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Is nothing impossible? Is it just that a lot of things have infinitely small probabilities of occurring?

(This evening, shortly after reading this, I had dinner at arestaurant in NYC — and there was Mayor Bloomberg at the next table. I heard someone say, "Nothing's impossible after all.")

I'm not sure what an infinitely small probability would be. Perhapsjust a probability of 0? But that sounds like an impossible event. Soperhaps you're asking whether all events have some finite non-zeroprobability of occurring — and whether the events we call "impossible"really just have a very small finite probability.

Philosophershave spent a lot of time trying to figure out what we're actuallysaying when we assign a probability to an event. Are we making someclaim about the world? Or are we making a claim about our degree ofconfidence in some judgment about the world? I won't go into that hereand instead will say a few words about impossibility.

Philosophersoften distinguish between different kinds of impossibilities. Somesituations would conflict with the laws of logic: for instance, thestate of affairs in which I am over thirty years old and not overthirty years old is one that conflicts with the law of logic that saysthat "A and not-A" is false for every statement A. We might say thatthat state of affairs is logically impossible, or impossible relative to the laws of logic.By contrast, some situations conflict only with the laws of physics:for instance the state of affairs in which I am moving faster than thespeed of light is not a possible one according to contemporary physics.It's one that is logically but not physically possible, one that is impossible relative to the laws of physics.Likewise, we might have situations that we would describe as impossiblerelative to the laws of chemistry, and so on. And perhaps, when someonesuggests that your spouse is having an affair you will find yourselfexclaiming that that's impossible, meaning not that such perfidy isinconsistent with the laws of logic or physics, etc., but that it'sincompatible with what you believe to be true about your spouse.

If this is the right way to think about impossibility, then nothing is impossible — tout court. A situation is possible or impossible only relative to certain assumptions. And relative to any given body of assumptions, many situations will be impossible.

To what extent does belief preclude speculative thought? If to believe is to accept a proposition as being true (as my dictionary claims), do we undermine our belief by testing the proposition? To what extent does testing a proposition imply doubt. I attend a private Christian university, so I find this question extremely important. I have given up using the word "believe" completely because it seems to undermine my need to question things. When people ask if I believe in God, Jesus-as-Christ, the Trinity, I feel I have to say, "no." Would proclaiming belief in those things while questioning their validity undermine what we mean by "belief"? Did this question even make sense?

Traditional discussions of this question suggest that thereare two ways of understanding the relation between belief and knowledge. On theone hand, there is a tradition (tracable to Plato) which says that havingbelief about something precludes having knowledge about that thing. (Plato usestwo different words for these notions: belief is “doxa;” knowledge is “episteme.”He suggests that the things we can know belong to a special class of abstractentities called “Forms;” with respect to everything else, all we have isbelief.) At the same time, there is a tradition (which can also be traced toPlato) according to which knowledge is a special kind of belief: roughly,belief that is both true and justified. So there are two traditional answers toyour question: the first says that if you know something then you don’t (just)believe it; the second says that if you know something, then you must alsobelieve it.

Suppose that I'm working on a medical treatment for a project with no known cure or even treatment. My subjects report that they feel much better after receiving the treatment, but subsequent study shows that the treatment is, in fact, ineffective and all that I'm seeing is the placebo effect. Can I ethically tell them the truth and thereby make them feel worse subjectively? Would that violate the "do no harm" principle of medical ethics?

The injunction “Do no harm” is hard to follow unless one knows whatcounts as harm, and there is no clear consensus about this issue. Itdoes seem that by making a person feel worse, I am harming her. Feelingbad is in itself a bad thing, and it might also lead to other badthings. If I feel bad, then I may not be able to do other things that Iwould otherwise enjoy, things that I might believe have value inthemselves. At the same time, it seems that I could be harmed if I amprevented from learning the truth about my situation. If I have falsebeliefs, I might make choices that I would otherwise not make, choicesthat lead me to feeling worse than I would otherwise have felt. Could Ibe harmed by being led to believe something false about myself even ifthis false belief never leads to any decrease of good feelings or anyincrease in feelings of pain, dissatisfaction, or discontent? Let’simagine that I believe about myself that I am widely admired and deeplyloved by my friends and family and that this belief gives me deepfeelings of contentment and satisfaction. But let’s imagine also that Iam completely deluded: I am ridiculed behind my back and privatelydespised by my friends and family who are hoping to achieve a biginheritance from me. Let’s suppose further that their secret is safe,unless you tell me the truth. Would I be made better off by learningthe truth about myself?

But returning to your particularcase. Even if one has figured out what counts as genuine harm, it'soften a tricky matter in any particular situation to figure out whichcourse of action will cause the least harm. For example, whether agiven patient would be most benefitted were he to learn that his deathis imminent (so that he could make wise decisions about what to do withthe rest of his life), or whether he would be most benefitted by being"blissfully ignorant", will depend on the nature of the person and whatchoices he has. But in any case, most of us value knowing the truthabout our situation, and even if we know that we tend to screw up ourown lives and even if we believe that others could make betterdecisions forus, we still prefer to make informed decisions for ourselves. For allof thesereasons, it has seemed to many that physicians should always discloseto their patients information about their medical condition (including,it would seem, what effect a given drug is having on the patient'shealth).

