So do the proofs you mention indeed first prove there exists a unique individual with such and such properties that is then named 'God'? — TonesInDeepFreeze

I don't think so, they define God as having certain properties (perfections or “great making properties”) first, and then through analysis of the concept of “God”, defined as the subject of all perfections or greatest conceivable being, they argue that the proposition “God exists” is analytically true, that is: that God's non existence is as impossible as there being an object that was both round and triangular at the same time and in the same sense.

Especially, one can't just assert without proof that there does exist a unique individual having certain properties and then go on to demonstrate that that individual then has other properties for a QED. — TonesInDeepFreeze

That's true, here:

But it would mean something like: Necessarily, there exists/is an x (God), such that a (the greatest conceivable being/ subject of all perfections) = x. — Amalac

...I should have just said that “there is [not “exists”] an x (God), such that...” (though as I said later in the ontological argument it is argued that God's existence is analytic), since otherwise one would just assume the existence of that “x” right away, which is not what I meant to write.

That way, the existence of x is not assumed, but (supposed to be) proved from analysis of the meanings of the terms involved.

How does a system of modal logic talk about its own semantics? I'm not saying it can't be done, but I'd like to know how it works. — TonesInDeepFreeze

The corollary of axiom M states that A→◇A , so systems that have axiom M do consider the actual world as one of the possible worlds, since a possible world is simply a world, real or imagined, that does involve any contradictions, and so the actual world is one of them.

That strikes me as being an additional premise. Of course we can't rule out that additional premises have consequences. — TonesInDeepFreeze

Actually, I think they claim that follows from the definition of God, using corollary B or corollary 5. So it's not a premise, but rather something that follows from other premises (they say).

You are right however, in that even if one accepted S5, the modal ontological argument would still have major problems, like dealing with the objection that existence is not a predicate or is a second order predicate, since that premise (that existence is a predicate) is required (it seems to me at least) to hold the claim that the greatest conceivable being or subject of all perfections exists in all possible worlds.

The argument would go something like this:

The actual world is one among the possible worlds (this again follows in some systems of modal logic). If one admits that god exists in all possible worlds, that would imply that god exists in the actual world.

And so, if one accepts that it is possible that it is necessary that god exists in all possible worlds (meaning: in some possible worlds, necessarily God exists in all possible worlds), then it follows that in all possible worlds, god exists in all possible worlds, and therefore “god exists in all possible worlds” is true in the actual world, which is one of the possible worlds in which that statement is true, and therefore god exists in the actual world.

All this follows if one accepts system B of modal logic, from the corollary of axiom B (if the modal ontological argument is valid):

◇□X → X (If it is possible that it is necessary that X, then X is the case).

Likewise in system S5, the corollary of axiom 5:

◇□X → □X — Amalac

Now, suppose an individual is a member of a certain universe, of course that individual is not a member of certain other universes. So, yes, there is no individual that is a member of every universe. — TonesInDeepFreeze

Hmm, but isn't that what the advocates of the modal ontological argument would reject? They would not be convinced with just “of course that individual is not a member of certain other universes” because they argue that God, and God alone, is a member of all “universes” or “possible worlds” without exception.

Or is there some significant difference between “universe” and “possible world” in the case of God?

B applies to a theorem, not an individual. I don't think we have an answer yet. — Banno

You mean the corollary of axiom B? It does not apply to an individual, but it could apply to a proposition which has an individual as its subject, that is: “Necessarily, God exists”. If this proposition is true in some possible worlds (meaning it does not entail a contradiction), then it's possible that it's necessary that God exists, and using corollary B, the advocate of the modal ontological argument will argue that it implies that God exists, unless one can show that God exists in no possible worlds, which is to show that the proposition: “Necessarily, God exists” entails a contradiction.

Is ▢ ∃(x)(a=x) well-formed? Is it a theorem of S5? — Banno

As TonesInDeepFreeze pointed out, it seems to be well formed, since it follows logically from “the pure predicate calculus with identity”, and truths infered from pure logic are necessarily true if they are deduced from principles which are themselves necessarily true.

But it would mean something like: Necessarily, there exists/is an x (God), such that a (the greatest conceivable being/ subject of all perfections) = x.

Well, I was looking for a second opinion. And further I don't see where my actual question was addressed. — Banno

Well, I only quoted your first question, and was waiting for somebody else to answer the second one.

As to that second question:

In predict calculus we might cheat and represent that an individual exists as ∃(x)(a=x); is there some way to pars this into modal logic, such that the individual (a) is in every possible world? — Banno

Well, that question just leads to: Does the idea of a being who exists in all possible worlds involve a contradiction? So it just goes back to the first one.

If you could elaborate on what you think entails a contradiction about the idea of such a being (or why it would be illformed) I or somebody else could give you a clear answer, otherwise the question might be a bit too broad.

The numbers of likes the user's posts have, I think.

I suppose my exception would be Bertrand Russell. He has a bunch of stuff on ethics pertaining to all kinds of problems. One book would be The Conquest of Happiness. — Manuel

That's a great book indeed.

I would also recommend:

Aristotle: Nichomachean Ethics.

Sextus: Against the Ethicists.

Hume: An Enquiry Concerning the Principles of Morals.

Wittgenstein: A Lecture on Ethics

Moore: Principia Ethica.

In S4 or S5, or a derivative therefrom, can an individual exist in every possible world without contradiction? — Banno

In S5 it seems one can, as I explained to you before. This video is helpful, though a little long (you can skip to 10:50 if you want the short version, but I’d suggest you watch the whole thing):

Put it this way: in possible world semantics it is possible to invoke a world that does not include a given individual. Hence there are no necessary individuals. (@Amalac - does that seem right to you? ) — Banno

First of all, apologies for quoting philosophers here (since you said to Wayfarer that you haven't the time to read too much) but I thought I should give a somewhat detailed reply to this, and because the work of Kolakowski that I quote here (“If There is No God...”) deserves far more attention than it receives at present.

