Yes; so an object with no start is a non-existent object; IE infinite time is impossible. Same argument for infinite space. — Devans99

I guess we're just supposed to take it as a given that infinite time is impossible, yeah? There's no contradiction in postulating an infinite series of moments, even into the past. It can even be given a simple description sans-contradiction:

For every moment before time "t" there is another moment.

We can even get simpler by just pointing out the infinite divisibility of time:

Between any two moments of time there's another moment.

Those are not contradictory, so how is it impossible?

Singularities are nasty beasts, and there's a better reason for eschewing them than past experience: singularities blow up your model in the same way that division by zero does (division by zero is one instance of singularity); they produce logical contradictions. — SophistiCat

It's a fair point. I would just like to point out the leeway I gave myself. I said the elimination of singularities was part of the reason, not all of it. ;)

That’s not correct, they make recourse to the limit concept which is not the same as actual infinity. — Devans99

No no no, calculus makes use of multiple legitimate infinities, namely having the reals be larger the naturals. This is absolutely indisputable.

I believe and so I thought did everyone that relativity is a close approximation only of the large scale universe. The plank length is very small so reality is approximately continuous hence the theory works so well. — Devans99

If you accept relativity as pretty close to the truth you necessarily must accept that space is infinitely divisible (basically true in quantum mechanics too). Hell, a large chunk of quantum mechanical interpretations are relativistic as well so I don't even see the objection here.

But numbers just exist in our mind and our minds have finite capacity so numbers are finite in that sense. — Devans99

Numbers do not just exist in the mind, that's silly. I mean, your argument can easily be inverted. If the mind is finite and mathematics requires infinity (it does), then mathematics can't be dependent on the mind.

There is a big difference adopting the maths because it is a useful model and accepting it as the actual metaphysics. And it should be telling that the central problems of modern physics/cosmology revolve around finding ways to avoid the mathematical infinities, or singularities, that are contained in the current best models. — apokrisis

If you accept nearly any mathematical system, you're going to assume some infinity or other. If you dont, you're either an ultrafinitist (who nearly all mathematicians see as borderline cranks) or you have some reason why you think that in *particular* instances they ought not be used. The resolution of singularities is in part due to the precedence of them turning out to be the result of mistakes in our models. We still use infinities elsewhere. From the continuous nature of space, to the recourse to infinitesimals (which aren't even allowed in classical math, but physics tends to be braver in pioneering the use non-standard maths), infinities are by no means barred from the metaphysical assumptions made in science, and certainly not as just a useful thing assumed for convenience (no more than other areas of math). It has to be treated carefully, because it doesn't always useful results (hence renormalization).

It's not even that i deny renormalization is used just so I can defend infinity, I just see the wholesale denial of infinity as applied to reality to often require dropping normal mathematics without a clear reason.

I’m not suggesting dropping infinity from maths. It’s fine with the limit concept and set concept. I’m suggesting dropping actual infinity in physics and metaphysics when used as the value for real world quantities. — Devans99

I know what you're suggesting, I even precluded it. The whole point is you cannot use standard maths and make this argument. Every science uses some math or other. But whatever mathematical formalism is used, they also make recourse to infinity. There's no coherent way of making sense of this if you then drop infinity in your metaphysics because you use the math and treating as true, you're already accepting it. It's ridiculous.

Relativity is an approximation of reality not reality - We don’t know for sure if space is continuous. Anyway continuous space is a Potential Infinity whereas I’m talking about Actual Infinity. — Devans99

You either think it's true or not. As fundamental assumption of relativity is the use of a Non-Euclidean geometry with an infinitely divisible space (although even Euclidean geometry posits an infinite plane). The theory requires an infinitely divisible spacial structure, this isn't something you can gesture at as an approximation that we need not think about. That's an actual infinity; between any two points of space there's more space. That's not potential at all.

There is an argument that the natural numbers are only potentially infinite - we have used finitely many of them so far and that will remain the case. — Devans99

That's malarkey. The natural numbers can be put into a one-to-one correspondence with a proper subset of itself. That makes it infinite. The use of the natural numbers has no bearing on the cardinality of the set.

’m hardly the only person to have a problem with actual infinity. The great German mathematician Hilbert posed his Infinite Hotel paradox. Just one of many paradoxes that stem from actual infinity — Devans99

Hilbert's Hotel is not a paradox in the literal sense. It makes perfect mathematical sense. The only issue is that people import their naive views about infinity when they think about it and it drives them off course. Hilbert's Hotel contains no contradictions, ergo it's only a paradox in the sense of it having a weird conclusion, it is provably the case that infinity results in no contradictions.

I know it’s possible to construct consistent mathematical systems around infinity; that is not what I’m objecting to. I’m objecting to the use of actual infinity in physical sciences. — Devans99

My whole point has been to ask, On what basis? As there is no contradiction, your only recourse (as I said) was to say there's some category mistake. But collections of things are exactly what we know, mathematically, can be infinite. You haven't given the actual reason to accept what you're saying is anything more than a bias for a view you already held.

Man, I went to a pretty big HS and they didn't have it. Or maybe they did, but it certainly wasn't a required class. Then again, Texas sucks most of the time so I guess I was just born in the wrong place.

in many instances and is holding back scientific progress. — Devans99

Name three instances.

Many, many paradoxes and speculative theories disappear at a stroke if we are simply willing to acknowledge the actually infinite cannot exist.

There are strong arguments against the actually infinite. For example, no matter how many times you add one you never reach infinity so actual infinity is impossible to achieve.

On paradoxes, for example, Zeno’s paradoxes, there is a very simple solution if you take the view that the actually infinite is impossible: — Devans99

Or we can just use calculus, which requires multiple levels of infinity and resolves such apparent paradoxes. I mean sure, dropping infinity is a "simple" solution if you completely ignore how much of mathematics crucially requires infinity. But hey, what do I know... (I know this is snarky but come on, do you really think it's a "very simple solution" to just drop an indispensable concept???)

In the physical sciences we used to be quite strict with infinity:

- used only as approximation of very large/small
- indicate of logic error when occurs elsewhere
- even in maths infinity = divide by zero = logic error — Devans99

Division by zero is not infinity, it's undefined (in most math systems, some do give it a result). According to Relativity, space is a continuum so it is infinitely divisible. No serious physicist is going around saying Relativity is fundamentally incoherent.

