By the way, I did read some of the responses, but not all, so if I missed anything that you may have responded to that's relevant to my ideas, please let me know.

I'm not sure I see a problem with the idea that some concepts must reference themselves to be analyzable. I feel like, coming from ideas of axiomatic set theory, people view "the world" or "the set of all true statements in a system" as a tree, where there are fundamental truths (axioms) that one must start with and everything branches from there. Such a visualization does make it seem difficult to reconcile understanding those fundamental truths because nothing grounds them—they are the ground. But rather than a "tree of truth", I view the world as more of a nervous system, a graph or network (whichever you prefer) where everything is interconnected, and there aren't necessarily "undefinable" elements like the axioms. It should be noted that in such a visualization, everything would perhaps technically be circular, just more or less removed because there is no presupposed foundation.

So with respect to your example about being, I personally have a somewhat sophisticated (at least more sophisticated than "being" is "to be") understanding of it, which does rely on some circularity, but also incorporates elements of other concepts, such that a network can start to be realized. In my view, existence means "to stand in relation" to other things in an ontological sense (this is ontic structural realism). So if we're looking at the "network model" of the world, to say something exists means it is a node (or perhaps bridge between nodes) in that world. With some additional understanding, this implies a few things about existence that informs us of its nature: 1) There can be no world of just one node (one thing, because it doesn't stand in relation to anything else), 2) Something that exists in one world need not exist in another world; i.e., existence is relative, or 3) there is some barrier between that which exists actually and that which exists conceptually (concepts, like a physical unicorn, may fail to exist actually, in which case we may be said to be non-existent, although the concept exists in some sense).

Also, you also pose truth/falsehood as potential fundamental concept, but related to this definition of being, that may be explainable too: recall (1) that nothing can exist by itself, so there must at least be, say, two things that stand in relation. The most primitive relation of this nature can only be that of "something", and "not that something": this I believe, without additional structure giving weight to the meaning of "true" and "false", is the relationship that truth/falsehood describes. It's also akin to the idea of being and non-being, and harkens back to the Greek beliefs about opposites.

Don't mean to pontificate about my own beliefs, but with regards to your topic, I would say I think ultimately, not just some, but all concepts experience some level of circularity, but with some being more closely entwined, such as that of being and non-being, which is essentially self-referential, but can still be analyzed in the context of other concepts, and is not arbitrary. So I guess I disagree that they are unanalyzable, but also disagree that they must be non-circular. I thus conclude the answer is D, none of the above :grin:

Perhaps this a good way to transition into a discussion about the possibility of leeway freedom also, because, as is clear, I'm not convinced that we cannot have it. I'm not sure whether or not I'm a compatibilist, but whatever determinism the world appears to have I believe is theoretically compatible with the ability to do otherwise, although the reasoning does invoke a type of indeterminancy.

For example, let me ask you this: how would you describe the determinancy of a die roll? Because to me a die roll can basically function as determinant so long as the chance governing the die roll does not change. If the rule is constant, then even if the outcome is random, we can still determine the prior events and its outcomes.

I agree. In order to avoid this, I think the OP needs to clarify that it is arguing for it being true that one should believe in leeway free will even if leeway free will is false. If it were presented that way, then I don't think it would be a fallacy anymore. — Bob Ross

This is pretty much what I was doing from the beginning, and perhaps the source of confusion. I wasn't arguing that free will exists, only that we ought to believe in (leeway) free will, even if it may not exist, because it's the only way to yield (in my opinion, and one I admittedly would need further argumentation to justify) a sensible position. That said, I did, albeit briefly, describe in the argument why I think each possible position in the matrix is or isn't sensible.

A couple things to note though. I'm not saying that one should believe in free will despite thinking the contrary is true because they "like" it or it makes them feel comfortable. In fact, I'm not even saying, "if free will is false, one should still believe in free will", because I don't believe it's known whether or not free will exists, if such a thing can even be known. If we knew for a fact that leeway freedom doesn't exist, I'd pretty much concede anything, because I don't think it would matter whether or not we believe, since we'd only do what we're determined to do anyway. But as it stands, as we don't know for a fact if leeway freedom does or doesn't exist, we ought to believe it, because we have nothing to lose if it ends up being false, and everything to gain if it is true.

Oh right. Still curious about my questions regardless, and I do think the question of the origins/transformation into knowledge is relevant.

