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"Infinity" poses a ton of problems for both science and philosophy, I'm sure, but I would like to ask about a very particular aspect of this problem. What ideas are out there right now about infinitely divisible time and human death? If hours, minutes, seconds, half-seconds, can be cut down perpetually, what does this mean for my "time of death"?

One might mean either of two things by "infinitely divisible time." One might mean merely that (1) any nonzero interval of time can in principle be divided into smaller and smaller units indefinitely: what's sometimes called a "potentially infinite" collection of units of time each of which has nonzero duration. Or one might mean that (2) any nonzero interval of time actually consists of infinitely many -- indeed, continuum many -- instants of time each of which has literally zero duration: what's sometimes called an "actually infinite" collection of instants. I myself favor (2), and I see no good reason not to favor (2) over (1). Both views of time are controversial among philosophers, and some physicists conjecture that both views are false (they conjecture that an indivisible but nonzero unit of time exists: the "chronon"). But let's apply (2) to the time of a person's death. Classical logic implies that if anyone goes from being alive to no longer being alive, then there's either (L) a last time at...

Dear philosophers: In my reading of Descartes's Discourse on Method, I am fascinated by his project of universal doubt and the promise it seems to give to eliminate the many presuppositions we have. However, it seems that Descartes meant whatever belief one has is not justified if it can be subjected to any doubt, including skepticism. Therefore it would seem that answering skepticism should be among the priority in philosophical research. But this is a very strict requirement - is it the case in current philosophy research? If not, how do philosophers justify not making it the priority?

Three points: 1. It's not clear that the project of eliminating all of our presuppositions even makes sense. For instance: Could we coherently try to eliminate our presupposition that eliminating a given presupposition is inconsistent with keeping that presupposition? I can't see how. Indeed, Descartes himself seems ambivalent about the possibility, or desirability, of eliminating all of our presuppositions, because in his work he frequently appeals to unargued-for principles that, he says, "the natural light" simply shows us must be true. 2. Your argument for the claim that "Answering skepticism should be [a] priority in philosophical research" relies on this premise: Descartes was correct to claim that no belief is justified if it can be subjected to any doubt. Most philosophers, now and in Descartes's time, would reject that condition on justified belief as far too strict. They would challenge Descartes to derive that strict condition from a recognizable concept of justified belief, rather...

What do you think is a satisfactory response to external world skepticism? I'm having a hard time finding one I can accept.

The external-world skeptic purports to show that I can't know any external-world proposition P. How about this response? 1. Conceptual analysis reveals that knowledge is nothing more than reliably produced true belief, where reliability falls far short of logical infallibility. 2. If knowledge is nothing more than reliably produced true belief, then the skeptic's sensitivity condition on knowledge is false: I can have a reliably produced true belief of P, and hence knowledge of P, even if I would falsely believe that P if I were being deceived by an evil demon. (Analogy: My gas-engine car can be reliable even if it wouldn't work at all if it were on the airless surface of the moon.) 3. In particular, I can have a reliably produced true belief, and hence knowledge, that I'm not being deceived by an evil demon even if, were I being deceived by an evil demon, my belief that I'm not being deceived would not be reliably produced. The skeptic then predictably asks: "But how do you know that...

In the Stanford Encyclopedia the predicate "is on Mt. Everest" is given as an example of the sorites paradox applied to a physical object--where does Everest end and another geological formation begin? It seems to me that people who climb Mt. Everest (including Sherpas who live in the area) know that the base camp is where Everest begins. The millimeter objection in the article seems arbitrary. Why not an operational definition of "being on Everest is at or higher than the base camp used to reach the summit"? I have no problem accepting that as fact. Likewise, if I describe something as a "heap", and the person I'm communicating with recognizes it as such, what difference does it make how many units are in it?

The problem simply recurs with the phrase "at the base camp" in your definition: Which millimeters of terrain belong to the base camp, and which do not? At the limit, nobody knows. But unless there is a sharp cutoff between those millimeters that belong to the base camp and those that do not, the sorites paradox shows that the phrase "at the base camp" has logically inconsistent conditions of application, and therefore either nothing is at the base camp or the entire earth is at the base camp. I see no hope of solving the sorites paradox for one vague phrase, such as "Mt. Everest" or "a heap," by appealing to some other vague phrase, such as "at the base camp or higher" or "what someone I'm communicating with recognizes to be a heap." If only it were that easy.

It is believed that space is infinite, therefore containing an infinite number of universes. Since there is an infinite number of universes, then there are an infinite amount of Earth's exactly like ours, an infinite number of Earth's with subtle changes, etc. However, if this is true, then there is also an infinite amount of universes in which this is not true, creating a sort of paradox. How would you solve this?