But I guess belief in the actually infinite keeps cosmologists in a job for an actually infinite period of time... — Devans99

Oh yea, I guess mathematicians and non-cosmologist physicists don't use infinities at all. Nope, the natural numbers are finite, as are the reals and so on. Guess space is actually finitely divisible, sorry Einstein.

And before you drum up a response like "I'm not disputing its use in maths but..." consider this. We take what mathematicians and logicians say seriously when we adopt the formal systems they create. That means that to use such systems we are committing ourselves to a particular kind of metaphysics. If you accept standard mathematics you cannot possibly claim that actual infinities are impossible in virtue of a contradiction. You might say that not every aspect of our particular universe can be infinitized, but there's no argument that the concept itself precludes instantiation in the world. After all, that would mean either:

-Infinite collections are a category mistake: False because collections are the very things which can be infinite
or
-Infinity entails a contradiction: False because we know that standard math systems are consistent (or rather, no contradiction is yet provable in them).

So since neither of those has any merit, there's no argument against infinities on the basis of the concept alone. You either accept the well-studied math systems or you don't, but you can't use them and yet deny the very assumptions they're built on. That's complete crankery.

Simply put, should we let evolution do what it does best which is filter out the weak? — intrapersona

Can I just point out this is a really stupid understanding of evolution? That's not what fitness is.

Good point. So, we can agree that the real world is logically prior to any possible world. — Dfpolis

Not logically prior (logically, all worlds are on par, it's the metaphysics where the differences come, e.g. being actual). It's prior in the sense that it's the world I start with and possibility will often be understood with respect to it.

So, when you say "if the laws of physics were different," you are excluding from S any proposition specifying the actual laws of physics, the evidence leading us to them and their implications. Thus, my definition is perfectly suited to your example. — Dfpolis

Can you clarify? I can't understand what you're saying here. Of course if I'm talking alternate laws of physics I'm excluding the actual laws of physics, that's a trivial observation. The point is when I speak about the possibility of those alternative physics and the consequences of them, that possibility of that proposition is not made true in virtue of the actual world. In the actual world, FTL is physically impossible. Not all possibilities are, contrary to your definition, possible simply by being consistent with the set of facts of the actual world.

My objection is that the construction of possible worlds does not add to our knowledge of the real world, which remains the same (except for our mental state) no matter what we imagine. In other words, imagining a possible world can give us no new data on the real world, which alone is relevant to understanding our experience consistently. — Dfpolis

This is false. If, for example, God's existence is possible (that is, if God exists in at least one possible world) then we can prove in S5 modal logic that God must also exist in the actual world. There are doubtlessly other examples of this, I just picked a fun one (even if I don't think the argument is sound).

Why bring in a construct of dubious ontological status? Why not be more parsimonious and say it means "I see nothing to prevent me from being a doctor"? What does the construct add to this besides an unnecessary discussion of the ontological status and semantics of possible worlds? — Dfpolis

Because modal statements are not like non-modal statements. "I am a doctor" has obviously clear truth conditions (true when I am in fact a doctor). But modal statements are often (even usually) about the way the actual world is not. Even your own rendering of it is just sneaking in a modal notion. "Nothing to prevent me" is just a longer way of saying "it's possible that X" ("prevent" specifically is being used to mean "It's not impossible that"), which is the very circularity we are trying to avoid. What makes "It's possible for me to be a doctor" true is that there's a world where I am such. That's a translation of a modal statements into entirely non-modal language.

Yes, but not in any essential way. Think of all the things we imagine that do not turn out. That some imagined possibilities become actual does not justify the claim that all imagined worlds are possible or self-consistent. — Dfpolis

There's no assumption that any arbitrary world is consistent. In fact, world which are not consistent are deemed impossible worlds. But this has no relevance in the use of PW semantics unless you think that it somehow renders various possibilities impossible.

"Our sensory representation of an object" is just another name for the modification to our sensory state brought about by sensing that object. What else can it be? — Dfpolis

Our sensory apparatus is not the same as our sensory state (our perceptual experience). By assumption, our perceptual experience changes due to what our sensory organs being modified by the world and that's translated in the brain as our experience of the world. But that representation is in no way perfect and we can even tell that we miss a lot of what's out there.

Of course, this is blatantly false. It's like saying, if we have a noisy connection, we aren't talking to our mother. In other words, it's nonsense. — Dfpolis

Yea that's a false comparison. We don't have a noisy connection so much as we have an experience of a representation of a partially received phone call from our mother.

Hardly! I've explained many times now that since they are not actual, possible worlds aren't "there." I've made it clear that their only existence is intentional -- the unparsimonious imaginings of overwrought philosophical minds. — Dfpolis

You're changing the argument again. Just previously your criticism was that W being a possible world was what made it possible that P (not true). Look:

It is the name of the concept because the employment of the tool requires one to construct, or at least recognize, worlds that are possible. — Dfpolis

Your criticism makes no sense. Our recognition of what worlds are possible requires consistency and a set of worlds to quantify over.

My point is simple: Independently of whether or not there is such a thing as modal logic, only one world exists simpliciter -- ours. Thus, unless you do add "possible" to "world," consideration is restricted to our actual world. So, using your definition, if p is false in this world, it is impossible. Appealing to modal logic is irrelevant misdirection and distraction. — Dfpolis

No no no. Ignoring the odd comment about whether modal logic exists or not (???), you've got it way wrong. If P is false at a world W, P is still possible so long as there is at least one accessible world W* (determined by the accessibility relation of the modal logic in use) that can be reached from world W. And to say appealing to modal logic is a misdirection is frigging ridiculous. The whole point of PW semantics is to give semantics to modal logic.

Which means that "Venus" picks out multiple objects (one real, many imagined) and so it is a universal, not a proper name. The only alternative is to say that an imagined Venus is numerically identical with the actual Venus -- but to say this is to deny the difference between reality and fiction. — Dfpolis

No, Venus is a name for an object in the actual world. We surely agree on this. What Venus's in other possible worlds are, are simply variations on Venus in, essentially, different situations; it's still the same underlying object. This is really no different an essentialism than what Aristotle argued for.

