OR reason as a circularity (it self-justifies). Can we say that what we're dealing with here is a vicious virtuous cycle? — Agent Smith

Or we could follow Kuro's lead and say that the circularity isn't vicious but virtuous; at the very least, reason ain't no hypocrite (it demands of itself what it demands of others and ... meets those demands; how exactly, Kuro will tell us). — Agent Smith

Excellent: exactly my point. :)

I don't understand how this addresses my argument. Can you specify which step you disagree with?

1. Physicalism is true (assumption)
2. Everything that exists is a physical object (from 1)
3. The set of all that exists is the set of all physical objects (from 2) — Michael

(1) entails that no sets exist, including that set in (3) regardless of its incoherent status. It could be any ordinary set, like a set of an apple, someone's toenail & an ant. A set whose members are physical objects is not itself, as a set, physical (for obvious reasons: it'd entail infinite interpenetration)

The other issue is that, obviously, this still instantiates the same contradiction (4-5) in my initial argument: the powerset is either not larger than its set because there aren't more members in it than in the set, falsifying either the powerset axiom or this set's status as a powerset, or there is no set of all that exists.

FWIW, this is technically not a valid argument since 6 seems to only follow from (what I assume are crudely skipped steps for brevity's sake) the assumption in 5, that the powerset is literally empty, which not only is an issue in the terms I explained earlier (falsifying the powerset axiom or just giving up the nonexistence of that set), this still never means that the powerset is empty. That falsifies the axioms we use for set building, namely in that we can join any urelement or set into a further set containing just that set or urelement (being a singleton), but if the members of that set can't be joined into singleton supersets, let alone the powerset itself, then we've falsified several of our basic set theoretic apparatus just to suppose the existence of this set (which still manages to be incoherent, regardless: this doesn't actually make a powerset of a non-empty set empty!)

. Everything that exists is a physical object. The set of all that exists is the set of every physical object. — Michael

If you assume physicalism, the set of all that exists, let alone the set of anything, since sets are not physical objects neither identical to their physical members nor the collection of their physical members (the proof of this is simple: suppose it is the case, then submerge that same set under a further set, which is mathematically non-identical!)

So physicalism just entails mathematical anti-realism, and it goes back to what I said earlier here:

There's one thing that the platonist and nominalist would still agree on, in that contradictory sets, like the Russell set, or this universal set, do not exist because they're incoherent (and so would their existence). Certainly the nominalist needs not raise the issue of whether any sets exist at all to just say that this one set does not exist — Kuro

The fixing to what sense of existence is unnecessary, namely because of the above, and further because the platonist/nominalist can perfectly disagree while holding to the same theory of existence (though they can differ if they want to, obviously), as I clarified earlier as well:

This is not to say that there's some different theory of existence necessarily being employed by the platonist or the nominalist (of course, there can), but the nominalist and platonist can perfectly disagree in using the same sense of existence (say, as a second-order predicate of concepts a la Frege, or as an instantiation of properties a la Russell) — Kuro

Alas, I think your request for clarity was preemptively satisfied unless you hold to the presumption that realists and anti-realists must be using different senses or theories of existence. I don't take you to be claiming this, since you didn't object to it when I asserted its negation, but just on the possibility this is a claim of dispute it can be falsified using a trivial example (i.e. Quine vs Field), a pair of platonist / nominalist(fictionalist) who disagree on the existence of mathematical objects while using 'existence' in the same sense. Obviously though, the reverse claim of them having to use the same sense is not true either, as there are indeed platonists/nominalists who disagree while using different senses, examples being along the lines of Meinong

principle (PSR) that all statements need to be proven ( — Agent Smith

No! This is not correct, the PSR is not an epistemic principle regarding justification. The PSR is a metaphysical principle regarding explanation, that is, any facts in reality out there are explained by other facts (these can be causal explanations, grounding explanations, or what not).

For instance, the fall of the apple is caused by, say, the properties of its mass, the laws of physics and what not, and these facts conjoined together explain the apple's falling.

This is completely different from principles regarding epistemic justification. For instance, we may think we need a reason for all our beliefs, including us believing the apple fell, and perhaps our reason for thinking this is that we think our senses are reliable (reliabialism), we're using induction (Bayesianism), so on.

The first is an explicitly metaphysical principle not about what we should believe & standards of justification but about the explicability of reality, the other are epistemic principles about our beliefs and justification

By the way, the PSR is usually restricted to contingent facts. Proponents of the PSR do not generally think necessary facts, like 2+2=4 or the law of identity require further metaphysical explanation, but only contingent facts like eating dinner today, though not everyone restricts it, obviously

Unlike logical circularity, which only makes for an unpersuasive argument (i.e. Q, thus Q) which is uninformative, epistemic circularity is actually necessary for any coherent epistemic principle.

Suppose we have an epistemic principle, like evidentialism, saying that for any P we believe, we need to have evidence that P: if this thesis of evidentialism itself doesn't actually have evidence through evidentialism, then either evidentialism is self-refuting or is not of global-scope (e.g. there are exceptions to the rule). But our epistemic principles should be our most general and topic-neutral principles, so we're in a very problematic spot if we lack any global principles for good reasoning.

But consider that, given evidentialism, it turns out we do actually have evidence of evidentialism for us to believe in evidentialism. This is clearly a case of epistemic circularity, but it is the only coherent route for us to take. It's not bad to have an epistemic circularity at all, in fact, we should be very worried if our epistemic principles failed to verify themselves!

Note: I'm not saying evidentialism itself is true here: it's used as a prop for an example defending epistemic circularity. Evidentialism itself does not entail epistemic circularity, there are evidentialists who are foundationalists, infintitists or other non-coherentists

The "existence" of mathematical objects in mathematical anti-realism is different to the "existence" of mathematical objects in mathematical realism. — Michael

Correct, hence why platonism and nominalism about mathematics here is far-reaching and beyond the closer phenomenon at hand, being just that universal set itself. Surely any ordinary set, even a coherent one like {1, 2, 3} does not exist independently for a nominalist about abstract objects (though, they might still insist it exists as a concept or, for Field, as a fiction abstracted from concrete reality) though it will for the platonist. This is not to say that there's some different theory of existence necessarily being employed by the platonist or the nominalist (of course, there can), but the nominalist and platonist can perfectly disagree in using the same sense of existence (say, as a second-order predicate of concepts a la Frege, or as an instantiation of properties a la Russell)

There's one thing that the platonist and nominalist would still agree on, in that contradictory sets, like the Russell set, or this universal set, do not exist because they're incoherent (and so would their existence). Certainly the nominalist needs not raise the issue of whether any sets exist at all to just say that this one set does not exist, which is the first point I made in this post: the fact that this universal set, the set of all that exists, is contradictory.

You seem to have missed the point. There is a distinction that needs to be made between the definition of a SET and the definition of a POWERSET. They are not one and the same. — ThinkOfOne

There's no point I missed: no where in any of my entries I equivocated sets with powersets. Tegwar does not contain all that exists in that universe, namely because the set cannot contain either itself or the powerset (and its powerset, ad infinitum). The notion of a set of all that exists is not possible. Similarly, you cannot exhaust all that exists in any universe obeying set-theoretic principles: some universe where all that exists is some ball in space denoted by a letter is a figment of the imagination.

