You suggest that Kant's criterion of wrong conduct turns on this question: "If everyone acted the way I am proposing to act, would this have undesirable consequences?"

I think Kant's actual question differs in two respects. Kant is not asking whether the agent would like some fictional world (find it desirable), but whether the agent can will it and her own proposed conduct in it. And the world Kant envisioned is not one in which all act the way the agent is proposing to act, but one in which all are permitted (and take themselves to be permitted) so to act. So Kant's question is: "Can I will the action I am considering along with its universal permission?" The basic idea here is that I should not permit myself an action that I cannot permit all others at the same time.

Let's see how this plays out in Kant's promising example. The agent considers extricating himself from financial difficulty by making a false (lying) promise. He then asks himself whether, in a world in which all took themselves to be permitted to make such promises, he could still will to act in this way. Kant's answer is no: in that fictional world, such promises would not be believed and therefore refused; and agents could thus not will to offer them because they would be useless for their intended purpose.

Now your objection survives this clarification. Suppose the world were such that some nice fairy fulfilled any promises that the promisor fails to fulfill. In that world, it would seem, making false promises would be permissible. For in that world, even if all took themselves to be permitted to make false promises, such promises would (not be believed but) still be accepted. In that world, then, the agent can will his proposed action alongside its universal permission. So it would seem that, as you say, the permissibility of making a lying promise turns on a contingent empirical fact, namely on whether there is some third party ready to step in to ensure that even lying promises are fulfilled.

I am sure Kant and orthodox Kantians would not want morality to be like this. But ask yourself in conclusion whether such responsiveness to basic empirical facts about the world isn't actually an advantage in morality. Would it really be wrong falsely to promise repayment if such false promises were to hurt no one? And is it really implausible to hold (to give another example) that the question whether one is duty-bound to procreate depends on whether enough children would be born even without such a duty.

The Celsius scale of temperature places the zero at the freezing point of water, not at "absolute zero" which is conceptualized as the time when molecular motion ceases. So 20 degrees C is not twice the temperature of 10 degrees C. The zero for temperature is minus 273C.

There is a saying among philosophers: "ought" implies "can." The application of this maxim to your question is as follows: It seems that anything that deserves to be called a "universal right" would be something that ought to be provided to everyone--no exceptions. But this could not possibly be true about education (or anything else, under the maxim) if the way the world is, as a matter of fact, makes it impossible, as a practical matter, actually to provide what such a "right" requires. So we might think about the question of whether or not there are people whom we simply can't provide with the resources necessary for the kind of education we might reasonably wish we could provide to everyone.

Now, I think the question of whether or not we actually can educate everyone will depend on facts about sociology, psychology, and economics that I do not pretend to know. But I am inclined to think that the idea of educating absolutely everyone to the extent we might wish to educate them is something we simply can't do. If so, I think it cannot be sensible to hold education as a "universal human right." Some things are very valuable desiderata; but not all of these are "universal human rights."

Great question, and one with very deep historical roots. The ancient Stoics, for example, thought that remorse and regret were not compatible with being a true Sage, and I think the same arguments they give about these responses would also apply to those of disappointment or frustration when things don't go as you had hoped they would. But to extend this way of thinking even further, you might then go on to ask whether it is even ever really rational to hope for something that is not under your own control. For the Stoics, the only thing that is under our control (or, at least, can and should be under our control) is how we react to things. As a result, such "bad" reactions as remorse, regret, disappointment, or frustration are not the right way to respond to things that happen in the world. The true Sage would understand how the world works so well that nothing he or she would ever do would give rise to remorse or regret. Similarly, the Sage would understand the world so well that nothing would frustrate or disappoint him or her, because the Sage would never be so irrational as to hope for something that was not the ways things really are or will be. The Sage is one who simply wants the world to be the way it actually is, so that one's will is perfectly aligned with what actually has happened, does happen, and will happen.