But, it may still be the condition that specifies to whom the proper name is assigned. If we are to pick out which object to call "Dennis" or "Venus" in a modified world we need a well-defined set of criteria. Lacking such criteria, who or what is designated by these names in some possible world is indeterminate. What if we imagine a new second planet; is it, or the third planet, to be called "Venus"? You may choose to ignore such niceties, but if you do, the possible worlds construct is ill-defined. — Dfpolis

What is designated by proper names is fixed across worlds. That doesn't mean people can't use them in different ways had the world been different. But definite descriptions are just one way of seeing who or what a term refers to, but it could never give them meaning of what proper names are. If we simply call a new second planet Venus, that's obviously not the same Venus we were quantifying over when we made modal statements about the actual Venus.

Inclinations are not a species of modality. They are actual. They determine how an object will act in well-defined circumstances. They are no more "modal" than the laws of nature. If we bring two particles of the same charge next to each other, they will exert a repulsive force according to Coulomb's law. That is a fact about the contingent structure of nature which requires no reference ot possible worlds. — Dfpolis

The possession of inclinations is actual, what an inclination refers to is the propensity to engage in a particular set of possible acts (because one does not always do what they are inclined to do). And inclinations certainly aren't like laws of nature. I am currently inclined to ignore you going forward, it's a possible act I may take.But that doesn't mean I will actually do so because my doing so is not necessary. That's how inclinations work. Laws of nature aren't fluid like they. Given a particular state of affairs they will remain fixed across them.

I think he's saying that if you cannot ever close one's set of beliefs under logical entailment because you're saying you could always yield new facts by taking the power set of the set of facts, doesn't epistemic closure fail? (sounds correct to me). After all, the facts are constantly increasing so even if I know that X is the case, since the facts can always increase I cannot say I can always determine that X implies Y is the case.

P.S. I like Meillassoux's work. I'm not very fond of the PSR as a metaphysical principle.

Sorry for the late response, busy few days.

This is like saying that a map with a misprint is not worth anymore than a possible map. — Dfpolis

Except that our justification about what's possible and what's not is usually grounded in the same thing as what we justify our belief about the actual world.

P is possible with respect to a set of facts or propositions, S, if P does not contradict S.

I do think "facts" should be restricted to intelligible reality. — Dfpolis

This makes total nonsense of everyday uses of modality. We don't always refer to possibility with respect to what is consistent with the world. So if I say "If the laws of physics were different, it would be possible to move faster than light", I'm very clearly talking about the way the world isn't, so the possibility claim is not made with respect to "facts about intelligible reality".

There is no claim of infallibility here. If you think there is, explain how.

The actual world is actual because it acts to inform us. Merely possible worlds do not act, let alone act to inform us. Instead, we inform (or perhaps misinform) them. — Dfpolis

Here's what you say in the OP:

First, it is unnecessary. As we can have no epistemic access to any world but our own, actual world, anything we can learn, we can learn from the real world.

Ignoring the fact that outside of modal realism possible worlds aren't postulated to be literal places, your criticism is clearly that lack of epistemic access to possible worlds is a problem for using possible world semantics. My point was that we don't have direct access to the actual world either. And furthermore, our claims of possibility are often justified by our experience in the actual world too. So if I'm eight years old and I say "I could be a doctor", this can be understood as saying that there is some possible world (however you understand those to be) where I am in fact an MD. And then say I eventually do become a doctor, meaning the actual world is one such possible world where my claim turned out true. Well that's perfectly obvious justification for my original modal statement being thought true. Nothing about the semantics of possible worlds makes this an issue.

We have no access to any possible world. We only have access to our imagination, which can easily be inconsistent. What we know of the actual world cannot "easily fail" if we exercise due diligence. It fails occasionally, but it is usually interpretations and constructs that fail rather than experiential data. — Dfpolis

I mean you can believe this if you completely ignore modal epistemology but then that's not a convincing argument. Whether it's conceivability or similarity or perception, there are any number of proposed ways one can access possible worlds. But again, "access" here is not causal, other worlds aren't "out there" acting on us in the actual world any more than other abstract objects act on us to give us access to them.

I said that a sensory object's modification of our sensory state is identically our sensory representation of the object. I said that the object informing the subject is identically the subject being informed by the object. — Dfpolis

So you did say what I claimed you said. There's no reason to suppose that our sensory representation of an object is identical to how our sense's are modified by the object in question. The rest of it is practically trivial. It's not identical, you're simply pointing out an inverse relationship. If an object modified our senses, then that is equivalent to saying that our senses are being modified by an object. But the point being made is there's absolutely no way to know that our representation of the small amount of sensory data our representational apparatus uses to construct our perception is infallibly done. Without that infallibility, we don't have even quasi-access to the world. That's the limit of our access to the world.

It is the name of the concept because the employment of the tool requires one to construct, or at least recognize, worlds that are possible. — Dfpolis

Oh my god, so your argument is, literally, that the world "possible" is there. OK, then my original point stands. If I call them "alternate worlds" then you have no objection. It isn't their designation as possible worlds that makes them possible. The (or at least a) minimum requirement of being a possible world is that the propositions true of a world must be consistent. There's nothing about that which uses "possible" in the definition, nor does the name "possible worlds" cause any issues.

This is inadequate as, unless P is actually true, there is no world in which P is the case. What you need to say is "P is possible if there is at least one possible world in which P is the case" -- and that is circular. — Dfpolis

You aren't making any sense. In modal logic, "truth" is always relativized to worlds in which the proposition is true or not. And if we aren't talking about possibility, that in no way requires that P actually be true (though it may we be). P being the case or not is a claim about the actual world. P being possible in PW semantics is about whether or not there's at least one world ("w*") accessible to "w" where P is the case. Nothing about that is circular, you do not understand PW semantics.