But that something is a member of a set isn't that it exists. For example, Santa doesn't exist and so isn't a member of E, but it is a member of the set {Santa}. — Michael

Sets do not have meontological members, because set-membership itself is a relation requiring that there are two relata of the set and the given member, yet the necessary condition can't be satisfied when one of the relata quite literally isn't there. Since Santa does not exist, {Santa} as a set doesn't exist in the real world (though there are possible, hypothetical universes out there where Santa does exist, and thus the singleton exists as well).

There actually is one set with no members, but it is a unique set. This is called the empty set, uniquely satisfying that ∀x x∉S. This does not mean that some spooky metaphysical concept of nothingness/nonexistence/emptiness/whatever is itself a member of the set, rather, literally that the set has no members.

No equivocation at all between "is a member of some set" and "exists", it's not a matter of conflating the concepts rather simply a matter of logical entailment. It's incoherent (and inconsistent) for anything to be a member of a set but also simultaneously not exist.

When I meet a married couple I don’t meet a married couple and the husband and the wife. Meeting the married couple is meeting the husband and the wife, and vice versa. The married couple isn’t an entity that’s additional to the husband and the wife, even though there are things we can say about the married couple that we can’t say about the husband or the wife individually.

If you try to say that the married couple and the husband and the wife all exist, and so 3 things exist, you’re counting the husband and the wife twice (or rather, 1.5 times each). — Michael

I've read your other (later) post prior to this one, but coincidentally it indulges in the same error that I pointed out in my response to your later post: you default to the idea that all sorts of plural quantification are identical with the sets corresponding to the plurality being quantified.

The set of the married couple {husband, wife} is not identical to the plurality of the husband and wife, nor is the arbitrarily infinitely many sets including the husband and wife (i.e. {{husband}, wife} identical with each other nor that first plurality.

Physical things, be they collections or singular, are never themselves sets: they just can join sets. By talking about a set of objects where that object is a member of the set, you've not counted the object again. It isn't the case that the wife exists infinitely many times because there are infinitely many sets that contain the wife.

What does this have to do with philosophy? It's pure Math. — Alkis Piskas

No mathematician will ever tell you that discussing whether abstract objects, like mathematical objects, really exist in the world or are just contained within minds is a mathematical topic: this is what a substantive portion of this discussion led into, so this is more accurately construed as philosophy of mathematics informed by insights from mathematics (it's very difficult to do philosophy of any x without pretty extensive detail into x itself).

The point that you seem to be missing is that it's a simply a matter of definition -and definition alone- that powersets don't contain "all subsets" of the "original set". The original set IS the "set of all that exists". To conclude that the original set does not exist is nonsensical. It is borne of a failure of conceptual understanding on your part. — ThinkOfOne

Powersets do contain all subsets of their original set, this is a well-proven theorem by Cantor that any elementary introduction to set theory should teach you. The set of all exists, by its very definition, includes the cardinality of a set strictly larger than it is, and is therefore incoherent/a contradiction (the proof of this is a very trivial exercise: Suppose E, then there exists P(E), P(E) is cardinally larger than E, therefore there exists x's that are members of P(E) and not E and thus E isn't E).

This does not mean the things that exist, like my keyboard or this screen, do not actually exist, but rather they cannot all be collected into set. If your standards of "conceptual understanding" is mathematical inconsistency, this is a problem on your end.

I address something like that here. The set of both metals weighs 3g but none of its members weigh 3g. It doesn't then follow that we should treat the existence of this set as being additional to the existence of each of its members, else the total weight of things which exist would be 6g, which is false in this example. — Michael

This is a category error namely in that sets never weigh anything (you're confusing mereological complexes with sets, a confusion many participants of this discussion took on and continued to presume despite my clarification of the distinction in an earlier post right here) Sets lack the physical properties of mass or weight, even if all their members have this property (hint: they're distinct from their members).

What you're looking for is either 1. plural quantification (in plural logic) or 2. mereological composition - both of these are distinct formalisms that are not isomorphic to our set theoretic apparatus. In plural quantification, you are quantifying over nothing over and above the x's, and not any notion of collection they form treated as a single. In mereological composition, you're quantifying over parts bearing a particular relation and arrangement, often proper-parthood, to some whole, and in that venue it's under dispute whether the wholes are identical to just the collection of their parts (this is not at all isomorphic to whether sets are identical to their members, whose answer is a trivial no)

That said, mereological wholes may have physical properties: for instance, an apple is a complex composed of its atoms, and it has weigh, though I'm not sure if weigh would also be possessed by its super subatomic particles, I suppose that debate would be fleshed out more there

Plural logic would be the most natural formalism of asking about, say, the weigh of a collection which all have physical properties, because the plural quantifier quantifiers over nothing aside those x's in the collection itself and would simply be a summation of their properties. When comparing these collective relations, the plural ≺ would be the "less committal", the mereological P being in the middle and the set theoretic ∈ being the most committal.

Apples can be members of sets but are never themselves sets. There are no instances at all where a physical object like an apple is a set, especially if it's just because it has parts.

The reason you and some of the others are getting mixed up here on this non-issue is that you're employing the inappropriate apparatus (set theory instead of mereology) to think of this whole-parts identity problem, but you're thinking about it with presumptions that are already at fault, like supposing of complex objects as literally being sets or that they themselves have physical properties like weight which are both incoherent.

Is my wastebasket a set ? — magritte

It's mereologically complex, and thus a composite by having mereological parts (as in, the parthood relation P). It is not a set, though there exists a set that contains exactly your waterbasket, and this set is not identical to your waterbasket (neither is the set that contains the set which contains your waterbasket).

I'm writing this reply not to just you in particular but also to everyone else reading because a good chunk of various people in this thread have confused the notions of mereological composition with that of being a set. There is indeed a debate in metaphysics on whether composition-is-identity, i.e., whether an apple is identical to its atoms or a further thing, but this has nothing to do with whether a set is identical to its members because ordinary objects are not sets.

And the answer to the latter question, of whether a set is identical to its member/s, it's a mathematical consensus of no, namely in that {x} has the property of "is a set" and x doesn't. This consensus much unlike the mereological debate of whether a composite is identical to its parts, which is indeed a heatly debated topic in metaphysics, and what a good chunk of this thread mixed up with its set theory counterpart that does not yield any real dispute.

FWIW, there are many interesting similarities between mereology & set theory, though they're not analogous at all in this particular respect. Their differences stem from the fact that mereology is intended to formalize our general notion of 'parthood', whereas set theory a regimented notion of collection & infinity. There are fascinating intersections like mereotopology.

I think you don't even need the set of everything to generate the problem. You just need any set that includes its own cardinality and it will blow up incoherently to a meaningless version of infinity. — Cuthbert

Correct! Though it's unclear if it's meaningless- meaningless per (I think all?) all set theories, yes, but certain notions of infinities that are too large for any cardinal to have meaning in set theory have actually been captured with the use of plural logic.