Now, many people would question this Stoic view as being "morally challenged," at best. It sounds, for example, like the Stoic Sage is someone whose response to a school bus full of innocent children hanging precariously over a cliff, but slowly tipping towards the point where it will surely fall over the cliff, would be something along these lines. "Hmmm...I see that the bus will go over the cliff and all those children will die on the rocks below. Well...that's fine with me!"

If this sounds like something has gone wrong in the Stoic view, then you can apply that to your thought. If the acquisition of something (such as a certain job) seems like it would bring genuine benefits, all things considered, then it strikes me as both natural and also reasonable to feel at least some disappointment or frustration if one does not obtain the valuable thing. The Stoics denied that things like jobs (or, for that matter, even loved ones) actually have any genuine value. Many people will find this element of the Stoic view implausible. If things do have value, then it is right for us to want them, and part of the logic of desire is to feel some kind of dissatisfaction/discomfort if our desires are not met.

So perhaps a more fruitful way to think about this question is not to frame it in terms of contraries (either we should feel frustration or not), but instead to think about what levels of frustration or disappointment are appropriate to the specific episode in which we do not get what we desire. Here, I think most philosophers will adopt a view that is not as extreme as the Stoic view, but which approximates that view more closely than the very exaggerated (and, I suspect, self-absorbed) way in which most people respond to the (often very petty) frustrations of their lives. We are encouraged to be "philosophical" about things, which means, I suppose, that we are supposed to evaluate the actual worth of things as accurately as we can, and also to remind ourselves of the generally very poor position we are in with respect to assessing the actual long-term value, all things considered, of what we find ourselves desiring.

A small anecdote might help here. I was very frustrated in my career for many years, and sometimes came close to being offered jobs that I know I would have accepted had they been offered at the time. I also now think, in retrospect, that accepting at least some of those jobs would have actually hindered my career even more than what I was already finding frustrating at that time, so...actually, it turns out to have been a good thing for me that I did not get what I wanted so badly at that time. Reminding oneself of such things can certainly help to allay some of the more negative aspects of the experience of frustration.

But if a desire really is for something good, and one does not manage to get the good, then it seems to me that at least some level of disappointment is quite reasonable, especially if that disappointment can help to motivate a continued effort to get some version of the good that was missed this time, or a better line of approach, so that one's next efforts might be more successful.

I think it depends on what precisely you mean by "feminist," but by most understandings of this term, I think there are a number of male feminist philosophers, and certainly an even greater number of male philosophers who are generally very sympathetic to and agree with feminist philosophy, even if they do not count feminist philosophy as one of their research specialties.

From an armchair sociological perspective, I'm inclined to think that actually most male philosophers agree with much of feminism--including some who are nonetheless still capable of very un-feminist behaviors at times. Alas, it is one thing to recognize the value of a certain philosophical point of view, and quite another to live up to the demands of that point of view!

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"

Others can no doubt give more nuanced answers, but most people (I'd be wiling to say virtually all) who earn a living depend either directly or indirectly on government-supported institutions and government-provided infrastructure for the possibility of their livelihood. This includes but is not limited to - military defense against external aggression, a police force, a court system to enforce legal rights, a public education, system, highways...

A setting in which a worker can avail him/herself of none of those things is a setting in which very few indeed would prefer to work.

It might not disqualify you at some programs, but it will certainly count against you at most. The writing sample is the primary way of distinguishing applicants' philosophical talents, at least once they have been narrowed down using other criteria (such as coursework in philosophy and grades, letters--though for the competitive candidates, they tend to be equally gushing--and perhaps GRE). A 5-page sample is unlikely to provide evidence that you can develop an argument responding to a particular position that you have adequately and charitably explained. (Of course, Gettier's famous paper is quite short!)

I say all this with empathy--I was a philosophy minor (not major) and did not have a good, long piece of writing to submit when I applied to grad school. I had to use a mediocre, long piece, and was lucky to be accepted in the few places I was. But that was (too) many years ago when the competition was a little less fierce. I would try to work with one of your professors to develop one of your short papers into something more substantial (12-18 pages).

(On the other hand, people should NOT submit pieces longer than 20 pages.)