The invisible and visible can't resemble each other unless we make both visible. — jkop

Why not? I must be missing something still. I thought such a resemblance was the point of your saying that "there can be resemblance between two states of affairs such as seeing things and thinking about things." One is visible, the other not. Oh well. Not a terribly important point, either way.

Ah, but can you? — Wayfarer

Good response. Maybe we need three categories: 1. genuinely contingent physical phenomena; 2. phenomena which we can imagine were otherwise but in fact could not be; 3. phenomena like mathematically necessary statements, which we can't even imagine to be otherwise.

I see three distinct grades of necessity in those three categories. 2 and 3 may both produce outcomes that are, in practice, non-contingent, but our ability to imagine 2 otherwise, but not 3, has to make a difference, modally. Rough guess -- 2 is about necessity of Being, 3 concerns necessity of Thought. The capitalizations are meant to indicate that these are placeholder terms, having something to do with the synthetic/analytic division.

There just isn't any reason to make the visible/invisible comparison central to resemblance.
— J

I didn't. — jkop

Not to run it into the ground, but here's what you said:

A resemblance-relation requires at least two objects which can resemble each other. Granted that all objects resemble each other in the abstract sense of being objects, but how can anything invisible resemble something visible?

My point is that they can't, unless you somehow make both visible. — jkop

Surely that makes visibility "central to resemblance" -- indeed, it sounds like the criterion for it ("you can't, unless . . .").

there can be resemblance between two states of affairs such as seeing things and thinking about things. — jkop

Good, this all makes sense. So why can't we claim that the "non-seeing" resemblance relation is just as central as the seeing one? You'd asked earlier, "How can anything invisible resemble something visible?" but I think you've answered your own question correctly. There just isn't any reason to make the visible/invisible comparison central to resemblance.

J: whether “the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws.”

Isn't "contingent causal law" a contradiction in terms? — RussellA

The term does invite confusion as it stands. If you read the paper, you see that what Jha et al. mean by "contingent causal laws" is no different from your "nomic laws." They're called contingent to distinguish them from mathematical necessity, which the authors believe is modally stronger. They're also contingent in the sense that we can easily imagine a physical world with different constants, different explanatory equations, etc. In this world, to be sure, they are nomic.

I'm trying to get at your reasoning here. — Harry Hindu

OK. My reasoning is based on what we would reason about the phenomenon of "life." As far as I know, the efforts at creating artificial life are all biologically based. I'm not aware that any scientists are working on the idea that a silicon-based digital entity might "come alive," begin reproducing, and/or provide evidence that it is having inner experiences such as animals have -- pain, for instance. (But by all means point me to any interesting new research along these lines.)

So, similarly, I'm guessing that consciousness will turn out to be a property of living organisms exclusively. Why? Because whatever it is that makes an entity alive is going to be turn out to be what makes it conscious. Or perhaps speaking of "subjectivity" is better here, as I don't know that a plant could be conscious but I find it plausible that it has experiences.

How likely is this to be true? I can only say "fairly likely" based on what we've seen so far: absolutely no evidence of either life or consciousness in digital entities. This gets muddled because proponents of mechanistic consciousness will define "consciousness" in such a way that a digital entity might have it (I think that's what you're doing, to a degree), so perhaps it's ultimately a philosophical rather than a scientific issue.

For you, who else? — Harry Hindu

But how can any such entity as "me" emerge from a working memory and sensory info processing? I think you're assuming that the digital toolkit will produce a "me" or a subject, but that's the very thing under discussion.

If my description does not resemble what it is like for you, then please explain what it is like for you. — Harry Hindu

Well, I am a subject, so in addition to all the ruckus going on, I experience my self. Transcendental ego, if you like. Moreover, as a subject I do a lot more than connect with the "outside" world. My imaginative consciousness is extremely vivid, and doesn't depend on stimuli from experience, unless we beg the question and say that it's the neuronal activity itself that is the stimulus. But I don't think brains cause consciousness, I think consciousness supervenes upon brains.

However, the general thrust of what you're saying is important and true -- WE DON'T KNOW. It is one of the great remaining scientific puzzles.

You're quite right; as I said, we don't yet know any of the important facts that would allow us to decide this. I haven't assumed anything. I've said that I think it's unlikely that non-biological entities will turn out to be conscious.

