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if Socrates died, he either died when he was living or when he was dead. But when he was living he did not die, since he would have been both living and dead, nor did he die when he was dead, since he would have died twice. Therefore, Socrates did not die. — Sextus Empiricus

Suppose the process we call “the death of Socrates” started at some time t and ended at time t+1.

At any moment in time, either Socrates was alive or he was not alive (dead).

Was Socrates alive at time t? If the answer is no, then he would have died twice (since at time t he would be dead, meaning he would've begun to die at time t-1, and also begun to die at time t, and so at time t+1 he would've died again), which is absurd, since in order to die again he would've had to come back to life.

If the answer is yes, then Socrates would be alive at time t (when he begun to die), and dead at time t+1 (when the process of dying ended). It does not follow from this that there was some point in time in which he was both dead and alive, since he was dead at time t+1, but not at time t.

If we define the first moment in which Socrates was dead not when the process of dying ends, but rather when it begins, then he would have died at time t but wouldn't have died at time t+1.

So if the question “was Socrates dead or was he alive when he died?" means: “Was Socrates dead or was he alive at time t?”, then the answer is that he was alive.

If it means: "was Socrates dead or alive at time t+1?", then the answer is that he was dead, that is: he was dead when the process of dying ended. The error in Sextus' reasoning would be to infer that if Socrates was dead at time t+1, than means he must've died twice, which simply does not follow, since he was alive at time t, and he was dead when then the process of Socrates' death ended at time t+1 (when he died), after which he never died again.

Therefore, though it may seem like a contradiction to say that he was alive when he died (“doesn't that imply he was both alive and not alive at the same time?”), or that he was dead when he died (“doesn't that mean that he died twice?”), that's only because Sextus does not clarify what is meant by Socrates dying.

Does this solve the paradox or did I make a mistake somewhere?
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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.
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I would like to contribute to this discussion. However I am new here and I have to know the following things, please:

1) Where is the question or how has this discussion started and who has posted/started it? I can only see the subject "The death paradox" and when I click on it the same page reappears! And if I search for "The death paradox" (verbatim) A list appears with a lot of answers/comments under the title "Death Paradox", which is not exactly the same ...
2) The space I am writing this message in is for comments. Where are the answer spaces, if any?

(I am sorry about this. I have no other means to know about all this except if I start a new discussion, which I don’t find appropriate.)
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Hi there.

how has this discussion started and who has posted/started it?

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?

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.
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died twice. — Sextus Empiricus

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!
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Besides Zeno's "paradoxes", this Sextus Empiricus's problem/paradox reminds also of Schrödinger's cat!

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:)

No, it's a false paradox. There's no problem there. And in this, it reminds of Zeno's paradoxes, which are not paradoxes at all because they are based on a fallacy, or wrong assumption, if you like: that time and space are discontinuous. Which they are definitely not.

These "paradoxes" are not real paradoxes because they can be very easily rejected. That's why I call them either "pseudo-paradoxes" or, better, "sophisms", in the modern use of the term (a clever but false argument, especially one used deliberately to deceive).
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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.
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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!

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.
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@Alkis Piskas Correct! What implications does this have for immortality?
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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:)

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.

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.

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.
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died twice

Could Sextus Empericus kindly expand and elaborate on the "died twice" bit please. Oh, wait! Sextus Empiricus is dead!
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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!

But he couldn’t have died twice, surely...
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I cannot draw implications about Immortality from that! :) The problem refers to the physical world (bodily death). Immortality is not a part of it ...
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@Alkis Piskas It shows how certain things cannot be subdivided. What cannot be subdivided is a unity/eternal.
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Re "I thought 'living' and 'alive' were synonyms": They would be synonymous if "living" was used as an adjective (adjectival gerundive), e.g. a living human being. However, I understand it is used as present participle ("he was living"), i.e. expressing a progressive aspect.

Re "my OP does show ... Sextus’ argument would still not be valid, right?": Right. Nowhere in my comment have I stated or implied that your conclusion is incorrect.

