be considered a part of nature. If miracles really do happen, if they influence the physical world that we live in, then in principle we should be able to evaluate claims of miracles using the usual methods of science. This is the point that I was trying to make originally.

    You also both objected to what I was saying about the universe being orderly. I’ve thought about this a bit more, and it seems to me that all scientific theories have to postulate some type of “order” in the universe. Indeed, the statement that a phenomenon does not obey any particular law is not a falsifiable hypothesis about the world. If we postulate a rule that explains a particular phenomenon, this can of course lead to empirically testable hypotheses, but how can we possibly test the claim that no general rule exists to explain an observation?

    So, I would say that any legitimate scientific theory has to postulate some sort of “order” to explain how nature works. This is very different from saying we need to view nature as “orderly” in order to get started doing science. In the former situation, “orderly” theories of nature are being forced on us by the methodology we’re using, while in the latter case we’re making a metaphysical assumption which could be incorrect for all we know.

    Tom’s comment was that we wouldn’t be looking for order in the universe if we didn’t believe it existed. Again, I don’t think that science requires any kind of faith on the part of the scientist that the world has any particular character. If the universe is not orderly, and every theory that we use to explain it eventually gets disproven, then I think science is still teaching us something. It’s teaching us that our well motivated ideas about how it might work are incorrect.

    Those were the issues that both of you brought up. Now I’ll talk about some of your individual concerns.

    G. Rodrigues, you say that the experience of doing mathematics supports the conclusion that there’s something nonmaterial about the human mind. Of course you’re right to say that there’s more to mathematics than symbol pushing. One also has to be able to recognize patterns, introduce new definitions, and so on. This is all true, but it doesn’t imply that there’s anything nonphysical or nonmaterial about the way our minds work. You talk about solving mathematical problems with a computer, but I think you have to be careful when comparing the human mind to a computer. The word “computer” has a very specific definition according to theoretical computer scientists, and there are serious proposals about how the human mind might actually differ from a computer. Roger Penrose has been arguing for many years that the human mind is non-algorithmic and yet completely describable in terms of physical principles. (His proposal is actually not one that I find compelling, but I’m including it here just to give a specific well known example.)

    Finally, I have a few things to say to you, Tom. First of all, I’m sorry I haven’t been going along with your technical definition. I’m happy to accept it for purposes of this discussion, but it’s very hard for me to evaluate your argument that the “aboutness relationship” points to a reality beyond nature. The problem is that I don’t really understand what “aboutness” is exactly. I hope you can forgive me; I just don’t know that much about philosophy. If you could recommend an accessible introduction to these ideas, I’d be happy to read more about it and get back to you. I might even conclude that your reasoning is valid. But you really don’t have to convince me that it’s possible to distinguish between the material and nonmaterial using some definition of nature, even if that definition is plausibly similar to the world that science is revealing.

    Anyway, I thank both of you again for the good discussion.

  36. Thank you, too, for the good discussion. I leave you with a question and a comment.

    For example, if God exists and has some physical manifestations, then he could also be considered a part of nature.

    Does “affecting” or “having an effect upon” equal “being a part of”? If so, then I am a part of the computer screen you are reading.

    Again, I don’t think that science requires any kind of faith on the part of the scientist that the world has any particular character.

    A fish could affirm the same about the importance of water. Our awareness of lawlike regularity in nature is so incredibly stamped upon us that we cannot imagine not thinking that way. Many people throughout history, however, have seen the universe as not being rational, regular, etc., and those people never developed science.

    To get the thrust of what I’m saying you have to imagine being one of the very earliest pioneers of proto-science, back in the eleventh or twelfth century. One might also go back to the astronomers before them.

    These men (yes, mostly men) and their successors were looking for empirical manifestations of order, and they found it. They looked for it because they thought it might be findable. Again, those who never expected there to be discoverable order in the universe never looked for it.

    I don’t recall where I learned about aboutness. My best recommendation for an introduction to issues that would be any of J.P. Moreland’s works on the mind, soul, and body, which is probably where I first picked it up; or else the textbook he co-wrote with W.L. Craig, Philosophical Foundations for a Christian Worldview.

    I hope to see you again here.

  37. @Robert Jones:

    Since this is your last post, I will not pursue the discussion and just make one point and one correction.

    So, I would say that any legitimate scientific theory has to postulate some sort of “order” to explain how nature works. This is very different from saying we need to view nature as “orderly” in order to get started doing science.

    Actually it is not. To make a long story short, denying that nature is orderly is tantamount to asserting its essential unintelligibility, or some corner thereof. Unintelligible = no science. It is not a question of falsification, as you do not even get to the stage where you can construct a predictive model around which experimental tests can be made, as unintelligibility excludes the very possibility of the phenomenon at issue being amenable to reason.

    G. Rodrigues, you say that the experience of doing mathematics supports the conclusion that there’s something nonmaterial about the human mind.

    Actually I never made that argument. I said, or tried to say, two things:

    1. The aim of mathematics, the experience of mathematics, is more than symbol pushing, it is to seek *understanding*.

    2. There are powerful arguments related to the nature of mathematics that purport to prove that there is an immaterial component to the mind. I mentioned J. Ross, but a more proper mention, since we are talking of mathematics, would be Frege’s arguments. As I said elsewhere, I reject Frege’s Platonism, but since I am a moderate realist I can coopt his arguments without problem. But I never fleshed out these arguments, so there is nothing for you to refute.

    I am sorry, if somehow, somewhere, I misled you into thinking that I was asserting that the experience of doing mathematics, by itself, is an argument for the immateriality of the mind.