I take Leibniz's definition of a possible world, according to which a world is impossible if it contradicts the laws of logic, and possible otherwise.

So long as the states of affairs in which some individual does not exist do not involve a contradiction, then yes: nothing exists necessarily.

Hume summarized the idea that nothing exists necessarily (in all possible worlds) quite nicely:

...there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable.

So those who hold that God is a necessary being/ exists necessarily would have to hold, it seems to me, that God's non-existence implies a logical contradiction.

There are, however, some propositions which could perhaps be both analytic and existential. Leszek Kolakowski gives as an example the proposition “something exists”:

However, we can look for an instantia crucis and ask if there is another example of judgment that combines these two properties — incompatible in terms of the conceptions of Kant and Hume—, that is, one that was analytic and existential in its content. A candidate for this impossible chimera is, I suspect, the judgment "something exists." The reason this judgment can be said to be analytic and therefore "necessary" is that its negation "nothing exists" is not only false, but also unintelligible and absurd: indeed, if there is something absurd, it is that. On that basis, one can argue that "something exists" is equal to "necessarily, something exists."

Wittgenstein made a somewhat similar point: “it is nonsense to say that I wonder at the existence of the world, because I cannot imagine it not existing”.

And so, Kolakowski says elsewhere, those who defend the ontological argument can argue in a similar way:

Thus, this argument (the ontological argument) could be expressed in another way by saying that if God is conceivable at all, he cannot not exist. This is how our contemporary defender of Saint Anselm, Charles Hartshorne, approaches the question; in his opinion, the ontological argument is perfectly reasonable if it is re-stated as a hypothetical judgment: "If God is possible, God is necessary." But is God conceivable under the assumption that to conceive him is to admit that his essence and his existence converge and, therefore, that he is a necessary being not only in the sense that he actually exists, eternally and immutably, but in the sense that it is inevitable that he exists, he is causa sui, so that his non-existence would be, as it were, an ontic contradiction?

Hopefully that helped clarify matters a bit.

"if god exists in every possible world, then god exists in every possible world" - not exactly enlightening. — Banno

The actual world is one among the possible worlds (this again follows in some systems of modal logic). So if one admits that god exists in all possible worlds, that would imply that god exists in the actual world.

So, in those systems, if one accepts that it is possible that it is necessary that god exists in all possible worlds, then it follows that in all possible worlds, god exists in all possible worlds, and therefore “god exists in all possible worlds” is true in the actual world, which is one of the possible worlds in which that statement is true, and therefore god exists in the actual world.

All this follows if one accepts system B of modal logic, from the corollary of axiom B (if the modal ontological argument is valid):

◇□X → X (If it is possible that it is necessary that X, then X is the case).

Likewise in system S5, the corollary of axiom 5:

◇□X → □X

Well, take the modal ontological argument for instance, they argue: “if God exists necessarily in some possible world, then God exists necessarily in all possible worlds”.

This may seem odd at first, but in some systems of modal logic, inferences with the logical structure: “If it's possible that it is necessary that X is the case, then it is necessary that X is the case, therefore X is the case in the actual world” are valid (replace X with God exists).

This is a matter of controversy in fact, related to the choice between systems S4 and S5 in modal logic.

I suppose a believer would retort that God exists in all possible worlds (an advocate of the ontological argument/ modal ontological argument for example).

I think both positions are not mutually exclusive.

Atheism is a negative answer to the question: “Do you believe in God?” whereas agnosticism is a negative answer to the question: “Supposing God exists/does not exist, can we have knowledge about God/the divine/God's non-existence ?”.

Even being an agnostic theist may not be incoherent, for instance: Nicholas of Cusa thought that God was essentially unknowable (he was agnostic, in that sense, about God), but he still was a christian (this of course is still problematic, since a christian must, in some sense, believe that we can have knowledge about God, even if through faith. But someone could say that God is unknowable and yet still be a deist).

One could object here, as Sade did, that it is impossible to believe in what one does not understand, but I'm not sure that's true.

Alternatively, agnosticism may be interpreted as the answer to the question: “do you know if God exists/ does not exist?”, and I think most atheists would reply: No, but I think it is very unlikely/implausible , since I haven't seen any evidence of his existence, and the arguments purporting to prove God's existence don't convince me.

There may be some atheists who would claim that they can prove that God does not exist with certainty, depending on how God is defined, because some definitions of God seem to entail logical contradictions, and, they would say, something that entails a logical contradiction simply cannot exist.

In my opinion, such a proof may not be possible, but that is a matter for another discussion.

What is "died" then? — TheMadFool

“Socrates died in 399 BC” has a clear meaning for me, “dying” is something that happened to Socrates, “died” means “ceased to be alive/ ceased to have living functions”.

My intuition, for what its worth, recommends that I should consider "died" as equivalent with "dead" and definitely not "die". This intuition may need further investigation but that's a topic for another discussion. — TheMadFool

“Died” is something that happens to a living thing, it means “ceased to be alive/ ceased to have living functions”.

“Dead” is a state, the state produced by having died, as in “She was found dead in her house”, it's a state just like the state of being unconscious, as in “she was found unconscious in her house”.

Clearly, they don't mean the same thing, and obviously neither mean the same as “die” either.

“Die” is just the present form of the past verb “died”.

If he dies, he's already dead. A person can't literally die twice. — Manuel

Of course, that's part of Sextus' point.

