The sorites paradox -- the paradox of the heap and similar paradoxes exploiting more important concepts than heap -- is a terrific topic. It's great to see people thinking about it.

You wrote, "we cannot say exactly where the transition occurs." Some philosophers would respond, "It can't occur exactly anywhere, because heap (or bald or tall or rich ...) isn't a concept that allows exact status-transitions. To say that there's an exact point of status-transition, even a point we can't know or say, is to misunderstand what vague concepts are."

Some philosophers would also object to your suggestion that the fuzziness can be "bounded," if by that you mean "sharply bounded." They'd say that any boundary around the fuzzy cases must itself be a fuzzy boundary: like the boundary between heap and non-heap, the boundary between definitely a heap and not definitely a heap isn't precise to within a single grain. (This phenomenon is usually called "higher-order vagueness.") In that case, the fuzziness that brought into doubt the existence of heaps also brings into doubt the existence of fuzzy boundaries themselves.

I don't think there's any way to cut the Gordian Knot here, if by that you mean finding a commonsense solution that cuts through the paradox. Why? Because the paradox itself results from commitments of common sense: (a) some number of grains is clearly too few to make a heap (maybe 15, as you say); (b) some number of grains is clearly enough to make a heap (maybe 15,000); and yet (c) one grain never makes the difference between any two different statuses (heap vs. non-heap, definitely a heap vs. not definitely a heap, etc.). Given commonsense logic, (a)-(c) can't all be true, but which one should we reject? Most philosophers who try to solve the paradox attack (c), but I certainly haven't seen a refutation of (c) that I'd call "commonsense."

I wish I knew the answer, or even knew of an answer that comes close to being satisfying. I sometimes worry that we human beings are smart enough to have discovered the sorites paradox but constitutionally too dumb to solve it. I'd love to be shown that my pessimism is unwarranted!

Recommended reading:
SEP, "Sorites Paradox"
SEP, "Vagueness"

How about this? A fallacy is an actual mistake in reasoning. A cognitive bias is a tendency to commit certain sorts of mistakes. Not all fallacies are the result of cognitive biases, and having a cognitive bias doesn't guarantee that you'll commit the corresponding error.

Thank you for these interesting reflections! As for your first point, there are a number of philosophers who address radical skepticism (e.g. can any of us know with certainty that we are not, as we seem to be, wide awake and acting in the world rather than, say, dreaming?) in the way you suggest. Arguably, life may continue just as it appears until one's death and yet there would be no decisive reason to rule out the possibility one was merely a brain in a vat. And because of this, some philosophers think that such radical skeptical hypotheses are idle or nonsensical or of no interest. I am somewhat of the other mind: I think we can imagine radical hypothetical states of affairs in which we are indeed systematically mistaken in almost all our beliefs about ourselves in the world (in brief, I think it conceivable that we might be in the matrix). While this does not have awesome practical consequences, I think it should humble us in our knowledge claims. As for the second point, Quine set out to dismantle the very categorical distinction between the analytic and synthetic. Today, some think he was spot on, but there are large numbers of philosophers (including myself) who believe the analytic category is sensible and intelligible. I think it is an analytic truth that 1+1 equals 2 --based on the principle of identity or A is A (because 2 simply is '1+1' and so 1+1 equals 2 because 1=1 equals 1=1. You ask about explanations. On that point, things get quite interesting. The concepts of necessity, impossibility, and possibility can be explained in terms of one another. So the statement '1+1 = 2 is necessary' is equivalent to '1+1=2 is possible and 1+1 is not equal to 2 is not possible. To many of this, explanations like this are acceptable, but to some radical thinkers, such explanations are considered insufficient. For a great defense of the analytic category and the concepts at issue, check out Alvin Plantinga's classic On The Nature Of Necessity.

This is an interesting one. One rather tangential aspect of your question is the fact that the backetball player formerly known as Ron Artest (whom I have watched play numerous times) seems a very poor role model on the topic of peace (or peaceful demeanor)!

Anyway, such sniping aside, the news is that he changed his name to Metta World Peace (not Meta)--go figure!

OK, so what is the philosophical issue here? Well, it seems there is a question as to whether or not we have a right to be called by our legal names. This does not seem to me to be a matter of "respect" for his choice of name, but a matter of recognizing that the name is now legally Metta World Peace. But I don't see why announcers couldn't refer to him as "MWP" or "Peace" without implied disrespect. In the end, public figures such as Metta World Peace (by any name) should get used to the idea that they do not have complete control over what others say about them or what others call them. I think one should expect as much respect as one earns. 'Nuff said!

Interesting question. But I'm wondering what rides on the answer. And what is connected to the question. Of course, we begin by wanting to distinguish the meanings of the two relevant clauses you give ("small rodent," v. "hand-held device"). So, separately, you obviously hold that there are two meanings in play. Now in logic it may be true that, strictly speaking, the proposition "P or Q" is a distinct proposition from either of its disjuncts, and can happily count as a "single" proposition -- but we also recognize that it is compositional, composed of parts, so we can think of it as one compound proposition or as a disjunction of two simpler propositions. But these are perfectly consistent with each other, so we can happily accept both -- it is both one compound, and a disjunction of two simpler, proposition(s). No need to choose! Why not just say the same with respect to your example? In any case you can raise the same question even of the component meanings in your example - your 'rodent' version is implicitly a disjunction too, as is, probably, ultimately, the 'hand-held' example .....

ap

You are confusing truth and logical validity. Your geometry book is writing about the logical validity of conditional arguments. Your math book is talking about the truth of conditional statements. Logical validity is much more than truth: it is truth that is independent of the truth or falsity of the premises.

