# I've recently read that some mathematician's believe that there are "no necessary truths" in mathematics. Is this true? And if it is, what implications would it have on deductive logic, it being the case that deductive logical forms depend on mathematical arguments to some degree. Would in this case, mathematical truths be "contingently-necessary"?

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. ...

# How, if at all, is the following paradox resolved? You hand someone a card. On one side is printed "The statement on the other side of this card is true." On the other side is printed, "The statement on the other side of this card is false." Thanks for consideration!

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.

# In discussing abortion, I've been told that the woman has a right to bodily integrity. Therefore she has 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). Some say any time prior to viability. Is there a fully fledged philosophical argument along these lines? I'm aware of Judith Jarvis Thompson's thought experiment about the room and the people-seeds, but that didn't invoke the intuition in me, "yes, the seeds can be pulled up at any time." Does the fetus have a competing right to bodily integrity?

@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.

# Here's a quote from Hume: "Nothing, that is distinctly conceivable, implies a contradiction." My question is this: what is the difference between something that is logically a contradiction and something that happens to not be instantiated? For example, ghosts do not exist. Could you explain how the concept of a ghost is not a contradiction? Thanks ^^

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 ...

# Is it true that anything can be concluded from a contradiction? Can you explain? It's seems like its a tautology if taken figuratively because we can indeed conclude anything if we suspend the rules of reasoning, but there is nothing especially interesting in that fact in my humble opinion.

@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.

# I'm having trouble appreciating Kant's moral philosophy. According to him an action is bad if we can't universalize it as a maxim of human behavior. Under that way of thinking being gay is bad because if everyone was gay nobody would have any babies and that means you are willing the non-existence of the human race which would be a contradiction if you want to exist. So I guess bisexuality is okay but being a monk isn't. The reasoning seems absolutely bonkers if you are gay whether from choice or from nature there is no reason to surmise that you think everyone has to be gay. If Kants moral philosophy is so lame I must admit that it prejudices me against his whole philosophical system. Is there any reason why I should give Kant's ethics more credit?

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.

# Since nothing could change without some kind of movement, and time would not be perceivable without some kind of change, why isn't time fundamentally motion. Likewise, since space would not be perceivable without some sort of motion, why isn't space fundamentally motion as well? In other words, what part of space or time is conceivable without bringing motion into the explanation?

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...

# Nowadays, I feel as if right now, in this current world, humans are only wanting to study really hard in school, get a job, and receive money for food and personal items. I feel like there's more to life than that but everybody I ask seems to only want a good job and a lot of money. I am 16 years old and I know that I still have a lot of years to live through but sometimes I feel as if just getting a job and getting money with that job is such a pointless goal. I keep thinking if that is the meaning of life, then that is such an uninteresting goal. But, I still try my best in school and academics because I have this weird, abstract feeling that I absolutely HAVE to or I will fail in life. I do not know the explanation of that feeling but I listen to it. Is just getting a job, doing that job and getting money for it the meaning of the vast majority of this world's people's lives?

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).

# I know that many philosophers might scoff upon being asked some variation of "What is the meaning of life or living" but isn't it about the most relevant question one can ask in relation to philosophy and its relationship with humankind? It seems this is studied very little or at all by philosophers in academia. As a follow-up, do philosophers either in the continental or analytic tradition place any value in the metaphysical writings of yogis or mystics from India; isn't it at least worth investigating?

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...

# If I "zoom out" for a moment, then any deliberations I'm making (well, really any thoughts at all that I'm having) seem like part of a process to which I am just an observer. It is certainly true that these processes are occurring in MY brain, which is part of MY body, however thoughts either come to mind or they don't. I can't help but feel as if the only me that really exists is simply a collection of concurrent processes that, via consciousness, are at times able to observe themselves occurring. And furthermore, given what we know about the fallibility of memory and yet also memory's crucial role in the development of character/personality/identity, etc., I can't also help but feel that what I am is the product of a lengthly string of inaccuracies. Pardon the confused language. It's quite difficult to speak about these matters without necessarily recurring to the very terms and concepts that are in question. What I'd like to know is how I can continue to think about these issues without becoming...

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,...