If he was living he wasn't dead by definition. A living person can die, they can be murdered or killed. But once they die, they are no longer alive. — Manuel

But what about the exact moment in which he died? Was he alive then or not?

Because “once they die, they are no longer alive” means: after dying, they are dead, which is of course true, but doesn't tell us about the state of Socrates exactly when he died.

It seems like this is a purely linguistic matter however, as I pointed out in my OP, once we give clear meanings to the terms the paradox dissappears.

So you'd say he died when he was alive? What's your response to Sextus then?: “But when he was living he did not die, since he would have been both living and dead”

1. If Socrates died then either Socrates died when Socrates was alive or Socrates died when Socrates was dead (premise) — TheMadFool

Speaking for myself, Sextus Empiricus has committed the fallacy of false dichotomy or false dilemma. There are actually 3 option, 1 more than those provided: alive or dead or die. — TheMadFool

I'm afraid what you said there at the end makes no grammatical sense: “Socrates died when he was die” makes no sense, or “Socrates died when he was to die” gives us no information as to whether Socrates was alive or not alive at that moment, since it still must be the case that in the moment in which he was “to die”, he was either alive or not alive.

That is because if dying is something that happened to Socrates, and everything that happened to Socrates happened to him either when he was alive or when he was not alive (which seems clearly true), then it must be the case that he either died when he was alive or when he was not, it couldn't have happened when he was neither alive nor not alive.

Let's say Socrates died at point t in time. Then he was alive in all points (not in the one previous point and before, since points do not touch each other, and between any two points, no matter how close they are together, there is an infinite number of points) previous to t, and he was dead a point at t and in all points after t. — god must be atheist

So you are saying, it seems, that there was no instant of time such that in exactly the next instant, Socrates went from being alive to not being alive,but that nonetheless Socrates was alive in all points in time previous to t.

Then Sextus is going to say that if Socrates died at point t, and he was already dead at point t (since the state of Socrates at any given point in time is defined by the changes in the previous points in time), that implies he died twice. How would you respond to him? He would also say you can't reply: “that doesn't mean he died twice, it means he died when he was dead, at point t, when the process of his death ended, not when it started”, because then Sextus will ask: when did he begin to die then? It can't be on the point immediately before t according to you, because you say there's no such thing.

Once you identify when he begun to die, in a point not right next to t (let's call it q), Sextus will claim that since there's at least one point of time which separates t and q, seeing how according to you they can't be right next to each other, then it's not the case that Socrates died at point t, he would already be dead between times q and t, unless you hold that Socrates' death didn't take only an instant (if not, how long did it take?)

Or alternatively, you could say that Socrates never begun to die.

If dying was something that happened to Socrates, and everything that happened to Socrates happened to him either when he was alive or when he was not, and your answer is that it happened to him when he was not alive, doesn't that imply, Sextus asks, that he had to die before time t in order to be dead at time t, and if he then died at time t, wouldn't that imply that after time t he would have died twice?

Then again, I think this is all merely a linguistic trick on Sextus' part, in order for his argument to work he would have to commit the fallacy of equivocation: he would have to change the meaning of the expressions: “Socrates died” and/or “...when he was dead/when he was alive” in ways that are convenient for him.

Died twice implies he already died once and the ball is now in Sextus Empericus' court - how did Socrates die once if Sextus Empiricus' conclusion is that Socrates didn't die? — TheMadFool

3. If he died when he was dead, then he would have died twice, which is impossible given that we know Socrates did not come back to life and then died again. — Amalac

Sextus says: assuming Socrates died when he was dead, then that necessarily implies that he died twice (that is to say: he couldn't have just died once if he died when he was dead, if he died when he was already dead, then he must have died twice). But those who assert Socrates died (the dogmatists, those who assert that they know Socrates died) hold that he must have died only once, not twice. Therefore, since the assumption that Socrates died when he was dead leads to a contradiction with the dogmatists' claim that Socrates died once, and only once, the dogmatists must grant that if their beliefs were true and consistent with each other, that means Socrates couldn't have died when he was dead.

Suppose a dogmatist (someone who is not a philosophical sceptic like Sextus) presented that part of the argument instead of Sextus, surely they would think: it can't be the case that he died twice, he died once and only once; therefore the assumption that he died when he was dead must be false, since that would necessarily imply the falsehood that he died more than once. Thus he, the dogmatist, wouldn't say: “well if he died twice, he must have died”, because he won't accept that he died more than once. Sextus is trying to use the dogmatist's assumptions/beliefs to show how they seem to contradict each other.

And the other option is that Socrates died when he was alive which, Sextus claims, is contradictory since it implies that there was some moment in time in which Socrates was both alive and not alive.

If according to the Law of the Excluded Middle, if Socrates died then one of those 2 options must be true, and yet they both lead to what dogmatists consider falsehoods, then either the Law of the Excluded Middle is false, or the assumption that Socrates died is false.

If Socrates was dead when he died, then, Sextus argues, that must mean he died before (before dying) since otherwise he would not be dead when he died (when the process of the death of Socrates began), rather he would be alive.

Oh, wait! Sextus Empiricus is dead! — TheMadFool

But he couldn’t have died twice, surely...

Edit: sorry, I misunderstood part of what you were saying here, so here’s my updated (edited) reply:

What I can immediately observe in his description --besides the totally irrational "died ... when he was dead"-- is the use of the word "living" instead the more realistic word "alive". Of course, because he could not have an argument then:) — Alkis Piskas

I thought “living” and “alive” were synonyms: a living human = a human that is alive.

if you like: that time and space are discontinuous. Which they are definitely not. — Alkis Piskas

Well, even then: my OP does show that even if time was discontinuous, Sextus’ argument would still not be valid, right?

