Your question is tantalizing. I wish it had included a citation to mathematicians who say what you report them as saying. On the face of it, their claim looks implausible. Are there no necessary truths at all? If there are necessary truths, how could the mathematical truth that 1 = 1 not be among them? One way to hold that mathematicians seek only contingent truths might be as follows. If some philosophers are correct that propositions are to be identified with sets of possible worlds, then there's only one necessarily true proposition, because there's only one set whose members are all the possible worlds there are. That single necessarily true proposition (call it "T") will be expressed by indefinitely many different sentences , including the sentences "1 = 1" and "No red things are colorless," and it will be contingent just which sentences express T. On this view, mathematicians don't try to discover various necessary truths, since there's just one necessary truth, T. ...

You've asked about one version of an ancient paradox called the "Liar paradox" or the "Epimenides paradox." One good place to start looking, then, is the SEP entry on the Liar paradox, available here . Philosophers are all over the map on how to solve paradoxes of this kind, and their proposed solutions are sometimes awfully complicated! Best of luck.

@Thomas Pogge: Thomson's violinist analogy doesn't address the questioner's puzzlement, because it doesn't support "the right to withdraw consent at any time to the fetus using her body, regardless of the situation of the conception (consensual sex, planned conception)." Thomson seems to recognize that it doesn't, so she eventually proposes the people-seeds analogy, the analogy the questioner found unpersuasive.

What is the difference between something that is logically a contradiction and something that happens to not be instantiated? As I think you already suspect, it's the difference between (1) a concept whose instantiation is contrary to the laws of logic or contrary to the logical relations that obtain among concepts; and (2) a concept whose instantiation isn't contrary to logic but only contrary to fact. Examples of (1) include the concepts colorless red object and quadrilateral triangle . Examples of (2) include the concept child of Elizabeth I of England . Concepts of type (1) are unsatisfiable in the strongest sense; concepts of type (2) are merely unsatisfied. Could you explain how the concept of a ghost is not a contradiction? Good question. I'm not sure the concept isn't internally contradictory. Can ghosts, by their very nature, interact with matter? Some stories seem to want to answer yes and no . If I recall correctly (it's been a while) the movie ...

@William Rapaport: Unless disjunctive syllogism or one of the other two rules used in the derivation fails, the "irrelevance" of the conclusion to the premise is irrelevant to whether the conclusion follows from the premise. Relevance logic has to give up at least one of those rules, none of which is easy to give up.

The topic is controversial (as I indicate below), but the inference rules of standard logic do allow you to derive any conclusion at all from any (formally) contradictory premise. Here's one way (let P and Q be any propositions at all): 1. P & Not-P [Premise: formal contradiction] 2. Therefore: P [From 1, by conjunction elimination] 3. Therefore: P or Q [From 2, by disjunction introduction] 4. Therefore: Not-P [From 1, by conjunction elimination] 5. Therefore: Q [From 3, 4, by disjunctive syllogism] Those who object to such derivations usually call themselves "paraconsistent" logicians; more at this SEP entry . They typically reject step 5 on the grounds that disjunctive syllogism "breaks down" in the presence of contradictions. I confess I've never found their line persuasive.

The nice thing about the Kantian approach is that it does not allow for exceptions in just my case. Of course, this result stems from the fact that the Kantian approach doesn't allow for exceptions in any case, which many philosophers regard as a reductio of the approach. For example, Kant famously prohibits lying to a murderer even to protect an innocent potential victim. Most people have strong intuitions to the contrary: lying is presumptively or defeasibly wrong, we say. A false theory can imply true consequences; it's the false consequences that are its undoing.

The reasons you gave for thinking that time is fundamentally motion and that space is fundamentally motion seem to depend on this principle: If A isn't perceivable (or isn't explicable ) without some kind of B, then A is fundamentally B. But that principle looks false. Motion isn't perceivable without some kind of perceptual apparatus, but that doesn't imply that motion is fundamentally perceptual apparatus. Motion isn't explicable without some kind of explanation, but that doesn't imply that motion is fundamentally explanation. Furthermore, if time and space are both fundamentally motion, are time and space identical to each other? Even physicists who talk in terms of "spacetime" nevertheless talk about time as a separate dimension of spacetime; I don't think they regard time and space as one and the same. One might also question whether space, or the perception of space, requires motion. When I stare at my index fingers held one inch apart, I perceive them as...

Just FYI: The link Prof. Pessin supplied isn't an essay by Thomas Nagel. It appears to be a paper concerning Nagel's work on the meaning of life, a paper written by a student (Lucas Beerekamp) for a course at a university in the Netherlands. Chapter 1o of Nagel's introductory book What Does It All Mean? (1987) is entitled "The Meaning of Life." Perhaps that's what Prof. Pessin meant to refer to (although it's barely seven short pages). More likely he meant to refer to Nagel's famous Journal of Philosophy article, "The Absurd" (1971).

It would be unbecoming of a philosopher to scoff at the question rather than engage it in some way, and philosophers do engage it. Another book to investigate is the third edition of The Meaning of Life: A Reader , edited by Klemke and Cahn. In his article "The Absurd" (widely anthologized, including in Klemke and Cahn), Nagel makes a tantalizingly brief suggestion that many who seek the meaning of life are seeking something flatly impossible: a life purpose so significant, so clearly ultimate, that it would make no sense to question it. Take happiness, for example. We can't simply define it as "the ultimate goal of life," because that would be a circular definition in this context. So we can question it as a goal: Is it the same as pleasure, or is it more like lasting satisfaction? Is it tied to virtue or not? Whichever answers we give to those questions invite the further sensible question "If that's what happiness is, then why is it the ultimate goal?" In this short magazine...

David Hume (1711-1776) famously sought to escape skeptical doubts of the sort you describe by distracting himself from them: "I dine, I play a game of backgammon, I converse, and am merry with my friends; and when after three or four hours' amusement, I would return to these speculations, they appear so cold, and strained, and ridiculous, that I cannot find in my heart to enter into them any farther" ( Treatise 1.4.7). But I don't think you have to seek distraction. My advice is to consider carefully (1) what it is you took yourself to be before you began "zooming out" and (2) whether the observations you make after zooming out really do cast doubt on (1). I think careful consideration of (1) and (2) may lead you to regard those observations as less threatening to (1) than they now seem to you. In your question, you concede that you have a brain and a body. You observe that thoughts often come to you unbidden, but isn't it also true that you sometimes can control, to at least some extent,...