Either way:
1. There is a set of "all that exists"
2. There is a powerset for "all that exists" — ThinkOfOne

The powerset will always strictly be cardinally larger than the set, and as you yourself understand, those subsets are not actually part of the original set (so there will exist members of the powerset not in the set, making the set not itself hence why the set doesn't exist) You've articulated precisely what I said in my post, so maybe this is a misreading? I'm not sure where exactly you're disagreeing with me or objecting

But I'll try to be more precise in future if this is a misuse of the term. — Michael

I understood that you referred to the fallacy of reification, as used by AN Whitehead, referring to that error of reasoning in where abstract objects are treated as if they were concrete. Coincidentally, reification came to mean the same sense in ordinary language. Not sure if contemporary analytic philosophy continues to give the term the same meaning, & I'm with you on valuing precision, so I opt for the standard terminology where platonism denotes the position that abstract objects really exist (and are actually abstract, viz. they're not mind-dependant) and nominalism the contrary. I'm basically answering the request for clarity here by saying we can use 'platonism' instead of 'reificaiton' to refer to the position of sets existing as abstract objects.

The point I'm making is that if we have a red ball and a green ball and a blue ball, then even though we can consider them in various configurations, e.g. (1) a red ball and a green ball, (2) a red ball and a blue ball, (3) a green ball and a blue ball, etc., it's not the case that there are multiple balls of each colour, and it's not the case that each configuration is a distinct entity in its own right, additional to the red ball, the green ball, and the blue ball. That realist interpretation of sets (what I think of as reification) is, I believe, mistaken. — Michael

This is an inaccurate understanding of sets. Recall the axiom of extensionality. {a, b, c} and {c, b, a}, as well as {b, c, a} are all just the same set, because they have the exact same members and thus satisfy coextension. Sets, plainly as sets, are therefore invariant with respect to these configurations you use in your example, which are otherwise too fine-grained of a notion. There's a grain of truth here in that a realist interpretation of sets would indeed count {b} and b as separate, distinct objects and thus count two things, but this is unrelated to your configuration problem.

Though worry not, set theory has exactly the notion to capture what you're looking for (the beauty of mathematics at work) for your configuration problem, that is, the notion of ordered pairs, triples, etc and so on- generalized as ordered n-tuples. While {a, b} and {b, a} are exactly the same set in set-theory, ordered pairs like (a, b) and (b, a) are strictly non-identical when a & b are non-identical (had they been identical, it'd be a singleton satisfying "co"extensionality reflexively, hence why non-identity cases fail here).

Now, a realist about sets presumably will be a realist about ordered n-tuples, so there you go, we've "fixed" the configuration problem on the technical level. This is still hardly a problem though, namely because of Leibniz's Law: there are predicates true of a set that are not true of its members. For instance, consider cardinality. The set {a, b, c} would be truly predicated of having the cardinality of 3, though none of its members have a cardinality of 3, in fact, it'd be a category error to speak of the cardinality of its members in any case where its members are urelements. There are probably even more obvious examples like sethood, but I wanted to appeal to purely mathematical properties. In other words, I think the problem you raise is completely artificial.

I don't think that attitude is wrong at all. I just have suspicions it's somewhat ad hoc, much like the charge that proponents of inconsistent mathematics complain of post-ZF mathematics.

The powerset axiom is clearly an intuitive (and correct) principle, but generalizing it completely (along with existential assumptions) entails some very exotic and "naughty" entities that we may want to ban! The question here may be a question of whether we should do this, or what intuitions do we prioritize? I'm not sure.

There are three senses of "is"

1. The predicative sense is of the form "x is F" where F is a property that x bears.
Example: The apple is red.
Logical form: Ra

2. The identity sense is of the form "x is y" where x and y are identical, they're the same thing.
Example: Superman is Clark.
Logical form: s=c
This also means that when counting, we'd not count Superman & Clark as two different people, for they're one and the same, and that they have the same properties.

3. The existential sense is of the form "There is x" which we just assert the existence of something.
Example: There exists an apple.
Logical form: \Existential-quantifier x x=a
This is philosophically controversial: certain Meinongians as well as proponents of free logic alternatively propose an existence predicate, though this comes with its own set of nasty problems.

Suppose x,y and z exist in the world.

This gives us 6 sets - (x) - ( y) - (z) - (x,y) - (x, z) - (y,z). — RussellA

Additional reply: this is technically incorrect. The existence of any object in the world allows us to generate infinitely many sets by reiterating supersets as well as empty sets, but these cardinalities are not at all problematic with respect to their powerset in the same way the set of all which exists is (whose identity defines it to include its powerset).

On the other hand, we might say a universal set can trivially exist without this problem by just defining it as an NBG class, i.e. as not a member of anything else.

That's not true. The power set includes repeated members. Taken from the Wikipedia article: — Michael

You're confusing singletons with just the elements. x, {x}, {{x}}... so on are all not identical with each other, and for instance the singleton set {x} is a member of the powerset but not the set, whose member would be x.

Right, so this is an issue of reification. Some people think of a set as being some abstract, — Michael

Reification deals with treating abstract entities concretely, like asking where the average family of 2.4 children lives (that average family is an abstracted notion that is not concretely instantiated). Reification does not target merely the existence of abstract entities, otherwise it's simply another name for the philosophical position of nominalism- a substantive metaphysical viewpoint- and not a general error in reasoning.

Is there any persuasive argument that "combinations" do exist in a mind-independent world ? I have yet to come across one. — RussellA

This is really a response to both your first and second reply, but I'm quoting the second one so that this message is shorter. Taking sets to exist is the most natural interpretation of the existential quantifier in set theory without awkward paraphrases: it's unclear what we mean by that the set of natural numbers N exists but not the contradictory Russell set if neither sets exist (in fact, the very invention of ZF, ZFC, and later NF over naive Frege-Cantorian set theory is just to prevent the existence of contradictory sets). That means the standard reading of mathematical facts, like "there are prime numbers" is that there really are prime numbers, along other things. Here, I'm just presenting a standard Fregean argument in virtue of the fact that mathematical terms and statements are meaningful, and in being meaningful they refer to something: namely mathematical entities which are neither mental nor material (thus abstract).

The other influential line of argument for this view comes from Quine-Putnam indispensability arguments, which owe to the fascinating empirical success of mathematics in the natural sciences. By regimenting natural scientific theories into a canonical language like first order logic, we have to quantify over mathematical objects in our domain. But if by quantifying over, say, electrons and their properties in our domain, we take those things to exist, then in an analogous manner by quantifying over mathematical objects that are necessary for our scientific theories we take them to exist. Field famously objected to by attempting to formulate mathematics from spatial relationships, although the project was unsuccessful. The Quine-Putnam indispensability argument can be seen as a move from scientific realism to mathematical realism.

Well, to me, modal logic is part and parcel of propositional logic — Agent Smith

This is untrue. Propositional calculus does not even have first-order quantifiers (forall, exists) to have modal operators. And modal operators are behaviorally analogous to quantifiers (and are rightly a kind of quantifier that doubles as an operator). Zero order logics, like prop. calc, by definition do not quantify over anything.

You might be conflating model-theoretic valuations (of prop. calc) or interpretations (of FOL) with the nodes that exist in possible world semantics for modally extended versions of FOL (like FOL₌ + S5).

A wff is a validity just in case it is modeled by all valuations (or interpretations).

I understand wisdom as an agential notion- i.e. a notion primarily with respect to your know-how and decisions rather than your know-whats & beliefs.

Omni is latin for 'all' and scientia is latin for 'knowledge'. So historically it has meant 'all knowledge'.

If one wants one can define omniscience as 'in possession of a potato'. Hell, one can define 'God' as a potato and then insist that you just dug God up in the vegetable patch.