If we say that consciousness is a type of working memory that contains sensory information . . . — Harry Hindu

Well, yes, then various things follow, but I don't think that's a good thing to say. My own consciousness doesn't at all resemble this description phenomenologically, and once again we're a long way off from being able to say that, despite this, it "really is" working memory plus sensory information. Just for starters, for whom is the information informative?

how can anything invisible resemble something visible? — jkop

It's hard to know what sort of answer is wanted here. I could reply, "Easily. When I read a biography, my mental imaginings of the subject of the biography resemble the subject quite a bit, if the book is well-written." This is ordinary-language talk, and no ordinary speaker would have any difficulty understanding me. But evidently you want to stipulate a meaning for "resemblance" that makes physical visibility more important as a criterion. I guess you can do that, but I think we need 1) an explanation for how the ordinary-language use became so common, and 2) a good argument for why this notion of "resemblance" is useful or clarificatory, in this context. What are you trying to ameliorate, with this usage?

Therefore, we can use the Correspondence Theory and say that the proposition "there are infinitely many prime numbers" is true because there are infinitely many prime numbers. — RussellA

Good, I think we're on the same page. A correspondence theory ought to work independently of the ontological status of various "worlds"; that was why I questioned limiting it to "facts about the world," which from your example I took to refer to the more-or-less-physical world that would exist without us. But now I see that your view is more inclusive, so that's fine.

But that's the thing. What makes a mass of neurons conscious, but a mass of silicon circuits not conscious? — Harry Hindu

We don't yet know. My hunch is that it's going to be a version of the same thing that makes a biological creature alive, and a computer not. And yes, this could all be off base -- the sort of thing people will marvel it a few centuries hence -- "How could those people have gotten it so wrong?" But for the moment, I haven't heard of anything that suggests a computer could have inner states. Do you know of anything along these lines? (Grant me, for the moment, the idea that an inner state would be a sign of consciousness.)

If a correspondence theory of truth demands that we do so, I'd argue that it represents a reductio ad absurdum and should be rejected on that ground.
— J

Very harsh. The word "true" has different meanings in different contexts — RussellA

So, to review the set-up here: The question is whether a standard correspondence theory has to invoke a match between statements in a language and facts about the world. If so, this would seem to rule out using such a theory to describe strictly logical or mathematical facts as true. Yes, you could say that, to demonstrate such facts, we don't need a correspondence theory and therefore we can call them true using a different meaning of the word. But isn't that a stretch? The appeal of a correspondence theory is that it seems to give a common-sense reply to the question of what it means for a statement to be true: We compare it to what is the case, and if it fits, bingo. Obviously it can't be that simple, but the concept is still powerful.

So, Euclid's proof about prime numbers claims to state a truth. When we examine it, we see that while it isn't exactly a "truth about the world," or something that is made true by facts found in the world, it nonetheless appears to express a match of language with something. What is the something? For me, none of the usual-suspect answers involves giving up using "true" to mean "agrees with what is the case." So we shouldn't limit a robust correspondence theory to "facts about the world" -- there are plenty of other facts that we want to call true in the same way. I can't defend that here, but I just wanted to give you a sense of where my objection is coming from. And yes, maybe calling this version of the theory a reductio is a bit harsh, but at the very least it requires a strong argument against its implausibility.

Any word yet on casting for L&L? I heard Tom Cruise was in the running to play Science. Or was it Metaphysics . . .

You might ask, 'Why would we need to be conscious of an imagining?" Why can't a p-zombie do the same thing but without the actual experience of imagining a purple cow? The answer is that I don't think the p-zombie is a valid argument. — Harry Hindu

I have a lot of questions about p-zombies too, but we don't need them in this instance. Any number of computer-generated entities can do all the things you mention: respond to their environment, learn, make predictions, use feedback loops, offload routines to different parts of memory. So I disagree that "Consciousness is necessary for learning and making predictions." This is why the purple cow is such an annoying example -- it doesn't do anything. It simply sits there, so to speak, being a mental image, again so to speak. If a computer-generated entity could do this, I would have to allow that it might be conscious, but I don't believe it can. Except by rather strained analogy, there's no equivalent of a digital state that also has a subjective appearance to the software that we cannot experience.

Having said this, some computer-savvy poster is going to show me I'm wrong! OK, I'm ready. . .

This is Jha et al’s argument, more or less. Math only appears to be causal when we state the problem in terms that remove, or demote to “background conditions,” the physical constraints that actually provide the explanation.

This is good. I would amend it slightly: Jha et al are asking the very question about whether logical principles can be more than contingently causal. They’re not at all “unwilling “ to entertain the idea; it’s the topic of their paper. They do end up arguing against it, true.