Still, they are not our world, as, if they are different in any way, they are not identical to our actual world. Any world that is not identical to our world is a different world. As each is a different world, each (actual or potential) object in them is a different object from any object in out actual world. — Dfpolis

The worlds aren't identical, that wasn't my claim. But the object with the name "Venus" is picked out by the same name no matter the world. "Venus" is the name of a particular object in the actual world, so it picks out the same object in any possible world. And since both "Hesperus" and "Phosphorus" are just other names for that object, they pick out the same object on any world in which Venus exists. To say otherwise is to just deny identity statements as a whole. This is what Kripke is saying:

When I use the notion of a rigid designator, I do not imply that the object referred to necessarily exists. All I mean is that in any possible world where the object in question does exist, in any situation where the object would exist, we use the designator in question to designate that object. In a situation where the object does not exist, then we should say that the designator has no referent and that the object in question so designated does not exist — Kripke

Objects are individuated by the network of relations that contextualize them. If you change one relatum, you change the object's individuation conditions. So, the individuation conditions may not return the same object. E.g. if I am the oldest child in the real world and in the possible world I have an older brother, the individuation condition of being the oldest child will not return me. — Dfpolis

That is the exact misunderstanding I pointed out. "The oldest child [in a particular family]" is description, not a proper name, and therefore it's perfectly allowable for that to fail to give the smae object. Venus, Hesperus and Phosophorus are names for the same object. Being "Venus" entails being those other two as well, not because the names have inherent definitions, but because they're just names for the same thing in the actual world.

Counterfactual propositions can be judged on the basis of real-world potencies. Steve would have enjoyed the trip even if he did not go on it because he is actually disposed to enjoy such trips. If we did not know his relevant dispositions, we could not say whether he enjoyed the trip or not. So, there is no need for possible worlds talk to deal with counterfactuals. — Dfpolis

You did not do anything here. "Disposed" is a modal notion itself, meaning to be "inclined towards" or something one might do given their characteristics. It's a set of likely possible actions, basically. So as opposed to that circular modal definition, under possible worlds semantics "Steve would have enjoyed the trip" is understood as saying that there's some world in which Steve enjoyed the trip. And since we know Steve's actual preferences, the worlds in which he did enjoy them are similar to the actual world, which justifies our belief in the modal claim.

not require that everybody else also deal with their choice. Even if 1 million English speakers out of the 1.5 billion people who speak English reject gender,it's still their problem, not mine. — Bitter Crank

You make it sound like an arduous task. It requires at most the reworking of the occasional sentence. Come on

I would probably use plural verbs for they simply for aesthetic reasons. It sounds better that way, basically. "They is" is a bit cringey to the ears

That seems wildly incomparable. If I say "You would have enjoyed yourself had you gone to the party", the "you" there (assume it means Michael) is stipulated to be the same object and a posited truth had you done something else. There doesn't seem to be any issue to most people in doing this. The Taj Mahal being made of something else would cause it to have a different identity and so it couldn't be reasonably posited as being the same object.

This seems an attempt to give possible worlds the same epistemological status as the real world, hence my justification of direct epistemic access. — Dfpolis

It was that, and hence my response regarding how you do not have direct epistemic access. If this access isn't infallible then there's no particularly superior access to your purported knowledge of the actual world over what is possible.

Facts are actual, not merely possible. Possible worlds might be a consistent set of posits, they are not a consistent set of facts.

Do you ever stick to what you say or do you change it on a dime when an objection surfaces? Here's what you said before:

Yes, I used "possible" -- not essentially, but to avoid circumlocution. So, here's the same definition restated: "P is possible with respect to a set of facts, S, if P does not contradict the propositions expressing S."

You yourself referred to facthood in your definition of what "possible" is, so there's no way you can object to me doing the same. That's ridiculous. You either contradicted yourself or you just can't use modal concepts in which case this is all silly.

If I didn't consider objections, I wouldn't have said "reliable." Yes, it's doing a lot of work, but that doesn't mean that we can't have true knowledge, where "truth" is understood as adequacy, not as exhaustiveness or infallibility. I've made no claim of infallible human knowledge, so the notion of infallibility is a straw man -- effectively replacing human knowledge with divine omniscience. Primarily, "knowing" names an human activity, so requiring infallibility as you seem to is a bait and switch tactic. — Dfpolis

It's not doing a lot of work, it's doing all the work. The reason why you required infallibility (whether you acknowledge it or not) is because your initial claim in the OP was this:

First, it is unnecessary. As we can have no epistemic access to any world but our own, actual world, anything we can learn, we can learn from the real world.

My point was that we don't have any better epistemic access to the actual world because of the limitations of perception. Without infallible means of accessing the states of affairs of the actual world, what we perceive to be the case can easily fail to be so. Whatever you mean by "direct access" is completely opaque, and so recourse to reliability here is equally so.

If you can't see that using possible worlds as the ultimate basis for defining possibility is circular, I can't help you. — Dfpolis

It seems you are incapable of actually defending your argument on the crucial points. Possible worlds as a means to give semantics for possibility is not circular. The only way you could claim that is because the word "possible" is part of the name of the concept. It does not appear in how possibility is defined. P is possible if it is not necessary that ~P; that is, P is possible if there is at least one world in which P is the case. There is no mention of possibility there, ergo the standard definitions of modal terms is not circular.

A "Venus" in another (possible) world is not our Venus. Therefore, one can only be call both "Venus" by equivocation or by universal predication. — Dfpolis

Seriously, this is asinine. Possible worlds are not (unless you're David Lewis) being posited as literal other worlds in the same sense as the actual world. It's right there in the name, there's only one actual world. Venus in another possible world is still Venus as it might have been, the individuation conditions return the same object (that's why the names are a rigid designator).

But, in my example, the terms are referential via the same types of experiences that give them reference here. Each rigid designator names is appropriate object: There are morning and evening stars and a second planet. It is just that the references are not what you want them to be. You response will define my possible world out of consideration. So, again, the conclusion is based on how you choose to construct a set of possible worlds, not on any observable facts of the matter -- and that is precisely my objection. — Dfpolis

"Second planet" and "morning/evening stars" are not proper names. They are properties which Venus has. They are definite descriptions, not names, therefore they aren't rigid designators (which is why their truth does not necessarily hold across worlds). So yes your worlds aren't considered because you're not necessarily talking about Venus by simply describing it with a generic property many objects might have. Rather, the identity holds across worlds (i.e. trans-world identity) because they have the same essential properties which make it Venus. It's really no different than analyzing "Steve, you would have felt the warm air had you gone outside" as talking about the same Steve even if it's a counterfactual (Steve, by assumption, did not go outside).