I have also justified this use of the term: if you define it differently, you'll get an incoherent collection of attributes, for it does not seem possible for a person to be omnipotent, and omnibenevolent and in possession of all truths. — Bartricks

The standard understanding of omniscience is alethic: if you're to go ahead and suppose that the way the term is standardly used is inaccurate on etymological grounds, then your charge is in the class of linguistic prescriptivism

I'll simply repeat what I said: to be in possession of all trees does not require being in possession of all potential trees. LIkewise, to be in possession of all knowledge dose not require being in possession of all potential knowledge. We're all potential murderers - should we all be locked up for actual murder? — Bartricks

This makes a conflation of the dispositionalism about propositions being in principle knowable versus propositions that are actually known with its generalized notion. If being 'omniscient' requires you to just know all that which you actually know, then it's trivially true.

Consider a child who only knows his 123's and ABC's. It's true for that child that he knows all what he actually knows, and not the wide array of what is potentially there to know, like the fact that his humans procreated to conceive of him, a true fact which is potentially knowable that he is completely clueless of with respect to his actual knowledge. Your analysis entails this child be omniscient, since he knows all his actual knowledge, which makes the term largely moot and absolutely useless. This is not uncharitable, this is quite literally your view: I initially took on a far more reasonable interpretation which you so kindly corrected me on by clarifying that it was not your view by asserting this ridiculous view that confines knowledge to just actual knowledge (and thus defining omniscience in terms of actual knowledge, which is as trivial as it gets).

Omniscience means 'all knowledge'. If - as many contemporary theists foolishly do - one defines it to mean 'all truth beliefs' then one is simply misusing a term (for one can be in possession of all true beliefs and yet not be in possession of all knowledge). Certainly it is no abuse of the term 'omniscience' to use it to label someone who is in possession of all knowledge. — Bartricks

This is just etymologically branded linguistic prescriptivism. Regardless, I already granted your analysis as you pointed out

But in fact you swapped my definition of omniscience for another. To be omniscient is to be in possession of all actual knowledge, not all possible knowledge. — Bartricks

I made the most charitable interpretation. If you truly mean 'all of actual knowledge' by omniscience then this is an awfully trivial definition wholly divorced from what anyone means by 'omniscient', since, I, like many other living people, know everything that I actually know, which has virtually nothing to do with knowing everything that is knowable (which was my initial charitable interpretation) let alone knowing every truth (what most theists think). This just prima facie renders anyone that knows anything to be omniscient, since they know everything they actually know.

God is in possession of all knowledge. — Bartricks

I think there can be two readings of omniscience. If we just take it to be the possession of knowledge, then the rest of what you said follows. However, perhaps a more intuitive notion that captures what theists usually mean by 'God' is K(God, p) ⟷ p (if something is true, then God knows that it, and vice versa). Generally, lots of theists will want to say that there are is no lack of awareness diagnosing their God, no truths he is unaware are true. In any case, they'll take your God to be 'less perfect' than theirs in this respect.

But allow me to take your analysis as a pretense and forget what I'll said. I'll give you a reason that satisfies your Cartesian hunger even with the stipulation of your analysis of omniscience, where, as an omniscient agent, I only know things which are in principle knowable, i.e., can have a justification.

Surely, this is the case for any arithmetic operation on the natural numbers 1, 2, 3, ... and so on: there is a mathematical method to derive the result of any of said basic arithmetic operations, and thus a way to justify (and know). But I can introspectively access the fact that I would not know what (49082423 / 234765) x 54 equals: I know that I do not know this because I do not even have any belief on any simplified expression that is equal to this expression, and surely a belief is one of the first prerequisites for my knowledge of anything.

In fact, since I can be introspectively aware of what I believe, disbelief, and lack an attitude of belief on, then the very fact of me knowing that I lack both belief & disbelief (i.e. withhold judgement) on arbitrarily many matters, like, "what is the first letter of the 3rd chapter in Harry Potter?" (I haven't even read Harry Potter!) allows me to verify that I am not omniscient.

The problem of scope is within your English phrasing (the worlds which we read the word 'possibly' to quantify over), not the trivial inference (Kp ∧ ¬□p) ⊢ (Kp ∧ ◇¬p), which really is just an instance of a replacement rule.

We could not be wrong about p given that we know that p when we already restricted 'could've been' on the condition of whatever is accessible from our epistemic modality (meaning that Kp is true in all accessible worlds). Kp entails p in all worlds where Kp, so p is true in all epistemically possible worlds. Had we not known that p, it could've been that ¬p, which is a trivial and uninteresting result.

If 'could've been' is just our broadest alethic modality, then Kp does not entail □p for all contingent truths. This just means that we could've not known that p (where not-p could've been the case), not that we could've known p and been wrong about p

As you yourself suspect,

Note that I'm not saying: ◇(Kp ∧ ¬p)

From here:

1. It is possible that I know everything and am wrong about something
2. I know everything and it is possible that I am wrong about something

The former is false but the latter seems possible as the argument above shows. — Michael

(1) and (2) are both false when the modality of 'possible' is epistemic, (2) is only true when the modality of 'possible' is alethic, or if we know that p fallibly. There's really not much more to it.

A standard reading of events is as four-dimensional objects (in the philosophical sense, not the physical one), that is, regions of spacetime occupying spatial and temporal coordinates. At least, this is the preferred reading of event for someone like Quine or Lemmon.

Naturally, then, it follows that their parts are 1. events whose spatiotemporal extension is a proper subset of the 'larger' event, 2. 'points in time', if they exist, i.e. instants/moments 3. some atomic unit of time, if you believe in time atomism. Since these are spatiotemporal, each of these times are associated with whatever is spatially the case at each time token, so you could literally say, per your example, that the person running the marathon is a part of that event describing the phenomena including the fact that this person runs.

That said, it's unclear if this is at all a reduction of events. There are disputes in the ontology of time and whether there exists timepoints, and the relation between instants, timepoints (infinitesimal units of time), time atoms (the smallest possible unit of time, if it exists), and events.

Is that the right parsing? If you know that p then p is true, after all, and you could not be wrong about p being true, even if p, in some other possible world, might have not been true... — Banno

Exactly my thoughts. This seems to be an epistemic version of a modal scope fallacy where the possibility that not-p entails some possibility of not-p as a conjunction with knowing-that-p. But this is impossible: while p is possibly false, there are simply no worlds where p is both known and false (these worlds are contradictory, i.e. impossible).

So in virtue of knowing that p, we know that p is actually true, which is perfectly consistent with the fact that the truth of p could've been otherwise.

On what principles would you decide how to count all the dark matter? — Metaphysician Undercover

Like I said, most of this is really speculative. A candidate particle is the d-star hexaquark d*(2380) which is hypothesized to account for the universe's dark matter. This particle is composed of six quarks.

Then again, there's also the debate about ontic structural realism and other types of scientific realism versus instrumentalism: whether our best physical categories really carve the universe or whether they're just useful to us. I'm obviously assuming the former is true so that this question is in principle answerable.

I read somewhere that the observable universe contains roughly 10^80 atoms. That should be a good place to start at least when it comes to matter, oui? — Agent Smith

Alright. Some extra suppositions, quarks are the simplest form of matter and are indivisible in principle. This is not currently known, of course, we have no idea if we'll discover something more basic in the future or if they really are fundamental. But for hypothetical's sake, we'll say so be it.