Interestingly, you've made similar arguments to those of @Philosophim about "effective" truths, and my response to him, just above, is similar to the one I'd make to you. It may well be that scientists don't much care whether equations are true, as long as they work. But philosophers -- and, I'm guessing, a lot of mathematicians -- care very much. We can't take "facts in the world" for granted and go about our business. A theorem (as opposed to an equation that's given a real-world interpretation) isn't described as effective, it's described as true, or at least provable in L. Do you want to abandon that way of talking? If a correspondence theory of truth demands that we do so, I'd argue that it represents a reductio ad absurdum and should be rejected on that ground.

Within the modern correspondence theory, "snow is white" is also within the object language whilst snow is white is a fact in the world. — RussellA

Similarly, I agree that this is a familiar version of a correspondence theory, but it leaves out the option of claiming truth for any facts that are not about the world (unless there's a "world" of math and logic). Is that OK? What would be the point of limiting ourselves in this way?

What a cromulent response! :smile:

This just pushes the question back a level -- why is it effective?

Now of course the picture you're painting is a perfectly good one if you're a pragmatist, or believe for whatever reason that metaphysical questions about the correspondence of thought and reality are either incoherent or unanswerable. But I keep pressing you on your use of "accurate representation" -- "accurate" simply doesn't mean the same thing as "effective" or "successful." Wouldn't it make more sense for you (if I've understood your thinking here) to abandon any talk of accuracy or truth?

Well, perhaps, but how can "accuracy" be a factor at all? What would make something an "accurate representation," to use your phrase, and of what is it a representation? None of the three factors talk about how such an idea could arise.

To put it in simple terms (borrowed from Sider), are we really not in a position to say that the Bleen people have gotten something wrong?

My understanding of truth is that it is defined by the schema "snow is white" is true IFF snow is white, where "truth" is the correspondence between propositions in language and equations in mathematics and what is the case in the world. — RussellA

Is this meant to be Tarski's view? Surely he didn't talk about what was the case in the world -- only about the correct relations between language and metalanguage. If one language has to be "about the world," then we wouldn't have any logical or mathematical truths at all, or at least that seems to be the necessary consequence. I don't think Tarski intended this. Unless I'm mistaken, he included these kinds of truths in his schema.

This is a great description of what mental imaging is like, and accords completely with my own experience. But then what do you mean when you say:

A "mental image" couldn't even resemble visible objects such as cats or images — jkop

What it's like to see the cat is a feeling, not an image. — jkop

Doesn't your description contradict these statements?

I appreciate your taking the time to lay all this out for me. Could I ask you to take this to a simpler level, and describe to me what you think happens when I imagine a purple cow? I'm still concerned about the hard problem, understood as the emergence of subjectivity (or the illusion of subjectivity, if you prefer) from chemical/neuronal activity,

I understand. Do you think there are mathematical truths that are independent of what is the case in the world? Plain old theorems, in other words?

OK, but you can see that even this weakened version represents an entirely different order of explanation than:

1. Real life effectiveness

2. Fulfills emotional desires

3. Fulfills a power structure

By referring to "accurate representation," you've introduced an epistemologically normative factor that is nowhere implied in the first three factors.

I find all this somewhat plausible in the case of images that arise from perception of the world, and are meant to "stand for" or "picture" or "represent" something out there. Quite possibly the "out there / in here" duality is either mistaken or badly conceived. But . . . I don't see how it applies to my purple cow, or any other of the myriad ways consciousness operates without any perceptual stimulus. We agree that my imagining the cow is no illusion. How is this still a question of dualism vs. monism? I'm not claiming that the cow represents anything in the (dualistically conceived) world; in fact, the choice of "purple cow" is meant to preclude any such representation.

You'd written this:

Are mathematical truths necessary truths
Following the schema "snow is white" is true IFF snow is white as a definition of "truth", then "d=0.5∗g∗t2" is true IFF d=0.5∗g∗ — RussellA

So I assumed you regarded d=0.5∗g∗t2 as a mathematical truth.

What do you mean that the equation d=0.5∗g∗t2 has no meaning? — RussellA

Without some interpretation, some assigning of the symbols, it says nothing. I can vouch for this personally, as I have no idea what d, g, and t refer to in this equation! If you simply placed it in front of me, uninterpreted, and asked me what it meant, I could only shrug.

