I recommend that you read this and this and see if you think they imply each other.

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...

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...

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 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.

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.

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.

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.

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...

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.