There are 22 quarks in an atom. So from simple multiplication N is 2.2e81 iff the only objects that exist are these quarks. Let's call this for now Nᵩ (and conceptually separate it from Nₘ).

But what about things that the quarks make up, like apples? Should we count some trillion quarks that make up the apple, and also count the apple? If we can overcount like this, Nₘ will be massively larger than Nᵩ. It can also be arbitrarily modified to be as large as we want in terms of approaching infinity (although it will never itself be infinite unless we deliberately define infinite objects).

This is because "apple" is not a joint-carving concept recognized by the universe but something imposed by us in our language; only the quarks that make the apple are recognized by the universe. Thankfully, one of our previous criteria already makes this qualification, so we can't "cheat" this number up using our massive array of sortals we can construct. That said, this notion of structure to the universe is itself controversial in the domains of metaphysics and the philosophy of science, but there simply is no Nₘ if no concepts are joint-carving and purely reflective of our language because we defined Nₘ in that structural way earlier (although this might not be true to your understanding of it in a literal sense, it's true to it in a spiritual sense)

There is also another thesis in mereology, "composition as identity," that holds that some whole and exactly the parts that make it up are identical. An apple and its quarks are identical, so it makes no sense to see "apples" as a problem because we won't be overcounting all the parts that make it up and the apple, as they're precisely the same thing (per this thesis). However, this itself is as controversial as some may find it intuitive (the controversy is to no surprise: this topic in general has very little consensus). One of the simple arguments against this view is that a whole is one and its parts are many, so this is at least one property true of the whole that's not true of the parts, so they can't be quite identical.

Well, the quarks also constitute everything else inasmuch as they compose everything else, so similarly as there is "composition is identity" there is the similar thesis of "constitution is identity." This runs into similar issues: consider a lump of clay and the statue it constitutes. We can intuitively say they are one thing, so this thesis has some intuitive force. But if somebody came to deform the statue completely, we will be no longer compelled to think the statue survived (since it is defined by its particular shape): however, we're fully inclined to think the lump of clay had survived, even if it now instantiates a distinct form. So this is another basic argument against the mirror thesis to say that they can't be quite identical. To connect this back to the apple and the quarks: the quarks will survive if someone ate the apple, even if they may now instantiate a different form altogether. But we'd no longer say the apple exists, perhaps some human waste and other chemicals now exist, so clearly the things that the quarks constitute and compose are not quite identical to them.

This motivates the idea that including our natural language concepts, referred to by our ordinary nouns and proper names, forces us to overcount. We can restrict the overcounting to be finite, but since we can make our language whatever we want it to be, we can still count to any arbitrary finite number, giving us no clear answer. While we can simply discard those, per our earlier criterion, it goes back to something else you said:

Now consider the fact that in a universe that's finite there's gotta be a number that is the upper limit of a counting processes that yields the largest number possible/required to describe this universe — Agent Smith

When it comes to us describing the universe, we usually don't care about joint-carving the structural properties of the universe itself whatsoever. When we ask "how many apples are on the table?", quite literally no one means "how many independent apple-forming quarks are on the table-forming quarks?", returning some massive number. We just mean our own language, instrumental to our utility, regardless of whether it reflects the universe's structural properties.

However, we still think we're meaningfully describing the universe: at least in the way it appears to us.

In omission of our ordinary concepts, we remove the "cheating" problem of overcounting to any finite number, but this also removes otherwise true descriptions of reality that exceed Nᵩ (it's not exaggerating to say, per the post's title, that we need these descriptions, sometimes for our own survival). But, when we include those ordinary language descriptions, Nₘ itself loses its intended meaning and becomes whatever we suppose it to be per the intensions of our non joint-carving concepts. Either we can't describe everything we need to describe (in a practical way) or there is no principled Nₘ, its value is only a function of our choice! We're at a dilemma here :(

By the way thanks for the detailed analysis of my query, much obliged! — Agent Smith

Cheers,
This was a fun write!

The process of counting itself depends on sortals, which can be arbitrarily stipulated per our intension. It's also unclear if an upwards finite universe (mereologically speaking) is downwards finite: that is, if there are atoms (not as in atoms with electrons, but as in the simplest, indivisible unit with no parts.)

In other words, it is possible to count infinitely in an otherwise finite universe just in case we stipulate sortals whose extension is cardinally infinite.

With these suppositions in mind, it's important to note exactly the kind of environments that can possibly satisfy this finite Nₘ project:

• The magnitude of any value in this environment, spatial, temporal or otherwise, is a finite value
• There is no mereological descent or gunk: there are atoms
• There is no mereological ascent or junk: there are only finitary unrestricted sums
• Only joint-carving sortals count: that is, we can't posit sortals with arbitrarily infinite disjunctions to count infinite
• Nₘ is the cardinal number corresponding to the cardinality of the largest extension with regards to some joint-carving sortal
• Nₘ is finite

To answer your initial question directly:

Question: What's the Nmax for our universe? — Agent Smith

Unfortunately, our actual universe does not satisfy these conditions. But on the plus side, there are infinitely many possible universes which satisfy arbitrarily many Nₘ values.

I think that metaphysics, whatever meaning you give to it, has the defect of being bound to being: in certain contexts it is almost a synonim of ontology. The consequence of being bound to being is that it ignores time and subjectivity. Along history metaphysics was criticized by historicists, because, by trying to understand how things are, it looses sight of the fact that things, rather than being, are becoming (Heraclitus). As a consequence, about any metaphysical system of ideas, we should never forget that it is itself conditioned by its own being immersed in the flowing of becoming, changing.
The problem raised by subjectivity is similar, because the fact that anything we think of is conditioned by our subjectivity makes our thoughts dependent on the variability, unreliability of subjectivity.
In other words, the defect of metaphysics is its intention to reach a system of ideas that is expected to be stable, definitive, ultimate, objective, reliable, solid. — Angelo Cannata

Several traditions of metaphysics start from the first-person subject perspective instead of the third-person "objective" perspective. The most prominent of which are among Husserl's Phenomenonology which regarded the study of phenomena as a science and its first philosophy, and perhaps Kitarō Nishida along with many, many others.

Moreover, it should be made clear that the philosophy of mind in itself, whether it was primary or peripheral, in various systems of metaphysics, was historically considered "specialized metaphysics" as opposed to "general metaphysics," concerned with the ontos in general.

This is the first part of why subjectivity is not ignored. As for time, with all respect intended, you could not have been more incorrect. Time is one of the more important topics in metaphysics, and has been investigated in particular among Heidegger's Being and Time, McTaggart's Unreality of Time and most importantly the tradition of process philosophy itself with Whitehead and others who focus on time as a central notion with static being as accident to the actual entities.

So I'm of the opinion this is no critique of metaphysics.

This generally depends on the scope of liberty you permit to what counts as explanatory power.

The issue is that at this rate, you might as well just count the state of being brute as a proper explanans. In doing so, you need to quantify over no entities aside the explanadums (the entities we want to explain) themselves in context of one of /their/ properties (bruteness) as an "explanation". (This is very ironic, by the way), which would default to be a more parsimonious explanation than the God one by quantifying over one less entity with no loss to explanatory power.

For these reasons generally there are much stricter measures on the theoretical virtues and their application, because using them in this manner strips them of their utility.

The predicate of existence: did it come from nothing, something else entirely, God? — chiknsld

Existence is not a predicate, this is a Meinongian view that has been rebuked very thoroughly by Frege and Russell. There is no distinction between an existing and a non-existing apple: "existence" really is just being.

