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First of all I want to say I'm sorry for my bad English. For I am Icelandic, I

First of all I want to say I'm sorry for my bad English. For I am Icelandic, I don't get a lot of English classes. ok My friend is always talking about "everything is a goat"; it makes a little sense to me but it is ridiculous. The opposite to everything is nothing. The statement "nothing is a goat" is not right. Isn't there some gap between everything and nothing? Can't we say "something is a goat"? I hope you answer :)

The negation of "Everything is a goat" is not "Nothing is a goat". Asentence and its negation must have opposite truth values; that is, ifone is true, the other is false. A sentence and its negation cannotboth be true and they cannot both be false. But, as I think yourealize, "Everything is a goat" and "Nothing is a goat" canboth be false: if there are some things that aren't goats and somethings that are, then the two claims will be false. So this shows that"Nothing is a goat" is not the negation of "Everything is a goat".Might the negation of "Everything is a goat" be "Something is a goat"?No, for both these claims could be true: imagine that there is at least onegoat and furthermore that everything is a goat.

(All these errors are facilitated by the false assumption that nouns like "nothing" and "everyone" function like "Harry" or "the animal in the shed" do. For more on this error, see Question 49.)

What then isthe negation of "Everything is a goat"? It's "Something is not a goat."If this claim is true then "Everything is a goat" is false. And if it'sfalse — false that there's at least one thing that isn't a goat — thenthat must be because everything is a goat. Finally, what is the negation of"Nothing is a goat"? It's "Something is a goat", for these sentencesalways have different truth values, that is, if one is true the otheris false.

Are there logic systems that are internally consistent that have a different

Are there logic systems that are internally consistent that have a different makeup to the logic system that we use?

On Dan's comment. The distinction between so-called weak counterexamples and strong ones is, of course, important. But it really is possible to prove, in intuitionistic analysis, the negation of the claim that every real is either negative, zero, or positive. The argument uses the so-called continuity principles for choice sequences. I don't have my copy of Dummett's Elements of Intuitionism here at home, but the argument can be found there. A short form of the argument, appealing to the uniform continuity theorem—which says that every total function on [0,1] is uniformly continuous—can be found in the Stanford Encyclopedia note on strong counterexamples.

There is an important point here about the principle of bivalence, which says that every statement is either true or false. It's sometimes said that intuitionists do not, and cannot, deny the principle of bivalence but can only hold that we have no reason to affirm it. What's behind this claim is the fact that we can prove that we will not be able to find a statement P and show that it is neither true nor false. That is to say, we can prove that there is no statement that is neither true nor false. But that does not, by itself, show that it is incoherent to hold that not every statement is either true or false. The two claims are intuitionistically consistent.

How do you tell the difference between a reductio and a surprising conclusion?

How do you tell the difference between a reductio and a surprising conclusion?

The crucial question is which is more plausible: the premise or the negation of the conclusion. Our answer may be influenced by diverse features of our broader 'web of belief'.

Is self-contradiction still the prima facie sign of a faulty argument?

Is self-contradiction still the prima facie sign of a faulty argument? How do we tell an apparent contradiction from a real contradiction if the argument is in words? (Most of us don't know how to translate arguments in words into symbolic logic.)

It is perhaps worth adding that self-contradiction is not the only sign of a faulty argument. An argument can be faulty but not lead to a contradiction. For example, suppose that you know that some number x has the property that x2 = 4. If you claim that x must be 2, you have engaged in faulty reasoning. The conclusion x = 2 does not contradict the hypothesis that x2 = 4; the two statements are perfectly consistent. But your reasoning is faulty because you haven't taken into account the possibility that x might be -2.

I was loading up to go on a trip the other day and asked my Dad why he was

I was loading up to go on a trip the other day and asked my Dad why he was taking a lot of extra stuff and he said: "Just in case the unexpected happens." So out of that comes my question: If you expect the unexpected, then doesn't that make the unexpected expected and the expected unexpected?

When someone says "I expect the unexpected" we might hear that alongthe lines of "I fathered someone fatherless". That is, we mightinterpret him as meaning that he expects some event which he also doesnot expect. That does seem like a contradiction. But isn't that tomisunderstand what he's trying to say? What he expects is not someevent (which he also doesn't expect); rather, what he expects is thathe doesn't expect some event. His expectation applies not to some eventitself but rather to his non-expectation of some event. What he expectsis that there will be some event that he does not expect. Thisexpectation is a second-order expectation: it applies to hisfirst-order non-expectation of some event. (My expectation that a credit card billwill soon arrive is a first-order expectation. My expectation that Melanie will expect me to pay for dinner is a second-order expectation. See herefor a similar distinction.) That's why, as Peter Liptonsays, "Even if you expect the unexpected, you may still be surprised":what surprises you and what you expected are different things. You'resurprised by the fact that there is a hedgehog in your glove compartment (are you serious,Peter?), but not surprised by the fact that something surprised you.

How widespread is the use of deontic logic?Hrafn Asgeirsson, Iceland

How widespread is the use of deontic logic? Hrafn Asgeirsson, Iceland

So far as I know, deontic logic has never entered mainstream work on moral philosophy. One of the key ideas of deontic logic is to allow for impossible (combinations of) obligations. My sense is that, while there have been proponents of the idea that there could be such things (notably, Bernard Williams), most have rejected the idea. The argument I have usually heard (this is going back to grad school, so it's been a while) is that the relevant notion of obligation is one of all things considered obligations, and these cannot conflict. Perhaps deontic logic would be of more interest, however, if regarded as a logic of prima facie obligation. But then the deep question is how conflicts between prima facie obligations are supposed to be resolved, and, so far as I know, that's not really the focus of work on deontic logic. Perhaps more recent work than is known to me has addressed that question.

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

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.