A plural pronoun for a singular meaning. Alright it's common in use when we don't know who we're referring to. But it gets too contradictory when we do know, and we use a plural pronoun to refer to one person. ...and it gets even more incongruous, contradictory and funny-sounding when we use a singular verb with "they". — Michael Ossipoff

How is it contradictory? It's just an instance of using a gender neutral pronoun to refer to a singular person who prefers such pronouns be applied to them. As you say, we often use "they" in its singular form when speaking of people we don't know. So if I hear someone talk about a person named Riley, I've no clue as to their gender because the name is fairly ambiguous due to being commonly held by people of any gender. So if I get no further information about them than their name, I just use "they" in the singular. In fact, I did so in this very comment.

Is it really so odd to see it used this way when it's for an explicitly gender neutral person? It seems exactly the same to me.

So, to say that we do not perceive what we are perceiving is an oxymoron and an abuse of language. — Dfpolis

That's not what I said. I said that perception is not identical to reality, which is what you said.

Yes, I used "possible" -- not essentially, but to avoid circumlocution. So, here's the same definition restated: "P is possible with respect to a set of facts, S, if P does not contradict the propositions expressing S."

A consistent "set of facts" is one way of articulating what a possible world is so I don't even know what you think you're arguing against at this point.

No, a circular definition is no definition, whereas my proposal is an actual definition. — Dfpolis

The standard definitions are not circular at all. Now you're just making things up.

By "reality" we mean what's revealed in reliable experience. So, to say that what we experience is not "real" is an oxymoron — Dfpolis

Naturally "reliable" is doing all the work here, being used to obfuscate the fact that there's no guarantee that perception maps to reality such that we can have an infallible means by which to say some experience is reliable. It's like you've never considered any objection to your views ever.

Yes, most of which are modal concepts, hinging on possibility and its correlative, necessity. So, yes, possible worlds talk is circular. I have seen "necessary" defined as true in all possible worlds. Since "necessary" means the contrary is not possible, this is circular. — Dfpolis

What? Necessity is indeed defined as truth in all possible worlds [of the set of worlds being quantified over], and yes X being necessary entails that it's negation is not possible. Where is the circularity? Necessity and possibility are simply dual concepts, and thus like may logical and mathematical things they are defined in terms of each other. What are you on about?

First, proper names name one, not multiple, individuals. So, to say it's nonsense to say that "Venus" names the same object in every possible world because Venus does not exist in every possible world. — Dfpolis

This is exactly what I was talking about, you don't understand this topic. These name something in the actual world. The meaning of the term is fixed across worlds within modal logic because it's a name, not a description. A definite description like "The brightest star in the sky" will fail to pick out the same object across worlds for obvious reasons. But that's not how proper names work, they pick out a specific object in the actual world, and the meaning of that name is fixed in modal logic (unless you just reject modality outright in which case this thread is pointless).

As I pointed out in my critique, your analysis does not consider all possible worlds, only those consistent with certain contingent facts. As you are constraining possibility with contingent facts, the result is only necessary contingently, not metaphysically necessary. For there are possible worlds in which the light in the morning sky has a different source than the light in the evening sky -- even though they both exist, along with a second planet from the sun. — Dfpolis

I'm done, you are literally ignoring key parts of the theory (or you don't know them) and thus are somehow skipping over the obvious. Obviously "Hesperus=Phosporus" isn't true in the possible worlds where the references to the terms do not exist. That in itself constrains the worlds being quantified over to the set of worlds where the object exists. That fixed denotation is exactly what makes these rigid terms, and thus examples of metaphysically necessary, a posteriori truths.

That example is of something nobody would ever say and expect to be taken seriously. I don't regard the lack of applicability to something nobody would ever seriously say as any reason to discount a definition. — andrewk

That's irrelevant, the point can be generalized to instances where speakers don't know they're contradicting themselves but other people do and thus they say the asserted contradiction is impossible without any recourse to "it would tear apart my worldview". And further, I don't regard narrowly applicable conceptualization of these ideas as any reason to endorse the definitions you gave.

The problem is the common sensical notions won't be able to be used broadly to understand many instances of how we use modal concepts and so it fundamentally doesn't do the job we use possible worlds semantics to accomplish (that is, to give a rigorous account of these ideas).

My understanding is that the modality the possible worlds paradigm seeks to explain is not the fancy modality of modal logic, but the modality of everyday speech, when we say something is possible, impossible or certain. — andrewk

But the everyday use of modal notions are what goes into how they're used in modal logic, no? Otherwise it would just be another area of pure mathematics that would be of little interest to mainstream philosophy, and yet there it is.

There's no need for possible worlds in that interpretation. I can't personally see any value in the possible worlds paradigm. — andrewk

Well the value is giving real, rigorous definitions of these notions that allows us to be confident in using them in theorization. The definitions you gave don't work. When people say "It's impossible that X", they do not always mean the "it would astonish" me stuff you used. Consider a regular Joe hearing someone say "It's raining and it's not raining outside". Understood naturally, he's obviously going to respond "That's impossible" because it's contradictory. Not that it happening we require large changes to his world view, but that the described scenario could not occur. Possible worlds talk allows us to give a more solid definition and semantics without being circular. Notice that I said "could not", which is a modal notion - it's just another way of saying "imppssible' - so that was technically circular.

For example, an object's modification of our sensory state is identically our sensory representation of the object. As one state belongs both to the sensed object and to the sensing subject, there is an existential penetration, not a gap. — Dfpolis

There's no possible way to justify this, you only have access to your perceptions. The world of perception is not identical to the world itself. It would be akin to treating a photograph as identical to the scene it depicted. Neither are identical, some things are true of one that is not true for the other. Ergo they are not identical. That is an epistemic gap, even if we made the stupid assumption that our sensory representations were perfect.

If you do not understand "possible" or "necessary" you will not understand "possible world." — Dfpolis

Demonstrate that. Possible world's really just a tool to explain set of concepts. You're getting hung up on the name for and leaping of the conclusion that it's circular.

I do not define "possible" in terms of worlds. P is possible if P does not contradict the set of propositions which it is possible with respect to.

That isn't an explanatory definition at all. You just defined possibility and used possibility within the definition. That's a complete failure as an understanding of modal concepts.