St. Thomas Aquinas, St. Gregory Palamas, St. John of the Cross, John Wesley, Immanuel Kant, Soren Kierkegaard, St. John Henry Newman, Dietrich von Hildebrand, Jacques Maritain, Edith Stein, Fulton Sheen, John Paul II, Benedict XVI, Martin Buber, Maimonides, Nikolai Berdyaev, Vladimir Lossky, Sergei Bulgakov, Richard Swinburne, David Bentley Hart, Psuedo-Dionysius, John Scotus Eriugena, and Kitaro Nishida. — Dermot Griffin

You definitely should check out Avicenna there if you're a fan of Aquinas, a good chunk of Islamic philosophy influenced Scholastic philosophy.

As for the later period, like Leibniz and what not, they got their access to that tradition through Ibn Tufail's novel which investigated some of the problems in epistemology that later became the focus of that era of philosophy

1. On theism, there is a mind that is distinct from matter and does not reduce to matter.
2. Any view in which their are minds that are distinct from matter and that do not reduce to matter entails dualism.
3. Therefore, theism entails dualism. (1, 2) — Raymond Rider

Premise 2 practically says, "if a view entails dualism, then it entails dualism." Since dualism is the view that mind and matter are distinct and do not reduce to each other, then any view on which there are minds that are distinct from matter and do not reduce to matter entails dualism. I do not think I need to defend this premise further. — Raymond Rider

I just skimmed over your post to these parts and I'll try to very briefly explain to you why you're wrong.

First, ever heard of Berkeley? He's a Christian man and an idealist. He believes in both a mind irreducible to matter and that minds are distinct from matter but he is not a dualist. How come?

Because ontological monism isn't confined to materialism. Idealism, the position that reality is fundamentally mental or that only the mental exists, for instance, would be monist, but also commit that minds are matter-distinct and non-reducible to matter, and still not be dualist.

Other positions are neutral monism, which reduce both mental and material to a single mode of existence that accounts for both. They're not dualists: notice the /monism/ in the name.

Your problem is Premise 2. You have a confused understanding of what dualism is.

I'm fairly surprised that not a single response to your post aside's says this.

When did I say empirical evidence? All I'm noting for the condition of falsification, is that we have a clear postulate we can put forward that would show when the proposition was false. If A=~A, then A=A would be false right? Take the simple note above and try to explain to me why A=~A is not a negation of A=A. — Philosophim

I've explained this several times in my earlier post that I can only refer you to what I've already written.

Have you heard of the phrase "when pigs fly?" It is a adynaton, namely in that when it postulates a subjunction believed to take on a highly implausible (or impossible) premise to ridicule on whatever follows. A is A in any valuation of A, so A is not A is simply never true. But entertaining A is not A simply entails trivialism in classical FOL, where any proposition you want to follow follows. (This is well known as the principle of explosion). — Kuro

Then you agree with me. The potential for something to be proven false, does not mean it can be proven false. — Philosophim

I've never implied that potential to be false is the same as falsity and I've clarified this an awful amount of times in my earlier post once again... you're beating the same strawman that I clarified isn't my position.

My position is that propositions like "a=a" simply /don't/ have the potential to be false. Yes, "a" can be false, but "a=a" is still true even if "a" is false.

And again, if something is provably true, it doesn't mean we can't invent a scenario in which it would not be true. The invention of the scenario in which it is not true, also does not mean it can be concluded that it is not true. You seem to be under the impression that falsification means "likelihood or chance" that it can be proven false. That's not what it is. Its just the presentation of the condition in which a claim would be false. And A=~A is that falsification presentation. It is of course, NOT true, which means that A=A is not false. But it can still be falsified. Does that clear it up? — Philosophim

No, Philosophim, I'm /not/ under the impression that falsification means likelihood or chance. The very fact that you reach this conclusion just to me shows, without any offense, your complete lack of understanding to any word that I've said, which is why I strongly feel like you should've picked up the introductory course I've linked you, or at the very least examined them, prior to this reply because I some of that information is genuinely necessary as a prerequisite for this conversation.

So let's start with the basics. Let's look at the truth table of a generic wff like "p → q"



Let's exhaust all the combinations of p and q's valuation to look at the valuation of the formula "p → q". Oh look! It seems that under the valuation of p being true and q being false, "p → q" returns false!



This will be our countermodel. Our counterexample. In this valuation, or in this combination of values, our formula returns false.

Ok, are you following me so far?

Now, certain types of formulas, known as tautologies, are special kinds of formulas. They're special precisely because /no matter/ the valuation, they will always yield true.

For example, let's look at "p → p"

Oh wait. It's still true even if p is false. And it's true even if p is true. In other words, there are /no/ countermodels.



No counterexamples. No conditions where this proposition can be false. No possibility of being false.

Wait, what if you don't trust the table? Luckily for you, there's something called a /truth tree/. A proposition can be verified to be logically valid, i.e. a tautology, in that if you assume its negation, you will always get a contradiction. Since contradictions are never true, the negation of the negation must be true. And the negation of the negation is the same as initial proposition, therefore the initial proposition must be true otherwise we have a contradiction, i.e. there are no falsity conditions. Don't believe me?



Okay, so let's find the feature that differentiates tautologies, like ("p → p") and non-tautologies, like ("p → q"). Wanna guess what this feature is? It's that non-tautologies have falsity conditions, countermodels where given certain valuations they /can be/ false. Tautologies on the converse do not have falsity conditions. They have no counterexamples. No conditions where they are false. In other words, their falsity is necessarily a contradiction.

That is because you are not understanding what I am saying. I am not saying 6=5. I'm just noting a case that IF 6=5 was true, then 5=5 would be false. Thus 5=5 can be falsified. It doesn't mean that 5=5 is false. — Philosophim

Have you heard of a vacuous truth? This doesn't matter because not only is the antecedent (6=5) false, which you agree, it simply /can't/ be true. You'll never, ever, in this universe, ever find that it becomes the case that 6=5. In fact, that is never the case in any possible world either.

This is different from, for example, the statement "all swans are black is false if there was a white swan." This is a falsity condition namely in that it is possible. It could be the case that we find a white swan right here on Earth and come to discover that our thesis "all swans are black" is false. Better yet, there are possible worlds where the conditions of a white swan existing are the case: the falsity conditions are /possible/.

This is different from saying "all swans are black is false if there was a green square circle number." This doesn't matter. This "falsity condition" is impossible and incoherent. Not only will we never find it to be the case in the actual world, it simply cannot and can never be the case in any possible world

Correct. But in both cases, there is a possible negation to consider. We may conclude that negation is impossible, but we can conceive of its negation, and what it would entail. — Philosophim

Of course you can /consider/ the negation, who said you couldn't. Remember the truth trees I just told you about?

In a contingent proposition that is /not/ a tautology, when assuming the negation you produce a /countermodel/: a set of valuation that is logically consistent but entails the falsity of the proposition.

However, in a tautology, assuming the negation /always/ results in a contradiction: i.e. it is impossible for the negation to be true. Because if the negation was true, and by consequence, there was a true contradiction, then trivialism entails which simply makes everything true. This is the principle of explosion I told you about earlier, didn't I?

And this method is exactly the method that lets you tell whether something is a tautology or not (there are actually more methods, like truth tables, but you get the point).