But the problem here is knowing and experiencing. You have to explain what exactly you meant by know to have a good definition. — Abhiram

I was just typing out a response to address this issue: My first instinct was to say "Something exists" or "I feel something", because I believe our experience is prior to any knowledge we might have, even of ourselves. But when does the mere sense experience start to come together to make a model of reality and our identity? Don't we need to have an understanding of self in order to claim knowledge of anything, or maybe knowledge of the concept of knowledge itself?

I think that I have the ability to choose because I can come up with reasons and reach conclusions in accordance with my will; but I don’t think I have the ability to do otherwise because if you rewound the clock, then I would expect nothing other than myself to generate the same reasons and reach the same conclusion—afterall, nothing changed other than the rewinding of time. — Bob Ross

I feel like this is boiling down to an equivocation more than anything, because my argument, as I mentioned in the OP, primarily relies on a leeway notion of free will, the ability to do otherwise. When I've said "choice", I've meant it as ability to do otherwise, so when you said (in your sample compatibilist counterargument):

because causal determinism [or some weaker variant] is true, one cannot do otherwise but they can choose — Bob Ross

it seems to just be a slight of hand.

Your point seems to be that just because people can value things under hard determinism, as long as someone happens to value truth (is determined to value truth), regardless of the reason, they shouldn't believe in free will if that's what they're inclined to believe. But my point is, if there is no leeway freedom, no ability to do otherwise, then there is no "should", there is no free choice (ability to do otherwise). If you can't freely choose your own belief, there's no point. Essentially, I'm arguing that 1) you ought to value leeway freedom (which I suppose is another argument in-and-of itself) and 2) if you value leeway freedom, then <insert above argument>. You might say, "well, people that don't believe in free will value truth over leeway freedom, so the argument is pointless", but I'd say that's, if not demonstrably false, likely to be incorrect in most cases, because a lot of people that tend to deny free will do value having that ability—it's where you get people lamenting over it's non-existence or trying to find meaning despite it—and so the argument should reasonably follow.

I don't mind discussing free will more generally (but particularly the necessary or sufficient freedoms required for it and the existence thereof). Ultimately, one could imagine morality and axiology and etc. to arise even without free will, but I think such an existence is meaningless, at least in comparison to a world in which we have the ability to do otherwise. Not only do I think it's meaningless, but I think denying free will is actively harmful because, as I say, it is convincing people that they literally have no control over their actions, and although that is unlikely to turn them into "robots" or resign them to doing nothing, it is still insidious and can cause damage to one's mind if they come to believe or merely fear it.

firstly, that in every act of willing there is, first of all, a multiplicity of feelings, namely, the feeling of the condition away from which, a feeling of the condition towards which, the feeling of this "away" and "towards" themselves, then again, an accompanying muscular feeling which comes into play through some kind of habit, without our putting our "arms and legs" into motion, as soon as we "will.". . . — Vaskane

So is his general point in this segment that it's reductionist to claim all of these different mechanisms going on almost simultaneously boil down to one act of free will? That when I make a "free" choice, it's nonsensical to say there's a single event or something I think or "will" that causes me to follow through with that choice?

And? Is that not just a pretentious way of saying everything is determined?

...one cannot do otherwise but they can choose

How? If they accept sourcehood freedom? Is that not different from choice, or do you speak of leeway freedom, in which case I ask again, how does one choose if they can't do otherwise?

one cannot do otherwise and they cannot choose; however, this does not negate the fact that they have values

I don't deny that one can value (or at least define values such that it is possible) under hard incompatibilism. However, notice I claimed we couldn't hold any value "freely", not just that we couldn't have values.

One can try to avoid error without having the ability to do otherwise nor to choose: this is just a non-sequitur.

And this is just an unsubstantiated claim. I ask again: how is it possible to "try to avoid" without being able to "choose" or "do otherwise"? Are these all diffferent things? If so, you have to explain how they're different, you can't just assert that "no, this doesn't mean that" and be done with it.

Pascal’s wager is a bad argument, because it renders the probability of the consequence occurring omissible when, in fact, it is the most critical factor for analysis.

There's no probability in this argument, there's no numerical "cost-benefit analysis". It simply claims that if you value truth, and additionally, you value "ownership", i.e. "free control", over your beliefs, then the only way these two values are satiated occurs if you believe in free will. I can further argue that our "ownership of beliefs" takes precedence over merely having true beliefs, because it is the reason for that value.

So let me ask you this to further the discussion: why do you value truth? Does it even matter? Will you argue that reasons for valuations don't matter, because so long as one just so happens to value truth, the argument is defeated?