I believe in allowing other people to live out their respective journeys in life - this requires a lot of tolerance sometimes. How does one reconcile respecting another person's journey with the great harm the person can do in the community by their actions? A right-wing zealot with his/her black-and-white world view versus a left-wing person whose view on life comes with a much more complex color-shaded world view. It is the right winger, that threatens the community with his/her worship of free-market capitalism (which really isn't so free-market), their dependence on lying and twisting the facts to fit their narrow view of the world (they just do it a lot more than liberals), and imposing their heretic version of Christianity on the rest of us. How does one respond ethically to counter the right-wing influence in this country yet respect this person's journey of self-discovery and their contribution (eventual perhaps?) to the community?

When you say that you “believe in allowing other people to live outtheir respective journeys in life,” do you make no exceptions? Do youthink that it’s a good idea to let anyone do anything that he or shesees fit? Liberals who are committed to tolerance often draw the lineat actions that threaten great harm to others. After all, even liberalsare committed to laws against murder, fraud, maiming, and the like, andmost don’t worry that their endorsement of such laws reveals a morallyobjectionable intolerance of people who are committed to different lifeplans from their own.

Your question raises interesting questionsabout when and why tolerance is a good thing. I think that many peopleare committed to tolerance because they believe that tolerance is theonly attitude that is respectful of other people. But if a respectfulattitude toward others is what people who are tolerant are attemptingto achieve through their tolerance, then their commitment to tolerancecannot be absolute (i.e., exceptionless). My respect for human beingsmight in some circumstances commit me to being intolerant of otherpeople's actions-- namely, those harmful actions that themselves reveal agrossly disrespectful attitude toward other human beings.

It seems to me that one of the things that philosophy does, at least for me, a beginner, is to expose mysteries where I thought there were none. Do any of you feel the same way, do you like that chill up your spine when you realize what you thought was self-evident might not be? Is the feeling that you have solved the problem more exciting than the feeling of wonder?

I think this feeling of wonder is common among philosophers. It's one of the things that attracted me to philosophy in the first place. And many philosophers have commented on this phenomenon -- e.g., William James in Some Problems of Philosophy:

Philosophy, beginning in wonder ... is able to fancy everything different from what it is. It sees the familiar as if it were strange, and the strange as if it were familiar. It can take things up and lay them down again. Its mind is full of air that plays round every subject. It rouses us from our native dogmatic slumber and breaks up our caked prejudices.... [A person] with no philosophy in him is the most inauspicious and unprofitable of all possible social mates.

If we built a computer that could analyse our minds, and it figured out how they work and explained it to us, would we be able to understand?

The great Austrian logician, Kurt Gödel, proved a remarkable theorem in 1931 that he thought was relevant to this question. His theorem wasn't about minds, but with a bit of license, it could be taken to have some implications about them. For instance, this one: Assume our minds are like powerful computers, devices that manipulate symbols according to well-defined rules. Assume, moreover, that these rules are consistent with one another, that is, that they do not yield conflicting results. Then it "follows" from Gödel's result that there is some basic fact about our minds that we cannot ever know, that we could not in principle access. I suppose you might put it, as Peter Lipton did, by saying that that basic fact is "too difficult" for us to understand. But just a slightly more powerful mind would be able to grasp the fact in question about our minds! And that slightly more powerful mind would, in turn, fail to be able to grasp the same basic fact about its own functioning! So, if all these assumptions could be made intelligible and were correct, it seems it would be right to say that there is something about the structure of our minds that makes them incapable of grasping some basic feature of that very structure.

Can Non-Being and Being occupy the same space at the same time or does Being displace Non-Being? Or Does Non-Being displace Being? Does Non-Being even exist?

How many hands do you have? Two? Or do you havethree? Your left hand, your right hand, and the non-existent third handthat's attached to your head? Obviously, that last "hand" shouldn'tcount. To say that you don't have a third hand isn't to say that youhave a hand that possesses the particularly stunting property ofnon-existence. We get ourselves into a real muddle if we take claims ofnon-existence to mean that there is some object that has the propertyof non-existence; for then that object must both exist (to have anyproperties) and not exist, and that can't be. So when we say that noone came to the party, we mean to deny that someone came to the party — not to affirm that at least one person did, namely "no one", the"non-person", the person with the rather anti-social property of non-existence.

This confusion becomes unavoidable if one assumesthat every noun in a language must refer to something. For if youassume that, then when you come upon a sentence like "Nothing beats aroyal flush" you'll be forced to conclude that something does after allbeat a royal flush, namely Nothing. This assumption is mistaken. Notall nouns contribute to the meaning of sentences in the same way. Inparticular, some (like "nothing") don't refer to anything while others(like "Manhattan") do.

So, to turn to your question, it's aconfusion to think of Non-Being as something that's jockeying Being forthe same space. In any given space, either there's something orthere isn't. And if there isn't anything there, if there's nothingthere, that doesn't mean that there's actually something there, namelyNon-Being.

Does the future exist in any knowable fashion? If so, can it be known in any absolute way? If not, why do so many of us believe it can?

On one view of time, the future is as real now as the present or the past, much as other places are as real as the place you happen to be; on another view the future is not yet real but will be. Either way, many philosophers would say that we can know some things about it, though Hume's great sceptical argument against induction attacks this idea. But Hume's argument is not especially about the future: it applies to any inference from what we have observed to what we have not observed, whether what we have not observed is in the future, present or past. In any event, it's not very surprising that we believe we can know something about the future, since we have so often formed expectations that we have subsequently found to be satisfied.