Can you address the point in which I provided an example of God vs. Jesus when it was not possible for there to be falsification? In the God example, there is not a consideration of anything which could be considered falsifiable. Let us not forget this debate is about providing evidence that is falsifiable for or against consciousness being physical vs non-physical. — Philosophim

Yup. I addressed this point earlier.

It would be a counterexample to the proposition "God exists and made the world" because that proposition is not a tautology. But "God is God" or "Making the world is making the world" is a tautology that is always true regardless of whether God existed or not. In the same fashion that "Santa is Santa" is a tautology with no falsity conditions. — Kuro

So what? Incidentally, if Descartes thought I was right, that's pretty damn good indirect evidence that I am. You do realize he's one of the greatest minds of all time? — Bartricks

I don't care if he's one of the great minds of all time. I'm mainly making a comment with regards to words and their usage in the sense that the most common philosophical understanding of omnipotence is actualizing whatever is logically possible.

If Tom can do more things than Roger, then Tom is more powerful than Roger, yes? — Bartricks

Sure. This doesn't forward an argument to your case namely in that the antecedent cannot be correct in terms of being able to actualize anything including changing logic. So this is literally the same as "if [something that'll never be true], then [my argument is true!]". Accepting it doesn't hurt me.

Now, a god who can do anything whatsoever - including things the laws of logic say cannot be done - is more powerful than a god who is bound by those laws. — Bartricks

Sure. The former God is incoherent whereas the latter God isn't.

Oh, oh, but Thomywombists would say that something forbidden by the laws of logic is 'no thing' and thus not being able to do it is no problem". Yes, and that's called 'begging the question'. Note, I do not deny that square circles are forbidden by the laws of logic. I deny that this makes them impossible. It makes them logically impossible - for label lovers - but it does not make them 'metaphysically impossible' — Bartricks

It's generally understood that metaphysical modality is a smaller modality subcontained within logical modality, in a smaller fashion to how nomic modality is encompassed within metaphysical and logical modality.

hy? Because God is not bound by the laws of logic.

Why?

Because they're his laws.

Why? — Bartricks

This does literally nothing if you're shifting the logical modality to a hypothetical metaphysical modality that encompasses the logical modality, because now I can just suppose my god "Timmy" who happens to be capable of changing the laws of metaphysics (which "supersede" logic! supposedly) such that Timmy is stronger than your god Joshua despite Timmy not violating the laws of logic while yours does. See? We can play this game forever. It's silly.

Remember Tom and Roger? Now the Thomywomby god is bound by the laws of logic and so can't make a square circle. Pathetic. My god can. So my god is.....more powerful than the Thomywomby god. — Bartricks

I'm not sure why you're making a logical inference here. It could simply be the case that your god changed the laws of logic such that despite changing the laws of logic he's still less powerful than my god Timmy. Remember? Not even logic is absolute, supposedly.

Contradictions aren't true, are they? So, if my god is more powerful than the Thomywomby god, then the Thomywomby god can't be the omnipotent one, can he? For that would be to affirm a contradiction. — Bartricks

I'm not sure why you care about a contradiction being true.

Yes, so, once more, no contradictions are actually true. You said that if there was a god who could make everything not make sense, then nothing actually makes sense. So you're just flipping and flopping.

God can make a square circles. There are no true contradictions. See? Things make sense. It is possible for them not to. They do though. See? — Bartricks

I think you're just awfully unfamiliar with modal logic to think this. Contradictions being possible is a contradiction, namely because contradictions literally /are/ impossible. So to say they're possible is to say contradictions are possible and not possible, which is a conjunction of a proposition and its negation, i.e. a contradiction.

Ah, so you're a dogmatist. You know already that there is no proof of God. Good job! There is.
And once more with the same mistake (am I the only one who doesn't commit it? What is it with you people??). 'Can be mistaken' doesn't mean 'is mistaken'. Christ almighty. — Bartricks

No one ever made the confusion between "can be mistaken" and "is mistaken," only the former was the premise of my argument, not the latter, and in either case simply the possibility of contradictions being possible is a contradiction in of itself. I'm not sure what of this is hard to parse.

The Principle of Universal Explanation (PE): everything must have some explanation (in terms of something else).
The second is:
The Principle of Unexplained Existence (PU): reality in total cannot have an explanation (in terms of anything beyond itself). — lish

I'd say these principles are needlessly strong. For example, the moderate PSR often talked about in contemporary metaphysics only extends so far as saying that all /contingent/ facts must have an explanation, but does not ask for an explanation of a plain everything: that is, axioms of logic, or the principle itself, or what not.

Furthermore, there are even more tamed versions of the PSR, like the one advocated by Pruss and Gale, that says that instead of every contingent fact having an explanation, every contingent fact has a possible explanation, i.e. an explanation in a possible world. This is known as the weak PSR, the WPSR.

Within his argument, Rasmussen defends PE by saying everything we are exposed to in this world has an explanation. While we do not have proof that this is 100% always true, no counter-examples come to mind — lish

This seems like shifting the burden. Isn't it Rasmussen's task here, first and foremost, to show why /everything/ has an explanation? Showing why /some/ things have an explanation does not seem to be a sufficient basis to generalize that /everything/ has an explanation unless the sample size of what we experience is a representative sample size of /everything that existed, exists and will exist/, which sounds like a terrible transgression on epistemic humility.

Moreover, playing this game will simply let Humeans win by default, since, while Humeans may not deny the examples of explanation presented, they will understand them in terms of temporal regularity contra causal relation, and, in virtue of the principle of no necessary connections, will make no further commitments: the kind of commitments you need to generalize regularity into causation, or causation into universal causation.

This is not to say Humeans strictly are /correct/, rather, that their opponent must do a lot more to motivate their position.

The probability of the conclusion being false is much greater than PE being true; therefore, we should deny PE. We are justified in using this deduction based on probability because Rasmussen used the same sort of probability deduction to defend PE. — lish

This seems like an odd mix of an inductive argument with something that looks like a proof by contradiction. Perhaps this is going through something like a Moorean shift where the probability of the conjunction of the premises is less likely than the denial of the conclusion, in effort to deny the premises?

In either case, this is poorly set up precisely because PE is so strongly-formulated that a lot of causality proponents can reasonably commit to causation and explanation without PE, for instance, counterfactual causation, the PSR, the WPSR, so on.

In short, I simply find no issue with rejecting PE, but I'm not sure what this is supposed to prove or in what way is it meant to be enlightening. It seems that a lot of metaphysicians, regardless of their position on causality, will gladly reject PE, so it does not seem to be a very powerful anti-causal argument. If not, then what it is? What kind of thing is this argument trying to establish if not something trivial and uncontroversial?

A god hypothesis would require atheism to be invalid. We look and that is what we see. Atheism as a non-belief in something never shown to exist is intangible in itself. Atheism is if anything a product of the Bible, a rejection of religion. — Gregory A

Fortunately, many religions preceded the Bible, so atheists existed far before Christianity did. For example, Epicurus, the Pyrrhonists, Diagoras, Kesakambali, Lucretius, and Theodorus, who, all of which, believe it or not!, lived before Jesus did. How could this be?

Are they simply a product of something that hasn't come into existence yet?