Firstly, A-D are all presupposing certain axiological claims that I would completely reject. For example, A and B are false. What matters is relative to values; and values are subjective and relative (e.g., if one values truth, then it absolutely matters if one believes that they have free will even when they don’t). — Bob Ross

Expand on this, if you would, because the implications of lacking free will make it clear to me that we can't hold any real (free) value in something like truth.

Starting with B, surely valuing truth implies avoiding error, and perhaps some sort of pride or otherwise virtue in comporting with reality. But, such a value implies we have the power to "avoid" error, i.e., we have a certain freedom to do otherwise. Denying free will (in certain senses at least) is to deny that we have this freedom, so, if it is the case that there is no free will, we can not value our belief in the truth of this proposition, because we could not avoid erring.

Same principle with A. It seems the fear we have with believing in free will is that we could be wrong. But as I say, if we are wrong, meaning free will doesn't exist, then, since their can be no value in having true beliefs, that means there's also no negative value in having a false belief. So there is nothing to lose for believing in free will, and, by C, everything to gain (which is where the parallel to Pascal's Wager comes in, even though they don't function on exactly the same principles).

Interesting. Perhaps this form of argument can be applied to something like the self, which seems necessary for experiencing the world and reasoning.

Are you referring to my A and B, in which case youre mistaken, or is this your own statement? Either way, I don't really get the point or where your contention of what I'm saying is, if there is a contention. Compatibilism argues for free will, no?

To address D, it's not so much that someone who doesn't believe in free will can't behave freely or do good. Clearly they can, because free will exists. But I am pointing out the absurdity in the belief, because even if you do do good, you don't have any grounding for it. Any grounding you might suggest necessarily will either invoke some conception of free will, or imply you actually do believe in free will.

If you don't believe in free will, then you can't intentionally fulfill your obligation, it's just happenstance. Of course I think people who dont believe in free will still have values and will act in accordance with them, but if you truly believe its not your choice, then you can't claim praise or blame. So you might as well believe it.

I would say it doesn't matter whether it's knowable or unknowable. If we know there is no free will, then it doesn't matter what we do, we'll just do what we're willed to do. But if we know there is free will, that would just make the denial of free will even worse.

Surprised you engaged with him as long as you did. But also, do you mind giving your opinion on this point I made earlier: Even though it may be wrong to introduce life, because you are forcing them to bear the burden of suffering, that doesn't imply that life itself is inherently suffering. Perhaps thats a strawman though to say the antinatalist claims life is just or predominantly suffering. In fact, this may be in favor of your point that, for the people living, there's no urgency to end your own life because there is still value to be had in it. But just because there is value, that may not outweigh the prevalence of suffering, nor the nonconsensual thrusting of children into potential suffering.

I feel like a significant part of belief in God, particularly a personal God like in Christianity, is having faith: believing without sufficient reason to believe, or trusting without sufficient reason to trust. And I mean this from the perspective of the believer, not any objective basis for sufficient reason. For example, I may not trust my friend enough to sufficiently believe that they will pay me back, but I nonetheless put my trust in them to do so. Similarly, I think a necessary part of belief in God is not knowing sufficiently if God may, say, answer my prayer, but nonetheless believe God has my best interests in mind, or that God exists at all, despite not having sufficient knowledge of His existence.

My point is, I don't agree with the sentiment that one must know God exists, or prove the existence of God, or even have sufficient evidence to warrant belief in God to believe. That feels like us testing God, rather than the other way around, and I think belief in God would be diminished if it could simply be proven or shown to be true as a fact. Personally, I simply can't put faith in something without reasoning my way towards it as I feel faith in God requires, so I don't think I'll ever follow a religion. That said, I am agnostic and have been able to reason my way to the potential existence of some God-like being. But if I do find myself believing in some God, it will be through reason, not faith.

I regrettably can't argue too strongly against the imposition of will against potential humans argument. The only way I can logically get around it is if the parents had altruistic motivations for creating a child, like wanting to allow a child to experience the joys of existing, and if existence itself wasn't inherently burdensome, as it seems to be, even by the most optimistic of folks. I suppose I'll continue to hold the stance that anti-natalism is a rational position, but one that I simply don't feel compelled enough to act in accordance with. Although, now that I think of it, I think I may agree for the previous reason that natalism is ethically questionable, but that life and existence isn't inherently bad or suffering, because I think suffering can be overcome, even if it isn't right to impose it on a potential human.