It doesn't seem difficult to solve, if we're willing to accept more than one universe. Analogy: There are infinitely many numbers that are even, infinitely many numbers that are odd, and infinitely many numbers that are neither even nor odd (because they aren't integers). The infinity of numbers satisfying the description "even" and the infinity of numbers satisfying the description "odd" doesn't preclude an infinity of numbers satisfying "neither even nor odd." It would be paradoxical only if there had to be numbers satisfying more than one of those descriptions.

How is this argument valid? Either Oscar is an octopus or he is a whale. Oscar is a zebra. Therefore, Oscar is an octopus.

Validity in an argument comes down to one question: Is it possible for all the argument's premises to be true and its conclusion false? If no, then the argument is valid. So, assuming it is impossible for Oscar to be both a whale and a zebra, the argument is valid. Even so, the argument is not formally valid, because the following is not a valid form: Octopus(Oscar) or Whale(Oscar) Zebra(Oscar) Therefore: Octopus(Oscar) Not all valid arguments are formally valid. Furthermore, assuming that Oscar is not both an octopus and a zebra, the argument is unsound despite being valid, because in that case the second premise and the conclusion are not both true. The same holds for this argument (on similar assumptions): Oscar is an octopus, or Oscar is a whale. Oscar is a zebra. Therefore: Oscar is a whale. Valid but unsound. So neither argument establishes its conclusion.

Is there any way to define coincidences so as to make their existence possible in a deterministic world?

I think so. Suppose you encounter an old acquaintance, whom you haven't thought about in years, on a street corner in a foreign city. That unexpected encounter sounds to me like a paradigm case of a coincidence, precisely because it was (as we say) "the last thing you were expecting." Nevertheless, the encounter might well have been guaranteed to occur by prior conditions, as determinism says all events are. Our very limited knowledge of the prior conditions -- indeed, our total lack of interest in their precise details -- makes such an encounter surprising, i.e., not at all predictable by us given how little we knew about the prior conditions. Even so, those prior conditions could have determined that the encounter would occur exactly when, where, and how it did.

Hi. I have been struggling lately. I was just wanting to confirm that determinism is a THEORY,correct, as to ask if it has been proven? Has there been any 100% consensus as to say we don't have free will? Will we ever really know for sure? I'm sorry I'm just going through many questions right now. Determinism (in any form) has not been proven 100% correct? And all of those theories on determinism, and indeterminism, are all not confirmed correct? They're just perspectives correct? Thank you so much for any relief/ information you can give me.

Determinism is neither as well-established as (say) the sun-centered model of the planets nor as well-refuted as (say) the earth-centered model of the planets. The truth or falsity of determinism is an open empirical question. But perhaps I can provide some relief from the threat that you think determinism would pose for free will. Please see this answer to a question posted here in 2016: http://askphilosophers.com/question/25905.

Hello my question is about the Kalam Cosmological Argument. I personally do agree with the premises and the conclusion, however a person on youtube said that you cannot say that an infinite regress does not make sense but an infinite being does. So my questions are what is the difference between an infinite regress and an infinite being, can you say they are both absurd? Does an infinite being make sense?

I myself have much more sympathy for the major premise of the KCA, "Whatever begins to exist is caused to exist," than for the minor premise, "The universe began to exist." It's true that the major premise faces pressure from quantum mechanics, but only from those interpretations of quantum mechanics that presume indeterminism. The minor premise is often thought to gain support from physical cosmology, but I have my doubts about that. It's one thing to admit that our equations go silent at the instant of the Big Bang, quite another to insist that nothing, not even time, existed prior to that instant. Anyway, to your question. Some infinite regresses clearly make sense, such as the regress generated by starting with 0 and subtracting 1 from every result you get. There is nothing absurd about that regress unless there is something absurd about the set of negative integers. By the same token, I see no reason why states of the universe cannot go back infinitely far into the past. To object that "The...
A response to Jonathan's point: To deny that the universe had a beginning is not to deny that a Big Bang occurred several billion years ago, nor is it to discount the evidence for such an event. But the available evidence doesn't imply, and it may not even favor, the claim that a Big Bang event occurs only once rather than cyclically, with the cycles going back, in principle, forever. So I stand by "eminently." While I'm at it: Jonathan wrote that "some infinite series don't make sense (e.g. an infinite series of events leading up to a present event, since one could never take the last step, since there is no last step)." I take it that Jonathan meant to write "there is no first step," since we're talking about a series that is infinite in the earlier direction. But either way -- "first" or "last" -- his reasoning sounds like Zeno's argument that I can never begin to traverse (or finish traversing) any distance because there is never a first (or a last) fraction of the distance that I traverse. That...

Hello, why a thing cannot exist without any properties ? (like being just itself)

I see no reason why properties do not include being identical to the number 7 and being distinct from the number 7 . If so, then -- necessarily -- everything that exists has exactly one of those two properties. The number 7 has the former property; everything else has the latter property. If there is no such thing as the number 7, then everything has the latter property. Either way, nothing can exist without having one property or the other.

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