But if none of that is so, and what I was calling "subjectivity" is in fact a dualistic illusion, we still need to know how this comes about, and why.
— J
But that is what I've been saying - that seeing this as a dualist illusion IS the problem. Abandon dualism and introduce the idea of monism and see if that helps you solve the problem. — Harry Hindu

We agree that subjectivity could be a dualist illusion. (I don't think it is, but I'm happy to assume it for purposes of argument.) But if it is, we still need to know why. You say, rather cavalierly, "Abandon dualism." OK, I imagine a purple cow and I follow this up by saying to myself, "This experience of me-and-purple-cow-image is illusory. There is no separation." But this doesn't make the purple cow go away, or change into something else. I'm sure you don't believe this would happen either, but what do you believe? What changes, for you, in this sort of experience when you introduce the idea of monism? Is it that experience, as presented, becomes a sort of brute fact, about which it's no longer possible to ask questions? This isn't meant to be snarky, I'm genuinely interested.

A "mental image" couldn't even resemble visible objects such as cats or images — jkop

For me, a mental image strongly resembles a visible object. So I can only conclude that you're already analyzing "mental image" reductively to refer to whatever physical substrates it may supervene upon. I think that begs the question.

What it's like to see the cat is a feeling, not an image. — jkop

Again, I have to say, Not for me. We all know that "what it's like," despite having become the go-to term for subjective experience, is quite imprecise. Maybe that's a good thing. In my case, the "what it's like" is a combination of an apparent image, often a series of memories associated with the image, probably some future projections about the image, and, sometimes, a feeling about what I'm imaging.

It sounds like where we differ is that you want to eliminate the idea of a mental image altogether. I think there are plausible and persuasive reasons for doing this in the case of perceptions. But not for imagined or remembered images. If these experiences are not, in some ordinary-language way, mental images, then what are they? And how could they be explained away as being identical with their physical substrates?

Are you sure we should call something like d=0.5∗g∗t2 a mathematical truth? I thought it was only true on some interpretation; as it stands, it has no meaning.

Let me try to work up an example that is less controversially stipulative. — J

How about this?

For "object" in the "23 objects" question, let's say "chickens." We wish to divide 23 living chickens evenly among 3 people; we discover this can't be done. Here there's no question of how to define the object, or whether fractions can ride to the rescue. So: Is this division impossible for the same reason -- a distinctively mathematical one -- that the number 23 can't be divided evenly by 3? Or, if you don't accept "distinctively mathematical," how would you characterize it?

OK. So no one of your factors would be something like "This set of concepts more accurately reflects the ontological structure of the world"? You'd rely on pragmatic and/or personal-preference explanations for the chosen set of concepts?

Cool comparison, I hadn’t thought of it!

I don’t think I agree with your interpretation, though. You recall that Quine’s target was meaning-synonymy as a supposed criterion for analyticity. He readily acknowledges, at the start of the paper, that logical truths are excluded from his criticism. So we have to ask, is there a “parallel exclusion” in the case of explanations that include part math, part facts-about-the-world?

Taking the math part to be parallel with “analytic,” we want to know whether maths are logical truths (and thus both easily identifiable and unexceptionable, according to Quine), or whether they are more like meaning-synonymy statements. Frege may be helpful here; he also divided analytic statements into two groups. The first is Quine’s “logical truths”; the second is supposed to be reducible to logical truths on the basis of purely logical definitions. As Susan Haack points out (in her Philosophy of Logics), this would mean that “the truths of arithmetic are, in this sense, analytic.” (And Kant, of course, would disagree.)

Do Jha et al. take a roughly Fregean stance here, concerning the relation of math to analyticity? They don’t address this directly, to be sure, but I think they do. The reason lies in their reasons for rejecting distinctively mathematical explanations (DMEs) in the first place. Math, according to them, can’t play an explanatory role in scientific explanations because it can’t say anything about “the world,” due to its a priori nature. Now I know Kant though math could be both a priori and synthetic, but that has never struck me as plausible, and I think we should go with Frege. (And anyway, as @schopenhauer1 pointed out, the synthetic nature of math for Kant is transcendental. It operates as we structure experience, it’s not something we learn “in the world.”)

So if we attribute the Fregean stance to Jha et al., then they don’t say that “you cannot tease out any supposedly pure math part, roughly”. It’s precisely because you can do this that DMEs won’t work.

Still, it’s not a simple question, and I’m not sure I’m right.