Further "alternate world" does not mean "possible world." I may imagine any number of alternate worlds that are not self consistent, and so impossible. If you want to bring in the concept of self-consistency, you may, but then you're not defining modality in terms of a set of worlds, but following my definition of the last paragraph.

It means the same thing if I define that way. The issue is you getting hung up on the word possible appearing in the name of the concept. As it doesn't appear in the definition of possible worlds, your criticism of it are off base. That said, some alternate worlds can exist and some cannot. The criterion of consistency doesn't favor your definition at all because it was a circular definition. That's why no one uses that understanding of modality in philosophy.

Yes, it is, because it leads back to circularity. To define any type of possibility you must specify what makes a world "possible" in that way -- which means that you need an independent definition of that mode of possibility -- in other words, the worlds cease to be a primitive, and are merely an unparsimonious wart on your theory. — Dfpolis

Lack of parsimony as compared to what? Not only are the usual definitions of the various modalities almost exactly as you defined them in your post, it's only your provided definition that was circular.

Now you can say that "Hesperus" and "Phosphorus" are "rigid designaters," but there is no intelligible property that allows us to determine one way or the other if they are. — Dfpolis

No intelligible property? Seriously? So taking a particular path in the sky, being the second planet from the Sun, having a particular level of brightness, having a certain atmospheric composition (etc) are unintelligible properties? The whole point is that we are talking about worlds in which Venus (and the solar system) exists and that the identity statement "Hesperus is Phosphorus" is therefore necessarily true because they pick out the same object *in worlds where the relevant objects exist*. So when you say things like this:

Is there an a priori possible world in which one planet appear in the sky in the evening and another in the morning? I don't see why not — Dfpolis

I can only conclude you don't know what a rigid designator is beyond reading the introductory sentence on the SEP, because as the article goes on to say:

Hesperus = Phosphorus’ is necessarily true if true at all because ‘Hesperus’ and ‘Phosphorus’ are proper names for the same object. Like other names, Kripke maintains, they are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world. The object that ‘Hesperus’ and ‘Phosphorus’ name in all possible worlds is Venus. Since ‘Hesperus’ and ‘Phosphorus’ both name Venus in all possible worlds, and since Venus = Venus in all possible worlds, ‘Hesperus = Phosphorus’ is true in all possible worlds.
— SEP

Clearly, the conclusion is nonsense, because "necessarily," does not even follow the norms of possible worlds talk. There are many worlds that seem perfectly possible where this is not so, but they are excluded by hypothesis and arbitrary dictate. — Dfpolis

There's is no world where the planet Venus and our solar system exists like ours and in which "Hesperus is Phosphorus" is false.

First, it is unnecessary. As we can have no epistic access to any world but our own, actual world, anything we can learn, we can learn from the real world. — Dfpolis

I don't see what the argument is for the claim that it's unnecessary. We don't even have direct access to our own world, so are we able to learn anything about the actual world?

Second, if the purpose of possible worlds talk is to define the meaning of modal statements, it is circular. If a person does not understand modality, they will not understand the meaning of "possible worlds."

This is confused. Yes modal semantics are used to define modal terms like "possibility" and "necessity" and the like. That doesn't mean you cannot understand what possible worlds are, they are part of how you define the terms. How does this even follow? I could just call them "alternate world" and use the same definitions of these terms, so surely the argument isn't that the world "possible" is used to refer to these.

Third, speaking of worlds as simply "possible" allows one to confuse logical, physical and ontological possibility. — Dfpolis

Then just stipulate what type of possibility intended. This doesn't seem like a real worry.

If possible worlds talk is nonsense, then rigid designators are undefined.

Um, didn't the SEP define it in your quote?

A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else. — SEP

There is no ''discernible'' difference between two electrons, for example. So, identity, as in uniquness, is a problem for electrons. Am I getting your point? — TheMadFool

By "indiscernible" it is meant they are ontologically indiscernible, not that we merely lack the means by which to tell them apart. So this:

So, if at all there's a problem with the concept of identity it lies with our inability to see the difference between electron A and electron B. It's subjective. But we know there IS a difference in location between A and B. That's objective.

Is not right. As an example of this, we have the Hong–Ou–Mandel effect. Similarly, standard quantum theory (to the limited extent that I can understand it, granted) seems to suggest that quanta cannot been distinguished or even labeled. Even those that disagree will usually say that their physical properties cannot be distinguished, but want to maintain some kind of individuation must be there.

Reference and self-identical aren't the same thing.

Why do you think the Law of Identity is required in classical logic? I'm guessing here that, as one of the three laws of thought, it is a necessity for logic. — TheMadFool

It's not literally required. Classical logic without identity is already a well studied formal system. But it's clearly very useful and an obvious starting point for a set of axioms.

Without this basic agreement conversation would be impossible right? — TheMadFool

Sure we shouldn't equivocate. But if you go back to some of the papers Andrew M and I were quoting, there's no equivocation here. The idea isn't that you should violate identity by saying it's false or by changing the meaning of terms mid discussion. But that there may be some class of objects where applying identity doesn't make sense (like a category mistake).

Dude this is hilarious to watch. I am truly stunned. You are a fucking saint.

it's of course true that "Everything" and "nothing" are in the majority of cases bounded when they're used as quantifiers, and sometimes as zero for the latter. So if I say "I put everything in the fridge" I'm obviously not saying I put the Sun in the fridge, but contextually some relevant set of things.

But notice we don't always use them this way. So take this:

"When you die, every experience ceases."

This quantifier is unbounded, I'm clearly not limiting it's scope to only a subset of experiences. So we do not always use the quantifier "every" and "no" words within a bound. However, you may be making a potential mistake. "Nothing" and "everything" are not always quantifiers, they can be nouns such as with:

"I was in the middle of everything."

I'm certainly not saying that "For all x, I was in the middle of x" because, obviously, I can't be in the middle of every individual thing in that hypothetical scenario. Rather, I'm taking all the objects there as a whole and saying I was in the middle of that. This can be done with "no" words too:

"God created the world out of nothing."

This definitely wouldn't be translated as "For no x, God created it out of x" because that would be true if God didn't create anything at all. People who believe that intend it to mean something like "There was nothing at all and then *bam* God created it without prior stuff." I wouldn't say that transparent things have a color of "nothingness", they just have no color (nothingness is the absence of anything at all).