A bad (negatively feeling) experience =/= badness overall. It's kind of the whole point of resiliency and growth: you fight through temporary displeasure to become a stronger person. You seemed to gloss over the argument I was making to nitpick a mostly semantic issue. Plus, it's kind of ironic that you seem to dismiss discussion right after ridiculing someone else for the same thing.

What are antinatalist counterarguments to a more stoic perspective on life? I.e., one that values self-improvement and a sort of indifference to suffering, such that avoiding suffering isn't necessarily a primary tenet of living a good life. In general, antinatalism seems to focus so heavily on the aspect of inevitable suffering, but if one doesn't think suffering is necessarily bad, what leg do they have to stand on?

I like this MinutePhysics video with Sean Carroll: https://www.youtube.com/watch?v=yKbJ9leUNDE. He gets straight to the point, explains in simple terms the (basic) nature of time, and gives an overview of how the universe started and how it's supposed to end. Sean Carroll also proposes an idea (don't know if it can be called a theory or not) in other videos you can easily find on Youtube that quantum fluctuations in empty space may satisfy conditions to initiate a Big Bang, basically beginning a new universe in the death of a previous one.

Yes, scientists don't say that the universe was "created" at the Big Bang, but it is commonly said that matter can't be created or destroyed, which is the only context I see Benj96 using the term.

I'm hopelessly confused. Let's try to start over from the beginning, leaving aside the logic of the statement for now.

First of all, to be clear: you are for PII, but only because the mere idea that two things are different can be predicated as thing 1 is thing 1 and thing 2 is thing 2. Is this a sort of haecceity or "thisness" as I eluded to before? That there is some substance underlying the properties that gives things their identity?

Secondly, and this is a rudimentary question, but what do you understand properties, predicates, and relations to mean, and how are they related or unrelated to PII? Are relations different from properties such that PII doesn't consider them as relevant to whether things are identical?

^ The above was written before Sophisticat's response.

No, I meant numerically distinct, as in the example of two spheres. If you are allowed to predicate anything by way of specifying a property, up to and including haecceity, then you will find a way to distinguish two apparently distinct objects, no matter how qualitatively alike they are. — SophistiCat

Which is why I don't think there's such a thing as haecceity, I suppose. If everything can be said the same about two things, except that one is this and one is that, then you're assuming PII is false, because if PII is true, then there aren't actually two things. You can't say one is this and one is that because there being two objects is just an illusion.

If there is a wider lesson here, it is that the traditional discourse of properties with its atomistic character, in which objects subsist without any external context, is inadequate. — SophistiCat

If this is what property is taken to mean, that they are intrinsic to objects and don't require external context, then I would do away with the notion of properties entirely. This is where my structuralist perspective comes in, because I don't believe objects have intrinsic qualities, rather that they are defined by their places in some structure, where the structure is just the composite of relations between things. However, property could still reasonably be defined of a thing as any relationship it has derived from the structure. This is why PII seems so important to me: if it were the case that two things related to everything else in exactly the same way, and those things were not actually the same thing, it would just shatter my worldview.

Random thoughts:

• Why is there something rather than nothing? Because there has to be something to have nothing of.
• Nothing is the lack of anything. It can be conceived, understood, and communicated. It is something.
• But nothing doesn't exist. It is the necessary non-existent that allows reality.
• But nothingness exists—it is everywhere, in fact. Wherever one may find something, there is nothingness, hiding what isn't there.

Also, physicists don't know nuthin' bout nothing. :roll:

Both you and QuixoticAgnostic have used numbers in both of your "non-mathematical" laws! — Harry Hindu

"You can say there is a dead cell with 3 live cells in its neighborhood" is a description of a state, but not a mathematical law because it doesn't describe the behavior of the system or how things interact, which was the point of me bringing that up. "However, I would qualify that mathematics isn't just about relationships, but interrelationships or, better put, interactivity. The distinction is in relationships that don't merely describe, but define."

I never denied that the first universe was mathematical. I specifically said that it was, and even bolded the text to make it easy for you to see, but you still missed for some reason. — Harry Hindu

Hmm. . .