By appointing a value to time and esp. dividing time, you do what Zeno did: assume that time is discontinuous. It's not. Time is continuous. It has no start or end or middle point, or any points in it. The same holds with space. Try to locate a point in space! We use points in geometry only for representation and description purposes, to show axioms and solve problems. — Alkis Piskas

Even if I did assume that, my argument does not reinforce the paradox, it refutes it by showing that Sextus’ inferences are not valid, even if my saying that the process of his death starts at time t and ends at time t+1 did assume that time is discontinuous, even then Sextus’ argument fails. But I’m not necessarily assuming that Socrates’ death happened during an instant of time, what if the time it took for him to die was very small, but not as small as the indivisible unit of time? Maybe the transition from being alive to not being alive was very fast, but not instantaneous (or was there no transition at all? Then what do we mean when we say that Socrates died in 399 BC?). Then I think whether or not time is discontinuous would not be very relevant to Sextus’ argument.

So he died once before! Problem solved! If Sextum Empiricus claims that he died once before, necessarily to have died twice, then Sextus Empircus has to admit that Socrates died! — TheMadFool

But Sextus’ argument goes like this:

1. If Socrates died, then either Socrates died when he was alive or when he was not alive (dead). (It must be the case that he either died when he was alive or when he was not alive, otherwise we have a failure of the Law of the Excluded Middle).

2. If he died when he was alive, then at that moment he would be both dead and alive, which is a contradiction.

3. If he died when he was dead, then he would have died twice, which is impossible given that we know Socrates did not come back to life and then die again.

4. Therefore, it’s not the case that Socrates either died when he was living or when he was dead.

5. Therefore, if we assume Socrates died, the disjunct “either Socrates died when he was alive or when he was not alive” is false, which violates the Law of the Excluded Middle.

6. Therefore, since the assumption that Socrates died has led us to a contradiction, we conclude that the opposite must be true, that is: Socrates did not die.

Hi there.

how has this discussion started and who has posted/started it? — Alkis Piskas

I started it, you just have to click on “new discussion” if you want to start your own.

The space I am writing this message in is for comments. Where are the answer spaces, if any? — Alkis Piskas

If you want to respond to a post, you have to click on the 3 dots at the end of the post, and then on the arrow pointing to the left that shows up.

The paradox seems like Zeno — Gregory

It is somewhat similar to Zeno's paradox of the arrow, yes.

If we use that other paradox as an analogy, we could say that Socrates didn't die while he was alive, nor after he died, but simply died when he died.

In his Mysticism and Logic, Bertrand Russell mentions a different solution:

As regards motion and change, we get similarly curious results. People used to think that when a thing changes, it must be in a state of change, and that when a thing moves, it is in a state of motion. This is now known to be a mistake. When a body moves, all that can be said is that it is in one place at one time and in another at another. We must not say that it will be in a neighbouring place at the next instant, since there is no next instant. Philosophers often tell us that when a body is in motion, it changes its position within the instant. To this view Zeno long ago made the fatal retort that every body always is where it is; but a retort so simple and brief was not of the kind to which philosophers are accustomed to give weight, and they have continued down to our own day to repeat the same phrases which roused the Eleatic's destructive ardour.

By this view, one could also solve the paradox by saying that there was no instant of time in which Socrates died after being alive the previous instant.

I have a feeling that you might want to look into, analyze thoroughly, an expression that seems to be, luckily or not, a stock phrase employed by those who face major employment issues, that phrase being, "my career ended before it even started" — TheMadFool

That's just a figure of speech, obviously.

How on earth can something end before it started? — TheMadFool

Did I ever say such a thing?

An infinite past has no start and yet, here we are, in the present, an end as it were. — TheMadFool

Something can't end before starting (if it started), obviously. A universe with an infinite past would not end before it started, it never would start in the first place (by definition), but that doesn't mean it can't end in the "now", or at least that needs to be proven first.

So, here’s some context: Matt Dillahunty sometimes talks about how Aristotle and his buddies sat down 2000 years ago and discovered all the valid syllogisms. That’s all of them and if your argument doesn’t take one of those forms, it’s invalid or something like that. Alex Malpass is trying to communicate to him that there are a lot of other formal logical systems that cover things that Aristotle’s logic doesn’t (I think he mentions modal logic as an example a bit before the start of the clip). In this clip specifically, Alex tells Matt that in classical logic for all x Px doesn’t imply exists x Px (which is correct) to which Matt pushes back. — Need Logic Help

If Dillahunty did say that (don't know if he did, and don't have time to watch the video), then I do think he made a pretty bad mistake. Bertrand Russell already talked about this subject quite clearly in my opinion:

(2) Over-estimation of the syllogism . The syllogism is only one kind of deductive argument. In mathematics, which is wholly deductive, syllogisms hardly ever occur. Of course it would be possible to re-write mathematical arguments in syllogistic form, but this would be very artificial and would not make them any more cogent. Take arithmetic, for example. If I buy goods worth $4.63, and tender a $5 bill in payment, how much change is due to me? To put this simple sum in
the form of a syllogism would be absurd, and would tend to conceal the real nature of the
argument. Again, within logic there are non-syllogistic inferences, such as: "A horse is an animal, therefore a horse's head is an animal's head." Valid syllogisms, in fact, are only some among valid deductions, and have no logical priority over others. The attempt to give pre-eminence to the syllogism in deduction misled philosophers as to the nature of mathematical reasoning. Kant, who perceived that mathematics is not syllogistic, inferred that it uses extra-logical principles, which, however, he supposed to be as certain as those of logic. He, like his predecessors, though in a different way, was misled by respect for Aristotle.