Those who are using the label 'omnipotent' to denote a person who is not able to do everything and anything are simply using the word in a misleading way - which is, of course, their right. — Bartricks

These individuals make up the majority of how omnipotence is understood, from Thomists to Avicenna to many others. Descartes seems to be the only prominent philosopher in dissent here.

Those who are using the label 'omnipotent' to denote a person who is not able to do everything and anything are simply using the word in a misleading way - which is, of course, their right. — Bartricks

As I explained earlier, a Thomist still would say that God can bring about any state of affairs or actualize any potential. They simply would say that the potential to violate the laws of logic is not an existing potential, so there's nothing to actualize. On a similar avenue, being good is understood as part of God's nature, so simply God is acting as himself by never doing anything evil. Other theists use that same avenue to argue that rationality is part of God's nature to produce an orderly universe, i.e. God is simply acting as himself as to be logical. So it is not anything they understand to limit God.

That's because you are confused and have once more conflated being 'able' to do something with actually doing it. He has not actually undermined anything, has he? So everything still makes sense. And thus it is not nonsensical to talk of a person who has the ability to make everything cease to make sense (unless you are supposing him actually do have exercised the ability in question - which he hasn't). This is what you have to do to generate nonsense - to generate actual contradictions. You have to suppose him to have done what he merely has the ability to do. Ironically it is those who think an all powerful being cannot do some things who are affirming a contradiction and thus talking actual nonsense. — Bartricks

There's no confusion. Ability to do something entails that it can possibly occur, not that it actually occured. So God being able to change the laws of logic or create contradictions does not mean he already did so, but can do so if he wants to i.e. it is possible that this can occur. You've done nothing but misrepresent what I said.

In any case, contradictions are fortunately not possible, so there's not any instance where God can possibly create a contradiction.

If you define your God as that which has the potential to actualize contradiction or other violations of logic, I will simply default to the nonexistence of your God in virtue of my commitment to logic:

1. Contradictions are never possible.
2. If (your) God exists, contradictions are possible or can become possible
3. Therefore your God can never exist.

That's just an article of faith on your part. What if I could prove to you that such a person exists? Would you decide, in advance, that no such proof exists? Is your agnosticism unreasonable? — Bartricks

No such proof can exist because you can never trust any absolute rule of reason, because any absolute rule of reason can be possibly false in the presence of a God that can possibly change these rules of reason if he wishes to do so. And from the perspective of a mortal, finite agent it is not possible to differniate between what rules of reason are the case versus what rules of reason simply appear to be the case in the same fashion as the former class but are deceivingly supposed to us by the kind of God that can undermine the very laws of logic and our thoughts about them.

If you go the Cartesian route, you get the Cartesian result. It's not hard. This is just another kind of Cartesian demon but made to collapse all kinds of knowledge, including logical and mathematical facts. Therefore agnosticism is simply necessitated: you can do nothing but rationally suspend judgement if any judgement is inherently unjustifiable. But we know some judgements, like ones in virtue of the fact of my experience being an experience, are justified. Therefore, your God does not exist since he'd entail not even these judgements are justified (since even basic conclusions, like my experience being my experience, can be undermined by this God who can supposedly change the behavior of identity).

Anyway, Frankfurt-style cases, if they work, refute the principle of alternative possibilities. They do not thereby demonstrate compatibilism to be true (even if they help that cause) and so they do not demonstrate incompatibilism to be false (and so tehy don't demonstrate libertarianism to be false).

The sourcehood condition is neutral between compatibilist and incompatibilist conceptions of free will. That's precisely why a Frankfurtian might nevertheless be a libertarian (or incompatibilist). — Bartricks

I don't disagree with this, I elaborated in my earlier comment that I called it Frankfurt style free will not because I'm referencing Frankfurt style cases themselves rather I'm saying that it's Frankfurt style free will precisely because Frankfurtian notions (including Frankfurt cases as well as theory of volitions, which I highlighted as /different avenues/ meant to support the conclusion, not as one thing) are most often what is employed to support that conception of free will.

That just demonstrates the falsity of those ideas. An omnipotent person can always divest themselves of their omnipotence, else they would not be omnipotent (it is absurd to suppose that a person who is unable to do something is nevertheless omnipotent). Thus, no omnipotent person is omnipotent 'necessarily' but rather they are omnipotent contingently. Indeed, there will be no necessary truths if there is an omnipotent being, for the omnipotent being will have the power to render any truth false if they so wish. Thus, all truths - including the truth that there is an omnipotent being - will be contingent if, that is, there is an omnipotent being (which there is). — Bartricks

This is just as the same Cartesian doctrine I was speaking about earlier. Yes, I said that /unless/ you're a Cartesian, you'd generally tend to think that omnipotent agents cannot actualize any potential that is non-logical because such potential does not exist in the first place, or bring about a contradictory state of affairs because it is not possible in the first place. Of course, a Cartesian takes the opinion that is otherwise, hence why I mentioned this in my initial comment as I am in perfect recognition of this position.

I'm of the opinion that it is not sensical to speak about any agent who is purportedly omnipotent in the Cartesian sense, because they can undermine any primitive conceptual schema we commit to (including the very idea that it can actualize any potential). It makes most sense first and foremost, for me, to stay wholly agnostic on any intrinsic features of this kind of entity. To be more clear, it is that I think supposing this kind of agents poses a bigger epistemic problem in virtue of the very claim supposing it (and any other claim).

What you said about Frankfurt type cases was mistaken. One can be a libertarian 'and' a Frankfurtian (plenty are). What Frankfurt type cases do - if they are successful, that is - is show that you do not need to have alternative possibilities in order to be morally responsible. But one could still argue that determinism undermines free will for other reasons. — Bartricks

Frankfurt /cases/ initially have to do with moral responsibility without free will, I agree. I'm referring to Frankfurt style /free will/, where free will is interpreted to be the actualization of whatever is in accord with an agent's higher-order volitions such that an agent can be free without being able to do otherwise. In other words, what matters is that an agent is the source of their actions. These conceptions of free will are collectively referred to as "sourcehood free will" and are primarily motivated through Frankfurt's work in two prongs: one, through Frankfurt cases, and two, through separation between internal and external reasons WRT volition. For these purposes, I call this "Frankfurt style free will".

According to consequentialists, have you done something wrong if your actions have terrible consequences that you could not have foreseen? Explain the options consequentialists have for addressing this issue. — Vely Fernandez

Depends on act or rule utilitarians. An act utilitarian strongly commits to the thesis that the moral value of an action is determined by its future consequences. While a rule utilitarian takes the same thesis, he also postulates several heuristics ("rules") for how to optimally maximize the value of future consequences in the majority of cases. This is meant to address the epistemic problems often thrown at consequentialism.

Free Will (can do anything one wants) = Omnipotence (can do anything one wants) — Agent Smith

No...

Frankfurt style free will and libertarian free will differ starkly. The latter, I'd wager, is far more characteristic of an omnipotent agent's free will, although the majority of theists would take a Frankfurt interpretation in relation to that agent's interaction with logic or morals (to be part of his nature).

Omnipotence is understood in the sense of bringing about states of affairs or actualizing potential in virtue of the possibility of that states of affairs or existence of that potential (unless you're a Cartesian).

Yes. An omnipotent person can kill themselves. Why would you think otherwise? — Bartricks

Not necessarily: if the omnipotent agent was necessary, and the omnipotence was essential, most metaphysicians would hold that this is not possible (once again, barring Cartesians).