The law of identity is not a law about reference, it says that everything is self-identical (the conclusion of investigating the formalism being we can even show that in the metatheory identity is not assumed). So long as the law is syntactically restricted to terms of a stipulated kind the other kinds of terms are thereby not subject to it.

By requiring that all terms carry a subscript to separate them into two categories. One where that's valid and the other where it isn't:

We allow the usual connectives, quantifiers, an identity relation symbol, and punctuation symbols. For one of the kinds of terms (variables and constants), let us say T p T2, ..., terms of the first kind, we allow that identity holds as usual. In the intended model they represent the individuals. For terms of the second kind, tp t2, ..., identity is not an allowed relation. In the intended interpretation those terms denote non-individuals, items with no identity conditions

Do you mean that sentence to be taken as truth? — Heiko

I don't even know what you're trying to say now. That I believe what I'm saying is true does not entail that it's impossible to give a coherent formalism where objects are not self-identical. Identity doesn't seem directly related to truth-predication, that's what I was saying. So restricting identity doesn't somehow prevent one from predicating truth to the purportedly non-self-identical objects.

This has nothing to do with the truth-predicate though. That some class of terms may not be self-identical does not mean that the terms aren't true when they appear. I don't quite understand what you're trying to say, maybe this is just a limitation on my part. If identity is restricted in a logic it simply means either identity is not an assumed law (such as in first-order classical logic without identity) or the terms are sorted into two categories, so that there is a failure of application when you try to assert something like "∀x(x = x)".

There's no contradiction because it's not asserting that ~(∀x(x = x)) or anything similar. Identity isn't false so there's no way to derive a contradiction here. Truth-predication isn't even directly involved, I think. We can still say say true things of non-identical objects, we just cannot (supposedly) truthfully say they are self-identical.

The problem is this isn't obvious in e.g. quantum mechanics. We seem to have plausible examples of objects which are not self-identical (I don't think the "asserting themselves" is quite the right characterization). That's the motivation for the type of logic previously described.

It does hold necessarily. Basically, the logic is structured to have two types of terms: Terms to which identity holds and terms to which it does not. Similarly, identity is defined as applying to the appropriate kind of term. So identity holds necessarily (it is a tautology in such logics), but that doesn't mean it can be generalized to all types of terms in the logic (or, correspondingly, to all types of objects).

Sure it does. While I did not quote the paper in which this is done, non-reflexive logics can and have been formulated within a metatheory that itself was non-reflexive. It's not that identity is entirely dismissed, it's restricted in scope.

"Quasi-set theory Q is a first-order ZFU-style set theory. Its underlying logic is just like first-order classical logic without identity (the system L mentioned before), with a significant difference: the semantics for that system L underlying Q is described in a non-reflexive metalanguage; just like classical logic has a semantics developed in classical set theory, this particular system of logic (i.e. L) has a semantics developed in a non-reflexive set theory (more on that topic soon). So, the system in question is not exactly classical logic, but it formally coincides with classical logic, although it is semantically different (since its semantics is provided in a non-reflexive metalanguage)." — Classical Logic or Non-Reflexive Logic? A case of Semantic Underdetermination

Yes I rather like the bank account metaphor. I'll do you one better (hope Sci-Hub links are allowed), here's the link to the full paper:

http://sci-hub.tw/https://link.springer.com/article/10.1007/s11229-015-0997-5

The article is really insightful elsewhere, as it makes this point that I thought was really profound (even if pro logicians might see it as obvious), because it's so often misunderstood by those making very strong claims about logic:

"This is also connected with a second point. What exactly is meant when we say that
we deny a tautology (or a logical law, or a logical necessity)? In denying that an axiom
of classical logic is valid in general, don’t we have to accept that this ‘axiom’ is false
in at least one interpretation of an alternative system in which the same formula may
be expressed? Consider, for instance, intuitionistic logic. In denying the validity of
some instances of the law of excluded middle, it is not the case that intuitionists accept
its negation in its place. However, they do accept that the law may be false sometimes
(mostly when we deal with infinite collections)."
[...]
"As we have said in the previous section, in non-reflexive logics we do not accept
the negation of the reflexive law of identity. Also, we don’t have to accept that it must
fail in at least some interpretations. Rather, we adopt its restriction in the form of
its inapplicability. Here, ‘inapplicability’ is couched in terms of identity not making
sense, not being a formula, for some kinds of terms. Recall from our discussion in
the previous section that this is the formal counterpart of the idea of something not
having TI. So, if this is correct, the link between metaphysics and logic that underlies
the non-reflexive formulation of the RV is reasonable, in fact, but it does not go in the
same lines as we think it is reasonable to reject some classical principles of logic in
any non-classical logic with the same vocabulary."

Some yes, but mostly it's binary. Planes either fly or they don't, etc. — gurugeorge

But "mostly" is by definition not exclusive. So sometimes we do reason differently and don't usually see the fuss in it.

That's my point - what they get from those things isn't very good, it would be better if they got things from clever people who had actually spent a lot of time thinking about them.

Well we can think that but what I'm saying is they don't care and in general aren't interested in being "better" at it., they're perfectly content to stay with their folk understandings of these things And for what it's worth, like most philosophers (Rand included) they would in all likelihood simply gravitate towards whatever was closest to their prior views anyway.

That's begging the question - we may not, but do we need to? Maybe we need to. Maybe a consistent, structured picture is better than an inconsistent, haphazard one. — gurugeorge

It's not question begging, I'm saying that to get through the vast majority (if not all) of the things we need to get done most days, these issues just aren't relevant.

Why not? Who would be a better person to ask so that you, as a philosopher, could be more informed about the topic and be able to incorporate it into your big picture?

You've misunderstood me (my fault). I was saying that specialization is necessary. The point there was that for, say, particle physics questions you should got to the particle physicist, not just any physicist, because the former has the best and truest grasp of the topics in that part of the discipline.

This is mistaken. For one, "nothingness" has to do with mereology, not set theory. Set theory and mereology are not the same, and use entirely different formal systems. So for example, all the parts of a thing, when taken together (fusion or sum), gives you the thing itself. But that's not true in set theory. So if we have a set whose only member is "x" we get the singleton of the set as {x}, we do not get "x" itself.