So I do think that Dillahunty is wrong if he really said:

So, here’s some context: Matt Dillahunty sometimes talks about how Aristotle and his buddies sat down 2000 years ago and discovered all the valid syllogisms. That’s all of them and if your argument doesn’t take one of those forms, it’s invalid or something like that. — Need Logic Help

The issue seems to be that there are formal logical systems that Dillahunty was not paying adequate attention to, but how significant was this error of omission? — Need Logic Help

Ignoring new formal logical systems, such as modal logic and mathematical logic, is a pretty big deal, it amounts to saying (as I think Kant did if my memory serves right) that logic has not made progress since Aristotle, and in modern times some hold that those systems are not important in comparison to aristotelian logic or the subject-predicate logic.

There's no doubt that Aristotle was a genius, being the inventor of formal logic in its first form, but the genius of one man has limits, however great it may have been, and it seems quite arrogant and due to an excess of worship of Aristotle to say that he discovered all there was to discover about logic, since as Russell pointed out:

(...)a man whose opinions and theories are worth studying may be presumed to have
had some intelligence, but (...) no man is likely to have arrived at complete and final truth on any subject whatever.

Ok, so let's suppose all that Kant/Popper meant when saying that an infinite amount of time passed/elapsed up to the “now” was to say that it is the case that the universe had no beginning in time.

What then is the alleged contradiction about that with the fact that time in the universe ends in the “now”? It is maintained by Kant that a universe with no beginning in time would never be “completed”/ would never “end”.

If all he means by that is to say that time would never end towards the past, then obviously yes, that's entailed by the very definition of such a universe, and there's no contradiction about that, since one cannot maintain that it must end towards the past in some beginning moment of time, without also rejecting/contradicting the definition of a universe with an infinite past, unless there's a reason why it must have had a beginning in time, which is what Kant had to prove and didn't prove.

But if Kant means that such a universe would also never “be completed/end” in the “now”, then that seems like a non-sequitur.

Again, one cannot use the claim that it could never end in the “now” because that would imply traversing an infinite amount of time in order to get to the “now”, because:

a) The assumption that it would necessarily imply that, as I said before, is false, and there's no reason for someone who held the universe to be infinite towards the past to make that assumption.

b) The models of a universe with an infinite past/ no beginning in time do not logically depend upon the claim that in such a universe one would have to traverse an infinite series of syntheses of time in order to get to “now”.

(Also, see my replies to Mww)

If, on the other hand, we take that word “elapsing” to have its usual meaning, then time “elapsing” necessarily implies a beginning and an end of an interval of time. In fact, a lapse of time is the same thing as an interval of time.

But intervals, by their very nature, must be of finite amounts of time, not infinite ones (otherwise you can't even construct the interval, since you would be missing at least one of the limits that define the interval/lapse of time).

So if that's what you mean by “an infinite amount of time elapsing up to the present", then I disagree with:

What does one mean by past? Elapsed time ending in the present (now).

So, if the past is infinite, an infinite amount of time must've elapsed. — TheMadFool

That definition would only be adequate if the past was finite, not infinite.

All “a universe with a finite past” means is: a universe with a beginning in time. Likewise, all “a universe with an infinite past” means is: a universe with no beginning in time.

That doesn't mean the same as “a universe in which an infinite amount of time elapsed ending in the present”.

So what one means by past is simply: the time before the present. With this definition, no assumption about time “elapsing” is required.

The only thing needed to make that universe consistent is to drop the false assumption that in such a universe necessarily an infinite amount of time must have elapsed up to the present, since such a claim implicitly assumes, for no reason, that a universe with an infinite past both had and didn't have a beginning, so obviously, as I said before, there's no need for one to assume that that must also be the case in a universe with no beginning in time.

The contradiction resides in your inclusion of the universe as an uncompleted series. If it was, then the elapsed time of the universe, your “infinitely many finite intervals of time” for the universe is impossible — Mww

And why would there being infinitely many finite intervals of time be impossible given a universe with no beginning in time/ infinite past, exactly?

Like I said, those infinitely many intervals (or “syntheses”) go backwards in time since the “now”, or since any other particular moment in time before “now”, so the only thing those intervals make impossible is for there to be a beginning moment which completed the series backwards, which is what is entailed by the definition of a universe with no beginning in time, they don't render the series being completed forwards by the “now” impossible.

The universe would never be “finished by means of successive synthesis”, from which follows necessarily that talk of “in a universe with an infinite past”, is meaningless. — Mww

I'm not sure how that follows:

1.In a universe with no beginning in time, there would be infinitely many finite intervals of time.

2. Those intervals or synthesis could never end (backwards in time)

3. Therefore, given that 2 is true, a universe with no beginning in time would not have a present moment, a “now” which completed the series (forwards in time).

4. The actual universe does have a present moment which completes its temporal series (forwards in time).

5. Therefore, the talk of “in a universe with an infinite past..." is meaningless.

The jump from step 2 to step 3 is what seems like a non-sequitur to me. That, or equivocation of the idea of a series being “completed”, which can have 2 different meanings.

When the natural thing to infer would be rather:

1.In a universe with no beginning in time, there would be infinitely many finite intervals of time.

2. Those intervals or syntheses could never end/ be finished (backwards in time)

3. Therefore, a universe with no beginning in time would not have a beginning in time, since that
would imply that the temporal series would be
completed (backwards in time), which necessarily can't be the case given 2.

And yes, that's just how a universe with no beginning in time/ infinite past is defined, 3 is an analytic truth and therefore contains no contradiction.