Quine himself had very mixed feelings about whether the laws of logic were subject to revision. I think his final answer was yes, but it's a last resort, and they are very insulated, resistant to revision. — Srap Tasmaner

Just as an aside, I think Quine believed the laws of logic were true because we could supply clear definitions for all the operators and connectives. This is in Word and Object. In a subsequent work which I haven’t read, The Philosophy of Logic, he extends this to non-classical logics, according to Haack. She says that he accepts “a meaning-variance argument to the effect that the theorems of deviant and classical logics are, alike, true in virtue of the meaning of the (deviant or classical) connectives; which, in turn, seems to lead him to compromise his earlier insistence that fallibilism extends even to logic.” So it sounds like your "very insulated, resistant to revision" is spot on.

By clarifying their ambiguity we can get rid of some of the problems.

For example, in talk of the experience of seeing a cat, the word 'experience' or 'seeing' can refer to what is constitutive for having the experience: the feeling. But they can also refer to what the experience is about: the cat. — jkop

Good, this is helpful. I'm not using "experience" to refer to what the experience is about (the cat). But nor am I quite using it to refer to a "feeling." I suppose people can differ on this, but when I see a cat, I don't find myself feeling much of anything about it. What I do find is that I have, or seem to have, a mental picture. This is, for me, what is "constitutive of having the experience," as you say. But I don't think it matters too much whether the "inner" part is more like a feeling or more like a picture. The important difference, which you have disambiguated, is between "experience" understood as the object (putatively "out in the world") that is being sensed or thought of, and the subjective event of doing so.

So, what is left to explain is this: How does my brain create the feeling?, and I believe we know at least something about how feelings are evoked by hormone levels, neurons releasing dopamine etc. — jkop

But here, your reliance on "feeling" as the correct subjective description does make a difference. It allows you to talk about hormone levels, dopamine, etc., as possible causes of feelings. I'm sure they are. But the kind of "feeling" involved in having a mental image of a cat is surely not explainable by hormone levels. I know you're not saying that it is, only that we're not as ignorant about the whole process as I've been arguing. I'm not persuaded, though. Can you sketch even the beginning of an explanation of a mental image that involves feeling-type causes such as hormones or other chemical items? I think this would be even harder to do in the case of an imagined image -- one that I simply "think of" as opposed to being stimulated by a perceptual event.

The impossible request that we ought to explain how hormone levels etc create the illusion of a Cartesian theatre seems to be based on a fallacy of ambiguity. — jkop

Can you explain? I thought you disambiguated it nicely. Is this a different ambiguity?

I realize I've been using the term "privileged structure" without much explanation, as if everyone is familiar with Theodore Sider. Let me expand a little. Sider uses the "grue and bleen world" example (which you can read about here, p. 16) to refer to a situation that he believes needs explaining: If we encountered a people who used grue and bleen as their concepts, we'd be unable to fault them on any logical grounds. Nor would anything in the world contradict their choice of these concepts, as concepts -- there really are grue and bleen things, and we know how to say true and false things about them. They would of course prove completely unworkable in practice. But why? What makes our green-and-blue conceptual world better? Is it simply a pragmatic question? But that only pushes the question back a step, for now we have to ask, Why does it work better? Is that just lucky for us, or is there something about the world, and its structure, that green-and-blue reflects with more than mere accuracy? If so, that would be a privileged structure in Sider's sense, and the grue-and-bleen world would not.

So, on that understanding, how would you explain privileged structure? I can see how you can demonstrate the pragmatic success, but what's the next, explanatory step?

I did read the summary. Is this the passage you're referring to (concerning "privileged structure" or the like)?:

"Applicable knowledge is when a form I have created in my mind, fits reality. The simpler the properties in the distinctive knowledge, the simpler the applicable knowledge accrued. If the essential properties of sheep are curly fur and hooves, this would be indistinguishabl[e] from for example a goat."

I think I could add "the illusion of" in front of every reference to "subjectivity" and it wouldn't alter the problem. If I understand you, you believe that subjectivity only becomes a "problem" when it is labeled as subjective and claimed to be a mirror or a window or something that validly reflects an external reality. But if none of that is so, and what I was calling "subjectivity" is in fact a dualistic illusion, we still need to know how this comes about, and why.

I see what you're saying. Let me try to work up an example that is less controversially stipulative. As for the analytic/synthetic distinction, I'm not sure we really have to go there. Perhaps it won't do as a description of the difference between logic and facts-about-the-world, but wouldn't you agree that Jha et al. are pointing to something that can be talked about, and represents a genuine question? Or perhaps you wouldn't.