"I believe you're describing what my first intuition was, that both universes are actually mathematical, just at a different level of description and precision."
— QuixoticAgnostic
No, that both universes are explainable. Like I said, you can use words or numbers to explain it, and numbers are just words. — Harry Hindu

Yeah, that certainly doesn't look like denial :roll:

Also, reducing mathematics to numbers and numbers to words (not even descriptive words, but literally just the denotation "one", "two", "three", etc.) doesn't make a whole lot of sense. Mathematics encompasses much more than just quantity and words don't always describe mathematical relationships. Your "numbers are words" argument is confused: just because numbers are words doesn't mean all words are numbers, which means it isn't necessarily the case that words describe mathematical relationships.

If you say:

a =/= b

Then I can write you a property that a has but b doesn't, namely:

LAMBDA x[x = a]

The only way to deny the conclusion is to stop me, somehow, from being able to express this property. — Snakes Alive

What formalism is this? I'm somewhat familiar with basic logics (propositional, first-order, second-order) but this doesn't quite look like any of those. Is it lambda calculus? How does the statement function then?

But I'm pretty sure your argument is circular; in trying to prove PII, you're assuming PII. You argue "If $a \neq b$, then there exists a property $a$ has that $b$ doesn't", but that is exactly what you're trying to prove! Your argument is of the form, $\forall x \forall y \left [ x \neq y \rightarrow \exists F \left ( \neg \left ( Fx \leftrightarrow Fy \right ) \right ) \right ]$,
which is just the contrapositive of PII, $\forall x \forall y \left [ \forall F \left ( Fx \leftrightarrow Fy \right ) \rightarrow x = y \right ]$. So your premise is equivalent to the conclusion, and your reasoning is circular.

Furthermore, if we grant you that the existing relation is that of identity, then the premise becomes, $\forall x \forall y \left [ x \neq y \rightarrow ( \neg \left ( x = x \leftrightarrow y = x) \right ) \right ]$ and logically reduces to:
$\forall x \forall y \left [ x \neq y \rightarrow \left ( \left ( x = x \wedge y \neq x \right ) \vee \left ( x \neq x \wedge y = x \right ) \right ) \right ]$,
$a \neq b \rightarrow \left ( \left ( a = a \wedge b \neq a \right ) \vee \left ( a \neq a \wedge b = a \right ) \right )$,
$a \neq b \rightarrow \left ( \left ( \mathrm T \wedge b \neq a \right ) \vee \left ( \mathrm F \wedge b = a \right ) \right )$,
$a \neq b \rightarrow \left ( b \neq a \right ) \vee \mathrm F$,
$a \neq b \rightarrow a \neq b$, which is a tautology.

I'm probably mistaken in my logic somewhere but I spent far too much time thinking about this to throw it away. So if I am wrong, please let me know, would be a good learning experience.

Well, I can certainly sympathize with that optimism. I suppose if any miracles do happen, they'd come from the mind, rather than elsewhere in nature. That said, although I do entertain romantic ideas more than I perhaps should, I am mostly grounded reality quite literally, in that I accept the physical world as it's been described and experimented with and come to the conclusion that it is self-contained, ordered, and describable. So to accept a disembodied, incorporeal mind has a causal effect in the world through a biological apparatus (the brain) is a leap in logic to accept. But the mind sure is amazing, and probably underestimated. I just wouldn't take the mysteriousness and our ignorance of it to reach unsubstantiated conclusions through literal magical thinking (thinking that disobeys the laws of nature)..

Well, why do you believe it?

Because you seem to be feeling some sort of existential dread and I'm trying to figure out why. So you think the only thing that exists is you. Strawberries don't exist. But do they still taste the same? Does a sandy beach still burn your feet? Do you still fear death? Do you still feel? And what is existence, if not feeling?

It's not that things aren't possible, it's whether or not there's "some world" in which the possible things are necessary. I haven't looked into modal philosophy too much, but I'd figure that by possible we simply mean that which we don't know to some degree of certainty whether the proposition is true or not.

As for your teacher's problem, adding that last part ◆P suggests to me that he did mean "any one". So then, if only one possible world exists, what does it mean if it's possible for there to be an alien on Mars? It means there's an alien on Mars. I suppose what he's thinking is that you could then say, "well, it's possible that there isn't an alien on Mars too, so that's a contradiction", but who says that that second proposition is possible? We were only asked to consider one proposition, and if that proposition is possible, then it's necessary, and so its negation is not possible.

Oops, I meant to distinguish between "only the self exists" and "only the self can be known to exist". Which category do you fall under? And why, while we're at it.

Okay, so we're just talking about knowledge then. In that case, what do you care if all you know is your own existence? Does the taste of a strawberry feel any less different? That's my crude, off the cuff response.