While it may not be contradictory to speak of a universe with an infinite past, given the existence of it, it is still contradictory to speak of a universe with an infinite elapsed time, which makes no reference to any given time. — Mww

Again, if by “infinite elapsed time” we mean that in such a universe there would be infinitely many finite intervals/syntheses of time, then I don't see why its contradictory with the premise of a universe with an infinite time, for the reasons given before.

The set of negative integers is an uncompleted series, in which the last member is impossible to represent. — Mww

If you sort the series in descending order, then there is no last member indeed.

But if you sort the series in ascending order, then its last member can be represented, its -1.

I'm refering to that series sorted in ascending order, and in that series the correct statement would be: “The set of negative integers is an uncompleted series, in which the first member is impossible to represent”.

In that case, the series of negative integers would be an uncompleted series descendingly since it has no first term, but not ascendingly since it has a last term (-1).

All in all, I just don't see how Kant's argument is that much different from the argument of the first cause of, say, Aquinas, if one just replaces “causes” with “syntheses” ( I mean besides the fact that Kant does not continue to deduce the existence of God from that beginning in time he got from this thesis, which is understandable given that the antithesis can be “proven” as well).

(...)take again the arguments (of Aquinas) professing to prove the existence of God. All of these, except the one from teleology in lifeless things, depend upon the supposed impossibility of a series having no first term. Every mathematician knows that there is no such impossibility; the series of negative integers ending with minus one is an instance to the contrary. — Bertrand Russell

So if one argues that Kant's argument “proved” that the temporal series of the universe must have had a beginning in time, by the same reasoning one could also prove that the series of negative integers must have a first term, a smallest negative integer, since otherwise the series could not end with -1, which is clearly not the case.

No, I said what I meant to say. — Mww

Sorry, that was a typo, I meant to write “a succesion in a series of times” with “times” in plural, what I was trying to ask was if by “an elapse of time” you meant to say “a lapse of time”.

Metaphysics.....the most fun to be had without paying for it. — Mww

Well, I hope you are at least having some fun, and not losing your patience despite my obstinance in trying to understand Kant's argument (if indeed I misunderstood him and am just hopelessly confused).

Let's me take a stab at your argument, for my own benefit. As I understand what you're saying: even if time had no beginning it would not matter because we are finite, so we can place ourselves anywhere on the timeline and no be bothered about how we got here. — Manuel

Well, my view is not that we don't need to be bothered about how we got to the present, but rather that we should not (and need not) say things like “an infinite amount of time has elapsed up to the present” when we examine the consequences of assuming that the universe had no beginning in time, we should only talk about time elapsing when talking about particular intervals of time. In fact, the very notion of time "elapsing" implies a beginning and an end of an interval in which it elapses (most definitions of the word I have seen do assume that, anyway).

If the word “elapsed” does not imply a “since X point in time to Y point in time”, then it means something different from what it means in a statement such as: “5 years have elapsed since my birthday 5 years ago up to now”, since otherwise necessarily one must be able to answer the question: “infinitely many years have elapsed since (when?) up to now”.

Isn't the counterargument here that in order to get to now, we had to begin somewhere. — Manuel

Why is it that we had to begin somewhere?
Doesn't that beg the question by already assuming that there must have been a beginning in time?

But if time is infinite, how could we place ourselves here? An infinite amount of time has gone on before we got here. — Manuel

If by “an infinite amount of time has gone on before we got here” you mean “ if the universe had no beginning in time, then an infinite amount of time would have elapsed before we got here”, then I have already said why I think that's not the case. Time can only elapse since some moment to some other moment. It is clear, therefore, that the idea of time elapsing only applies to finite intervals of time.

Kant therefore can't use the idea that if the universe had no beginning in time then that logically entails that an infinite amount of time would have elapsed, to show that a universe with no beginning in time would imply a contradiction, since such a universe doesn't logically entail what he says it entails.

Such is my current view on the matter anyway.

Either a part of infinity is finite or if not, it is also infinite. If a part of infinity is also infinite, regardless of not having starting conditions, we could not be here. — Manuel

A part of “infinity” can be infinite, yes. In the set of all positive integers, the set of all even numbers which is part of the set of all positive integers is also infinite. But of course a part of infinity could also be finite, for instance the set of all integers bigger than 0 and smaller than 5, which is also part of the set of all positive integers.

So, when talking about the timeline of the universe, which part of it are you saying would be infinite, and how would that imply that “we could not be here”?

But this raises more problems, if a part of infinity is finite, wouldn't we have to go through an infinite amount of time to reach a portion of infinity which is not. How's that possible? — Manuel

Again, when saying we would have to “go through an infinite amount of time”, you must specify since when we would supposedly have to “go through” an infinite amount of time, since in the very definition of time elapsing, a beginning and an end of the lapse of time are pressupposed.

So no: if the universe had no beginning in time, it's not the case that that would necessarily entail that we would have to go through an infinite amount of time to get anywhere.

Man, this hypothetical’s got a farging mind of its own donnit? Seems “up to the present” makes an appearance in this current iteration, which changes the entire proposition. — Mww

Well, the first time I thought the “up to the present” part went without saying, but seeing how that lead to misunderstandings, you are right that I should have been more careful and should have stated it explicitly.

The Popper quote in the OP does mention it though, so I thought the “up to the present” was implied:

(...)Now, in his first proof, Kant simply argues that the world must have a beginning in time, since otherwise an infinite number of years would have elapsed at the present moment, which is impossible. This concludes the first proof. — Karl Popper

Hmmm......and what of the idea of a succession of a series of times that never completes? Isn’t a succession in a series of times the same as an elapse of time? — Mww

I guess you meant to say “Isn't a succession in a series of time the same as a lapse of time?”