Yes, that all seems right to me. The question you were raising, though, was about particular "matches with reality" that, in addition to being logically consistent and uncontradicted by the facts (such as grue and bleen), also constitute an "identity" -- perhaps like natural kinds? I just think this needs further explanation; logic and noncontradiction alone won't get us to why some matches seem more natural or reality-mirroring than others ("privileged structure").

Ok, please explain to me why we can't talk about all this without using the word 'observer'? — jkop

I was hoping that, by working together on a version that didn't use subjective words, the reason would become clear. But OK, I'll be didactic: Descriptions of consciousness in physicalist terms presuppose the existence, as conscious states, of the phenomena they're meant to explain. (This excludes versions of physicalism that simply deny the existence of consciousness, but that's not your thesis, nor mine.)

Let's look at your original thesis again:

Moreover, conscious states such as visual experiences have a hierarchical structure in the sense that the experience is not solely a biological phenomenon. It is also causally constrained by the behavior of light, and influenced by the observer's psychology, sociology, language and culture. All of these can be described, but none of them is a complete description of the experience. However, the lack of a single complete description is hardly a problem. — jkop

We need a physicalist translation, or reduction, of "experience," for starters. In what sense is visual experience biological? Do we know how our brains create the illusion of the Cartesian theater that characterizes subjective experience? Not at all. You can say, "Someday we will," and I agree that's likely, but at the moment it's unsolved, and it's not a matter of lacking a description, as you put it. We lack any theory at all about how and why it happens.

Even more concerning, the use of "observer" postulates an "I", a subjective point of view. This, for me, is the really hard part of the hard problem. We can't just help ourselves to the term "observer," in trying to explain or describe consciousness. On the evidence, there's nothing in biology, psychology, sociology, language, or culture that even hints at an explanation for a first-person point of view. In fact, you'd expect the opposite -- these living systems are so beautifully and intricately evolved that they seem quite capable of doing their thing like zombies, or robots, with no "there" there. Why isn't that what happened, and what did happen? Again, we can't just say "And along came consciousness . . ." or "Then consciousness emerged as a property . . . " because these are just placemarkers for our inability to solve the hard problem (yet).

Whew. But I really think it's more useful to try it yourself, just as an experiment. Try taking the above quoted passage and rewriting it without any subject-based or experiential terms. I think you'll wind up with something that either doesn't talk about consciousness at all, or else merely defines it as physical, or assumes it to be physical, rather than explaining it.

So where are abstractions taken from? I suggest "the world" is a sensible answer, and one that explains the "mystery" rather well — unenlightened

It is indeed a sensible answer, but doesn't explain what appears to be the modally necessary character of the abstractions, and their role in explanation, if any. Have you read the target paper I cited? It might explain the problem better than I have.

I can see that you wouldn't like this approach on the grounds that it shoots your fox and spoils the fun of the chase. — unenlightened

My fox is quite healthy still, thank you! And anyway, I'm an animal rights activist and must urge you not to shoot at any foxes, real or metaphorical. :wink: (You can imagine how I grit my teeth whenever Ted Sider (and Plato) go on about "carving reality at the joints.")

These two responses show a similar approach to the problem, which I think is mistaken. We shouldn’t be conceiving of the “Distinctively Logical Explanation” question as a question about how to define terms, or about whether language can resolve the question. The DLE problem assumes a linguistic stipulation that is uncontroversial or at least agreed-upon, or at the very least accepted for the purposes of discussion. With this stipulation in place, we then go on to ask about the relation between logic-or-math-as-necessity and the alleged necessity of events in the world, such as the 23 objects that can’t be evenly divided, or the cat that can’t be here and in Paris too.

It is trivially true than any given definition of an “object” will determine what we can say about it, using math or anything else. The larger puzzle is this: How is it the case that, no matter what definition we use, we discover these regularities between math/logic and the world? Even the bizarre definitions of “cat,” once accepted, have unambiguous consequences in terms of regularities. Wayfarer calls this a case of the world “mysteriously agreeing with our abstractions,” but that begs the question. Is it the world that is doing this, or are our abstractions mysteriously agreeing with the world? Are there abstractions that “agree” better than others? This is the Phillips-head screwdriver problem. We can just accept the agreement as a brute fact, not mysterious at all, or we can claim a coherent evolutionary explanation, or we can continue to ask why. My only point here is that I don’t think we should look to language for a solution. Resolving a linguistic ambiguity won’t tell us whether math/logic is a genuine causal constraint on the world.