Re: Even if I did assume that, my argument does not reinforce the paradox: Right, it doesn't, and I didn't say or implied that.

In short: I have commented only on your using time as if it was discontinuous.
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It shows how certain things cannot be subdivided. What cannot be subdivided is a unity/eternal.
Well, from that aspect, yes, it could be. But it has to actually exist, i.e. be substantial. E.g. the universe may be called eternal or infinite (although this is disputable). Time and space on the other hand do not exist physically. They are just dimensions. Like a line in space. They cannot be actually measured or divided, but only arbitrarily, in order to be used, e.g. as representations in geometrical descriptions of axioms and problems. So, we cannot speak about them as eternal. We can call them infinite, and this only for descriptive purposes.
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@Alkis Piskas Time and space are obviously physical.
They exist. But humans are also time and space.
Time and space must be eternal and infinite,what do they flow into otherwise?
One cannot even imagine no space and time.
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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!

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

Sextus Empiricus' argument is vacuous if he states that Socrates died twice is entailed by it. 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? Sextus Empiricus has shot himself in the foot - self-refuting argument!
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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?

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.

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.
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This can be explained by calculus. With using the concept of limits in functions, and the limits approached from the left or from the right.

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.
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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.

@Amalac

Now I get it. Apologies if I've hampered the discussion.

Sextus Empiricus seems to be saying this:

1. If Socrates died then either Socrates died when Socrates was alive or Socrates died when Socrates was dead (premise)
2. If Socrates died when Socrates was alive then Socrates was both dead and alive (premise)
3. If Socrates died when Socrates was dead then Socrates died twice (premise)
4. Socrates died (assume for conditional proof)
5. Socrates died when Socrates was alive or Socrates died when Socrates was dead (1, 4 MP)
6. Socrates was both dead and alive or Socrates died twice (2, 3, 5 CD)
7. If Socrates died then Socrates was both dead and alive or Socrates died twice (4, 7 conditional proof)
8. False that Socrates was both dead and alive pr Socrates died twice (premise: the first disjunct is a contradiction and the second disjunct can't possibly be true)
Ergo,
9. Socrates didn't die (7, 8 MT)

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. Though life seems to be ambiguous as regards whether it's a state (alive) or a process (living), to die is usually considered a process as opposed to a state. Death, surprisingly, isn't ambiguous on that score, it's a state.

Thus,

10. Socrates is alive or Socrates is dead or Socrates did die

is the real truth of what Socrates experienced: alive (470 - 399 BC), died (399 BC) and dead (399 BC - end of time).

As you can see, Sextus Empiricus' argument fails when all possibilities are considered as I've attempted to do above.

However, it seems to have made sense to Sextus Empiricus and by all accounts he was no fool. We're tempted to come to the conclusion that Sextus Empiricus was resorting to cheap sophistry against the dogmatists but what's more intriguing is how the Greeks in Sextus Empiricus' time saw/thought about death.

Go back to what I said about our intutions regarding life - is it a process (living) or is it a state (alive)? Both views seem not to raise any eyebrows as far as I can tell. How does this state/process ambiguity in re life affect our intuitions of death? We seem oddly certain that it's a state as opposed to it being a process. What if it too is seen as a process? Is Socrates still dying at this very moment and...let's face it...till the end of time? Under this interpretation, just as I'm living and alive (as of this moment of course), is Socrates both dead and dying? It's puzzling. Nec caput nec pedes, I'm afraid! The Greeks were onto something, we just don't know what!
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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.

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

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.

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.
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Socrates can't die if he's dead.
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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”
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Time and space are obviously physical.

"Physical" from Oxford LEXICO: "Relating to things perceived through the senses as opposed to the mind; tangible or concrete.". Can you perceive time or space with any of your senses? Can you locate a point in time or space?
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@Alkis Piskas
Yep and yep. By pointing. By saying now.
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If he dies, he's already dead. A person can't literally die twice.

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

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.

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.
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