A succession in a series makes no need of an amount for each time of the series. — Mww

Not quite sure what you mean by this, but if you mean that it doesn't need to have an interval with an infinite amount of time elapsing, then that is my point, since an interval must, by definition, have a beginning and an end, whereas a universe with an infinite past doesn't have a beginning, although it would have an end (the present moment/ the “now”). An interval of time must have both a beginning and an end in order for time to elapse in it.

Even so, isn’t an infinite series of successive finite intervals of minutes, still an infinite amount of time? — Mww

In a universe with an infinite past, one could say that there would be infinitely many finite intervals of time, which, when added, make up an infinite amount of time.

But if that's all that Kant meant when he said that:

“....up to every given moment of time, an eternity must have elapsed, and therewith passed away an infinite series of successive conditions....” — Mww

... then I don't see what the supposed contradiction is, he says (in my translation of the Critique):

the infinity of a series consists in that it can never be finished by means of successive syntheses. — Kant

To make things clearer: if we were talking about an infinite future, and modify what Kant says so as to apply to a universe with an infinite future, then we could interpret what Kant says in a way that makes sense: time could never, going forward in time, be “finished”, in a universe with an infinite future time. What would follow from that is: therefore, the infinite future temporal series of finite intervals can never be completed (forwards in time) since you will never arrive at a final interval of time, and therefore it would be contradictory to hold that in such a universe we could arrive at a final moment/interval of time in the timeline, since that would imply that it both can and cannot be completed.

However, when saying that the infinity of a past temporal series consists in it never being finished/completed, what would be meant, it seems to me, is: If you start from the present moment/the “now”, and go backwards in time, then you will never arrive at a moment in time that is the beginning of time/ a first finite interval of time, therefore the infinite series of finite temporal intervals can never be completed (backwards in time).

And so, if that is what is meant by “completed”, then there is no contradiction in holding that a universe with no beginning in time would not be completed backwards in time, but would be completed forwards in time, since it would be completed/finished by the “now”/ the present moment, in the same way in which the series of negative integers cannot be completed towards the left direction of the x axis if you start with any particular negative integer/ any particular interval between two integers, but can be completed towards the right direction of the x axis if you start with any particular negative integer/any particular interval between two integers, since it is “completed” by its last interval from -2 to -1.

So, to make the mathematical analogy clear:

-1= the present, the last element of the series, which finishes/completes it .

The x axis in the cartesian plane, ending/ being completed with -1= the timeline of the universe.

- infinity/ the three dots to the left of the timeline= The infinite past.

The series of negative integers is “completed”, forwards from any particular negative integer/ interval (so to speak) between integers by its last interval from -2 to -1 (which represent the moment exactly one year before the present moment, and the present moment, if we use years as our units of time) ; but is not completed backwards from any particular negative integer.

Hopefully now I made things clearer.

Well, yes, by the very fact of how bias and norms create quasi-rules of how language is used in a society. I understand that terms become reified with time as these tendencies abate or are pressured due to how social norms progress. — Shawn

I think this is correct, basically one has to respect (to some extent at least) the rules of language implicit in each particular form of life, to avoid social dissaproval, or even going to jail.

One of my university professors gave as an example of this a time where he was invited to give a talk about corruption in a very corrupt country (one where he was very critical of it), and during his talk he had to go with a group of cops who were behind him, because his life was literally in danger just by doing that.

From what I've heard, such things do happen more often that one would think at first.

That is how I would define it, but I didn’t use “past” in my statement. You transcribed the term into it. — Mww

Then what did you mean when you said “there is no present”?

So is this where you’re coming from? And by association, is this the hypothetical proposition the truth of which you find doubtful? — Mww

The hypotetical I'm refering to is “If the universe has an infinite past, then an infinite amount of time has elapsed up to the present”.

You’re equating your “if the past were infinite” with his “an eternity must have elapsed” — Mww

No, I don't think those two mean the same thing, I'm saying: The past is infinite ≠ an infinite amount of time has elapsed, because to say that time has elapsed implies that it elapsed since some moment in time to some other moment in time, and hence the notion of time elapsing is not applicable to infinite amounts of time, but only to finite intervals of time.

For example: 20 years have elapsed since I was born, up to the present. But you can't say: infinitely many years elapsed since ???, up to the present day.

If one can't say since when the infinite amount of time elapsed, then I maintain that it couldn't have elapsed, but that a universe with an infinite past does not rest upon the supposition that an infinite amount of time has elapsed up to the present day.

My view on definitions is that they should be stipulative: First one determines the goals that one wants to achieve by the definition, and then one chooses the definition that is most suitable for achieving those goals.

So the answer is: depends on what you want to use it for, on what you want to accomplish with it.

Well that's what I meant, it seems I expressed myself poorly (english is not my mother tongue). — Amalac

Actually, never mind: going back to that post you're refering to, what I said was that he maintained that if the past were infinite then that implies that an infinite amount of time has elapsed.

I'm not saying Kant maintained that the universe had an infinite past, I'm doubting the truth of that hypothetical proposition.

I diverge from Kant here, and adjoin Schopenhauer, re: the world as “will and representation”, in that I consider the world to be the immediate unity of phenomena, that which directly appears to my representational faculties, a much narrower view of experience proper. All else, being possible experience doesn’t change the my idea of world, but rather, enlarges its content and thereby its limits. As such, the boundary of my world is the totality of my possible experience, and, because of that restriction, the CMB is irrelevant. — Mww

Hmm, ok.

I think more the simultaneity of the initiation of phenomena, with the possibility of the representation of them, by an eventual intellect equipped with a cognitive system predicated on it. Within such a system, time is not an object so doesn’t depend on the ontology of objects, but it is used by the system in referencing objects to the system or to each other, so as soon as objects become possible, so too does the possibility of referencing them. Time is therefore irrelevant if there are no objects and if there is no system. — Mww

Ok, that makes sense (I guess?)