Similarly, zero is not the same thing as nothingness. As a first issue, zero has properties while nothingness is standardly thought of as falling outside of the possibility of having properties. What you are describing sounds like emptiness, not nothingness. Also, you initially confused "nothing" as in the quantifier with "nothing" as in the noun phrase "nothingness". "Every" and "no" words can be nouns, they're not just quantifiers.

But how the ordinary world behaves is of concern to the vast majority of people in their everyday lives, and part of philosophy's job is (or Rand and I would say ought to be) to give ordinary people in their everyday lives some sense of the big picture - otherwise, in lieu of a rational big picture, they'll accept an irrational big picture, or flounder around in a state of permanent anxiety. — gurugeorge

Number of points here. In the first point, if that's the role of logic, well, I don't see what binary logics will be doing here. People don't inherently think everything is either true or false. They're apt to treat some things more fuzzily.

On the second point, I'm afraid I just don't see it. Ordinary people in their ordinary lives don't care about the big picture that philosophers paint. Outside of what they get from religious activities and social networking, ontology, logic and the rest are mostly regarded as boring and unnecessary by most people. And those have been staple of philosophy for forever.

And as it happens, even coherent big pictures can leave one anxious. Most people, even the non-anxious ones, probably have an inconsistent big picture and they get along fairly well despite it. We just don't hardly ever need to think about that wide range of things at once in ordinary life.

All I'm saying is that the discipline is skewed too much to specialization, — gurugeorge

That's true of basically every field though. I'm not going to hit up any random physicist for, say, particle physics questions. This seems like an issue with it any real resolution. If we want to curb specializiation we will have to stop drilling down on the very debates that drive the numerous parts of philosophy. And that seems unlikely to produce novel developments in those areas. Interdisciplinary work is all well and good.

Well, andrewk. Firstly, I'm not a theologian. I'm a metaphysicist. — Lucid

I just started laughing when I got here. I mean come on I know all of you did too.

I somewhat confused. In the part you were quoting, I was talking about whether it's possible have a logic to represent the idea that some objects might not be such that Identity is applicable to them. Quoting Arendhart:

In a nutshell, non-reflexive systems of
logic are systems that violate the so-called ‘Reflexive Law of Identity’ in the form
∀x(x = x). In its ‘metaphysical reading’, the Reflexive Law of Identity is known as a
version of the ‘Principle of Identity’, roughly stating that everything is self-identical.
Versions of this law are restricted in systems of non-reflexive logic, and those systems
are said to incorporate in a rigorous fashion the idea of entities somehow losing their
identity.

As they and others go on to point out, this is a restriction on identity by means of separating the terms of language into those to which identity applies and those of which it does not. Whether identity applies to all objects or not doesn't seem to invalidate that if you proof of p(x) then x has that property predicated of it.

Sure there are alternative logics, but the question of interest is which form of logic does the world happen to behave in accordance with? At the level of the middle-sized furniture of the world, at least, it seems to be good old-fashioned binary logic. — gurugeorge

Presumably the way the world "behaves" matters at all levels and in all disciplines as opposed to just being restricted to the everyday world. I mean, I assume this sight has SQL as it's database language and that uses a non-classical logic. Or take quantum mechanics, where quantum logic might be needed (seems like an open question, unclear to me). Or where we surely need logic, mathematics, where constructive mathematics (e.g. intuitionistic logic) is very well liked (it's computationally useful too). That's to say nothing of issues in semantics and ontology.

But really, my point there wasn't about logic specifically. Just that even at nearly the most fundamental level, the approach you mentioned isn't viable in some terminating way. We just know too much about the possible ways to articulate these different views that making the assumption that it's impossible to do otherwise that some specific base assumptions isn't true.

And that's something philosophers can do, but the question is whether it's worth doing - or whether philosophers doing that has been simply an artifact of the academic system. — gurugeorge

Well if we want to do things that will make us informed on those issues the yes, it's worth it. I've mentioned some examples as to why it needs to be done this way (specialization basically, just as in other fields). It's not simply an artifact of academia, trying a systematic approach just isn't going to yield new developments in specific areas. At best you'll get an attempt at unifying other people's work. Which... is fine but everyone can't be doing that otherwise the entire discipline stagnates.

I doubt the average taxpayer actually cares about what exactly philosophers are doing. We accept the government funds things we might not specifically want or care about. I mean, I've never cared about the issue on that level at least.

What I ''feel'' is that the Law of Identity is required in logic. May be it's only classical logic that requires it because if you deny that water=water then how are we to have a meaningful discussion on water? Isn't consistency in the meaning of words and terms a requirement for sound argumentation? — TheMadFool

What does "require" mean here? I'm assuming we don't want to beg the question and say "We need identity because otherwise things aren't identical" or something like that. Identity appears in basically every logic (even non-classical systems), but that's not because it's impossible to modify it or do without it (it just seems like such an obvious thing to assume). Nor does it follow if you limit identity that "water=water" is false. Take this bit from Krause & da Costa:

We begin by recalling the infamous Problem of the Identical Particles. According to a widely held interpretation of non-relativistic quantum mechanics, there are many situations in which one cannot distinguish particles of the same kind; they seem to be absolutely indiscernible and that is not simply a reflection of epistemological deficiencies. That is, the problem, according to this interpretation, is seen as an ontological one, and the mentioned indiscernibility prompted some physicists and philosophers alike to claim that quantum particles had "lost their identity", in the precise sense that quantum entities would not be individuals: they would have no identity. Entities without identity such as quantum particles (under this hypothesis) were claimed to be non-individuals."

The logic they use to formalize this idea doesn't drop into incoherency because it's not saying identity is false, but that it's inapplicable within a certain domain. It's a non-issue for me if the above is correct or not, I merely want to say there's no technical impossibility of doing this sensibly.

If, in a discussion, the meaning of ''sex'' changes from gender to intercourse we would have a problem:

Name: John Smith
Age: 24 years old
Sex: Daily with my partner OR Male??!!

That's just an equivocation though, it doesn't really bear on claims about identity being limited in some cases.

Nothingness is the dual concept of everything (or would it be "everythingness"?) "Everything" would be the mereological sum of all objects. So nothingness is the mereological sum of no objects.

I suspect if you get down to it nothingness I probably a contradictory concept.