Wel, fore a starrt, speeling mistaches can mak itt dificcolt two reed & undestand wot u ar actuwally tryin to saye, eh? An getting yours grammer awl rong can makes mawr problem of comprehention.

Of course, there are occasions where pointing out slips in spelling or grammar can be a bit rude and pointless. But equally, it is -- to say the least -- impolite not to try to smooth communication by using standard spellings and constructions.

It's an interesting question and not easy to answer. Let's start with what may seem to be a minor point but actually isn't. It's not right that we should never be direct. The most obvious exception is when two people already have a sexual relationship and they're both comfortable about it. But even there, being blunt isn't always welcome. Sex isn't one-dimensional. There's lusty animal sex and there's also tender romantic sex. What works for one doesn't necessarily work for the other.

If it's complicated even for people who are in a relationship, it's not hard to see why rude and crude doesn't tend to work when that's not so. Human relationships just are complicated; after all, there are completely non-sexual matters that most of us don't like having broached too directly. When we add sex to the mix, things certainly won't get simpler.

Leave male vs. female aside for a moment. If someone hints to me that they're interested but the feeling isn't mutual, I can ignore the hint in ways that get the message across but don't hurting the other person's feelings or make them lose face. This doesn't go just for sex, but it seems safe to say that it goes particularly for sex. Being less direct can make things a lot less awkward.

A different sort of case might help. If I'm upset with someone, then depending on the relationship and the reasons, being clear and straightforward might be best. But the old saying "least said, easiest mended" often has a point. A certain amount of indirectness seems to make social life easier.

The fact of the matter is that there's a lot of communication that doesn't take place using words, and on the whole, we humans seem to like it this way. The advantage is that this adds a lot of nuance and subtlety to the way we communicate. But not everyone is equally fluent in the language of gesture, gaze, tone of voice and standard dictionaries are hard to find.

As noted, all of this is general and applied to a lot more than sex. But there's another issue here that's at least as important. There's often a lot at stake in sexual encounters, and there's usually a lot more at stake for a woman than for a man. For the most part, unwanted sexual attention isn't a problem for men. For women it very often is. At the very least, staying away from the rude and crude is a way of acknowledging that important fact.

--

Afternote: a friend pointed out this very instructive youtube video in which Steven Pinker says a lot about all these issues. Stick with it to the end.

http://www.youtube.com/watch?v=3-son3EJTrU

Let me add a few words to Sean's excellent response.

I think one thing worth keeping in mind here, which I may have said already in response to a similar question, is that the institution of marriage in the United States, and in some other places in the developed world, has changed a great deal over the last sixty years or so.

A friend of mine once joked, "Of course marriage has to be between a man and a woman. Otherwise, how would you know who gets to beat up whom?" Not very funny, of course, in one sense, but perhaps you see her point. There was a time, not very long ago, when it was legally impossible in many states for a woman to be raped by her husband. A married woman's ability to own property independently of her husband was curtailed in some jurisdictions. Men had, by law, that kind of control over their wives, and the entire institution of marriage was one of ownership. That is why many radicals of the Victorian and post-Victorian eras were deeply suspicious of the entire institution. One of these people was Bertrand Russell, who wrote a book, Marriage and Morals, on the topic.

With the explosion of the feminist movement in the 1950s, these things begin to change, and marriage starts to be seen as a partnership between equals. The fact that one of these partners was male and one female slowly, over time, came to be quite irrelevant. Neither party has rights or privileges that the other does not have, simply on the basis of gender, and any such privilege would be seen as sex discrimination.It was essentially on this ground, that the gender difference had no legal significance, that the Supreme Judicial Court of the Commonwealth of Massachusetts made its historic decision legally same-sex marriage.

That is why it is no accident that those who trumpet the "one man, one woman" line are anti-feminist, too.

This phenomenon is well-known. It's a form of zeugma that is known as "syllepsis".

I think most linguists would say that this sentence cannot mean that Miles has a trumpet and a narwhal a protrusion from the head. The reason is the obvious one: that "horn" has to be interpreted a single way. Note that, if correct, this shows that "Ms and Ns are F" is not, as we sometimes tell our introductory logic students, simply an abbreviation (or something) for "Ms are F and Ns are F", since, in the latter, "F" could be interpreted differently in its two occurrences.

When one makes a claim like the one just made, we are talking about how the sentence is immediately, unreflectively, and automatically understood by a hearer. So what I'm observing is, in effect, simply that our "language faculty" operates a certain way, and not another way that it could, in principle, have operated. And put that way, the point should be fairly uncontroversial. The humorous effect one can get from syllepsis depends the fact that syllpetic utterances strikes us in the first instance as odd.

But language-use is complex and one can, of course, reflect on what has been said and arrive at a kind of secondary interpretation. Certainly we do that will sylleptic utterances, and so one can manage to communicate something by such an utterance that it cannot literally mean.