Again, he doesn’t maintain it, he supposes it in order to have something to debunk. — Mww

Well that's what I meant, it seems I expressed myself poorly (english is not my mother tongue).

There may be an infinite time regressively from the beginning of the world, but not from an infinite time progressively to the beginning of the world. — Mww

If the past is infinite, then there would be an infinite amount of time regressively from the present moment, right? You say, it seems, that there is no “present moment”. But how, then, do you define “the past”, if not as the time previous to the present moment?

If you read the antinomies, you should have found he did the same thing in the antithesis. In the thesis he supposed the world had no beginning then proved it did, in the antithesis he supposed the world had a beginning and proved it didn’t. They are called conflicts of transcendental ideas for just that reason; either can be proved in its own way. — Mww

Yes, I know how his antinomies work, but if one of the arguments for a thesis is fallacious, then one can't even say that you can “prove it in its own way”.

Russell seems to assume an externalist, causal conception of empirical knowledge, and then projects that assumption onto Locke and then Hume, for whom this would be a stolen concept, given his stance on causation. But whether or not Russell is right about knowledge, the question here is whether Hume espoused the same view: only then would he be open to the charge in the OP. Hume actually seems to hold an internalist view, at least some of the time, i.e. his account of knowledge refers only to mental states. — SophistiCat

I think this passage of his Enquiry does seem to show that Hume did not hold an externalist conception of empirical knowledge:

It seems also evident, that, when men follow this blind and powerful instinct of nature, they always suppose the very images, presented by the senses, to be the external objects, and never entertain any suspicion, that the one are nothing but representations of the other. This very table, which we see white, and which we feel hard, is believed to exist, independent of our perception, and to be something external to our mind, which perceives it. Our presence bestows not being on it: our absence does not annihilate it. It preserves its existence uniform and entire, independent of the situation of intelligent beings, who perceive or contemplate it.

But this universal and primary opinion of all men is soon destroyed by the slightest philosophy, which teaches us, that nothing can ever be present to the mind but an image or perception, and that the senses are only the inlets, through which these images are conveyed, without being able to produce any immediate intercourse between the mind and the object. The table, which we see, seems to diminish, as we remove farther from it: but the real table, which exists independent of us, suffers no alteration: it was, therefore, nothing but its image, which was present to the mind. These are the obvious dictates of reason; and no man, who reflects, ever doubted, that the existences, which we consider, when we say, this house and that tree, are nothing but perceptions in the mind, and fleeting copies or representations of other existences, which remain uniform and independent.

119. So far, then, are we necessitated by reasoning to contradict or depart from the primary instincts of nature, and to embrace a new system with regard to the evidence of our senses. But here philosophy finds herself extremely embarrassed, when she would justify this new system, and obviate the cavils and objections of the sceptics. She can no longer plead the infallible and irresistible instinct of nature: for that led us to a quite different system, which is acknowledged fallible and even erroneous. And to justify this pretended philosophical system, by a chain of clear and convincing argument, or even any appearance of argument, exceeds the power of all human capacity.

By what argument can it be proved, that the perceptions of the mind must be caused by external objects, entirely different from them, though resembling them (if that be possible) and could not arise either from the energy of the mind itself, or from the suggestion of some invisible and unknown spirit, or from some other cause still more unknown to us? It is acknowledged, that, in fact, many of these perceptions arise not from anything external, as in dreams, madness, and other diseases. And nothing can be more inexplicable than the manner, in which body should so operate upon mind as ever to convey an image of itself to a substance, supposed of so different, and even contrary a nature.

It is a question of fact, whether the perceptions of the senses be produced by external objects, resembling them: how shall this question be determined? By experience surely; as all other questions of a like nature. But here experience is, and must be entirely silent. The mind has never anything present to it but the perceptions, and cannot possibly reach any experience of their connexion with objects. The supposition of such a connexion is, therefore, without any foundation in reasoning. — Hume

By the same token, Hume could admit that he cannot prove that impressions are caused by external objects.

It seems to me Russell's point is that Locke's thesis that all ideas are copied from impressions is implausible if that's the case. That seems kind of unreasonable though: Russell is basically saying that Hume cannot define impressions like that unless he can refute external world scepticism.

Hume admits he cannot do that, and that neither can anyone else (including Russell). Yet that doesn't stop Russell from developing philosophical theories which are only plausible if there is an external world.

So yes, I think you might be right after all.

If punishing an evil person is pointless, then choosing not to punish them is just as pointless.

If praising someone who is good is pointless, not praising them is just as pointless.

Of course we'll continue to do those because of habit — Marchesk

That's what I was hinting at, and yes: We can't do anything except believe that, even though we have no reason for doing so (but then again, we don't have any reason not to believe it either).

Still, it's pretty hopeless if Hume is right.

Take the examples of a perpetual motion machine or accelerating up to the speed of light. Both are ruled out as impossible by physics. — Marchesk

The problem of induction goes even further actually: although in the past the laws of physics have not changed, that doesn't justifiy the expectation that they won't change in the future.

So why hold people accountable? Why blame them for anything they do? — Marchesk

Let me turn that around for you: Why should we not hold people accountable? Why should we not blame them for the bad things they do?
I'm playing devil's (Hume's) advocate here.

I see, that does make sense I guess.

Hmm, ok. I meant that you may need the excluded middle (as it applies to mathematical statements) to show that the Gödel sentence was not meaningless despite being self-referential, like the sentence “this sentence is false”.

I thought the law of the excluded middle was also needed for mathematical proofs by contradiction, like Euclid's proof that there are infinitely many primes.