I think the mistake would be the opposite: if he meant "any one", as in if there is this possible world, and I say something is possible, then that possibility must be necessary. If he meant "any and all" propositions were possible, then that would just lead to an infinite infinity of contradictions.

What do you understand solipsism to mean?

Yeah that was his response, I didn't receive any credit lol. — Justin Peterson

Wait, what? How is that the case? By "any proposition" does he mean "any one" proposition or "any and all" propositions? Although, I don't like the concept of "possible worlds" AT ALL so I wouldn't be surprised if there's some strange philosophical stipulation.

I can't tell if we're disagreeing or not lol. I'm happy to accept that mathematics describes the relationship between things. In fact, that is the basis to most of my philosophy. However, I would qualify that mathematics isn't just about relationships, but interrelationships or, better put, interactivity.

The distinction is in relationships that don't merely describe, but define. For example, in Conway's Game of Life, you can say there is a dead cell with 3 live cells in its neighborhood. I just described a relationship between a cell and its neighbors, but this isn't a mathematical description because it doesn't tell me about how these things interact with one another. If I say, however, that cells are initially either "live" or "dead" and transition states according to rules X, Y, Z, then I am making a mathematical statement because it is defining the behavior and interactivity of things.

Although what I'm confused about is you say both universes are explainable, but deny that the first universe is mathematical? You say "if things are interrelated, then they are explainable in mathematical terms", so in universe A the two objects are interrelated, so they are explainable in mathematical terms, which means the universe is mathematical, no? Regardless, we're both in agreement that there is no fundamental difference between universe A and B.

I believe you're describing what my first intuition was, that both universes are actually mathematical, just at a different level of description and precision. But this seems to run into problems, which I think you may or may not be addressing by specifying the symbolizing of relationships.

If we speak about a universe where there exist 3 masses that follow the classical laws of gravitation, you have the 3-body Problem which is mathematical. But if you imagine the universe of a cell (I'm not going to pretend I understand how the cell works at even a high school level), you can define all the parts and describe how all those parts interrelate, and even though this may be a consistent and determinable system of relationships, we wouldn't generally consider that mathematical. Yet, we can go on to consider something like Conway's Game of Life, which is similar to a cell in the sense that you describe the parts (the grid of cells, "live" and "dead" states, neighborhood, tick) and how those parts interrelate (the rules by which cells are born and die according to their neighborhood and their propagation through ticks), but this is mathematical in nature. Which brings me back to my initial question: what makes one thing mathematical and the other not?

I suspect the devil's in the details. The cell is defined and described in non-quantitative means, by empirical observation. Something about this is different from how we define and describe the Game of Life, which is a priori, in a sense. I don't think it's merely quantitative though, as plenty of mathematics isn't quantitative, in the sense that not all mathematics is about numbers and measurement. But if it's not quantitative, what is it?

I've been busting my brain over this question for the past several hours now: what makes something mathematical? Is it a level of rigor? Must you reason from fundamental concepts? What makes physics so mathematical as opposed to the "higher-level" sciences? Is it the quantitative nature over qualitative? Maybe I'm just having a bad night but I can't figure it out for the life of me.

I don't know, tbh. All I'm saying is, given how strange it is, and with how physicists say things of the like, I wouldn't be surprised if it was the case (though if I'm being perfectly honest with my beliefs, I expect it is).

You need to run this by me again. I don't get it. If you have the time and patience that is. Perhaps you can link me to a detailed account of Max Black's thought experiment. Thanks — TheMadFool

I'm speaking of the arguments other people have made in this thread. Specifically, unenlightened argued that even if they are in different locations, because the observer can't discern between them, PII is false. I don't think anybody actually made the argument that the two objects are actually in the same location though.

Here's the link to Black's original dialogue: http://home.sandiego.edu/~baber/analytic/blacksballs.pdf. Honestly, I think defenders of the argument might be reading too deeply into it. If you read it, there's a lot of waffling about what symmetric universe means. Like, initially the mirror of symmetry is literally a mirror, and so to be copied in the mirror means your heart is on the right side of your chest. That seems clearly ridiculous and unecessary to the argument, but shows, to me, that the argument isn't as profound as it seems to be. Of course, I'm probably just not understanding it properly.

By the way, anticipate a response in your other thread, it's basically the starting point to my metaphysics, and will probably shed some light onto my claims about space and time not being fundamental.