This is a question about pure logic. There are two theries: Theory A and Theory B. Theory A assumes AssumptionA. Theory B assume AssumptionB. The two assumptions are mutually exclusive: if AssumpionA then not AssumptionB and vice versa. I believe that a philosophical result is that Theory A and Theory B cannot prove anything about each other. All you can do is preface each result with the assumption. For example, if Theory A proves X and Theory B proves Y, then we can say "If AssumptionA, then X" and "If AssumptionB then Y". Who first proved this? Where is it documented? Eugene

I'm going to step through this carefully to make sure I follow. We have two theories: A and B . Theory A has an assumption: A and theory B has an assumption B . And A and B are mutually exclusive—can't both be true. Let's pause. To say that a theory has an assumption means that if the theory is true, then the assumption is true. It doesn't mean that if the assumption is true, then the theory is true. A silly example: the special theory of relativity assumes that objects can move in space. But from the assumption that objects can move in space, the special theory of relativity doesn't follow; you need a lot more than that. Otherwise, the "assumption" would be the real theory. You ask if it's true that neither theory can prove anything about the other. If I understand the question aright, it's not true. For one thing, trivially, if we take A as a premise, then by your own description, it follows that B is false. That seems like a case of proving something about B ...

My one distinguishing feature is that I don't have a distinguishing feature - paradox?

Fun question. Let's say that a characteristic or property or whatnot is intrinsic if we can tell whether someone has it without needing information about other people/things. The fact that I have blue eyes is an intrinsic feature in that sense. My eye color doesn't depend on your eye color. But to know that I'm the shortest person in the room, you have to know things about the other people in the room as well as things about me (namely, our heights.) Being the shortest person in the room isn't an intrinsic property/quality/characteristic. Note that we're using "property", "characteristic", "quality" so as to include abstract things, and things that depend in possibly quite recondite ways on how an individual is related to other individuals, sets of individuals... We don't tend to use the word feature so abstractly. Your features are the things we'd talk about to describe you yourself. Some of them, like height, may not be purely intrinsic, but to make things simple, we'll set those aside. If we...

I am reading "The Philosopher's Toolkit" by Baggily and Fosl, and in section 1.12 is the following: "As it turns out, all valid arguments can be restated as tautologies - that is, hypothetical statements in which the antecedent is the conjunction of the premises and the conclusion." My understanding is the truth table for a tautology must yield a value of true for ALL combinations of true and false of its variables. I don't understand how all valid arguments can be stated as a tautology. The requirement for validity is the conclusion MUST be true when all the premises are true. I must be missing something. Thanx - Charlie

I don't have Baggily and Fosl's book handy but if your quote is accurate, there's clearly a mistake—almost certainly a typo or proof-reading error. The tautology that goes with a valid argument is the hypothetical whose antecedent is the conjunction of the premises and whose consequent is the conclusion. Thus, if P, Q therefore R is valid, then (P & Q) → R is a tautology, or better, a truth of logic. So if the text reads as you say, good catch! You found an error. However, your question suggests that you're puzzled about how a valid argument could be stated as a tautology at all. So think about our example. Since we've assumed that the argument is valid, we've assumed that there's no row where the premises 'P' and 'Q' are true and the conclusion 'R' false. That means: in every row, either 'P & Q' is false or 'R' is true. (We've ruled out rows where 'P & Q' true and 'R' is false.) So the conditional '(P & Q) → R' is true in every row, and hence is a truth of logic.

What is the difference between "either A is true or A is false" and "either A is true or ~A is true?" I have an intuitive sense that they are two very different statements but I am having a hard time putting why they are different into words. Thank you.

I think you're getting at the difference between the principle of Bivalence (there are only two truth values—true and false) and the Law of Excluded Middle: 'P or not-P' is always true. Suppose there are some sentences that are neither true nor false. That might be because they are vague, for example. It might not be true to say that Smith is bald, but it might not be false either; it might be indeterminate. So if S stands for "Smith is bald," then "Either S is true or S is false" would not be correct. Our assumption is that S isn't true, but also isn't false. However, if by "not- S " we mean " S isn't true," then " S or not- S " is true. That is, bivalence would fail, but excluded middle wouldn't. But as you might imagine, there's a good deal of argument about the right thing to say here.

An elementary precept of logic says that where there are two propositions, P and Q, there are four possible "truth values," P~Q, Q~P, P&Q, ~P~Q, where ~ means "not."   Do people ever apply this to pairs of philosophy propositions? For example, has anyone applied it to positive and negative liberty, or to equality of opportunity and equality of condition, or to just process and just outcome? On these topics I can find treatments of the first two truth values but none of the second two.   If this precept of logic is not applied, has anyone set out the reasons?

I'm not entirely sure I follow, but perhaps this will be of some use. Whether two propositions really have four possible combinations of truth values depends on the propositions. Non-philosophical examples make the point easier to follow. Suppose P is "Paula is Canadian" and Q is "Quincy is Australian." In this case, the two propositions are logically independent, and all four combinations P&Q, P&~Q, ~P&Q and ~P&~Q represent genuine possibilities. But not all propositions are independent in this way; it depends on their content. P and Q might be contradictories, that is, one might be the denial of the other. (If P means that Paula is Canadian and Q means that she is not Canadian, then we have this situation.) In that case, the only two possibilities are P&~Q and ~P&Q. Or P and Q might be contraries, meaning that they can't both be true though they could both be false. For example: if P is "Paula is over 6 feet tall" and Q is "Paula is under 5 feet tall," then we only have three...

I'm still puzzled by the answers to question 5792, on whether it is true that Mary won all the games of chess she played, when Mary never played any game of chess. Both respondents said that it is true. But is it meaningful to say "I won all the games I played, and I never played any game."? It seems to me that someone saying this would be contradicting himself.

I think you're right to at least this extent. If I say to someone "I won all the games of chess I played," the normal rules of conversation (in particular, the "pragmatics" of speech) make it reasonable for the other person to infer that I have actually played at least one game. Whether my statement literally implies this, however, is trickier. Think about statements of the form "All P are Q." Although it may take a bit of reflection to see it, this seems to be equivalent to saying that nothing is simultaneously a P and a non-Q. We can labor the point a bit further by turning to something closer to the lingo of logic: there does not exist an x such that x is a P and also a non-Q. For example: all dogs are mammals. That is, there does not exist a dog that is a non-mammal. Now go back go the games. If Mary says "All games I played are games I won," then by the little exercise we just went through, this becomes "There does not exist a game that I played and lost." But if Mary played no games at all,...

Are there any books or videos or blogs or anything easily accessible that provide actual English translations of symbolic logic? If I could just read some straight-up translations it would be far easier for me to learn symbolic logic. I have some textbooks, but that's not what I'm looking for: I just want translations of sentences. (This was inspired by a reading of Alexander Pruss's "Incompatiblism Proved" of which I tried to paste an example sentence but was unable to do so).

More or less every textbook I can think of has many, many translations of symbolic sentences into English. Many, though by no means all, of the translations are in the exercises, and often you need to work from answer to question, but any good text will include lots and lots of examples. What I mean by "work from answer to question", by the way, is this: the more common kind of symbolization problem goes from English into symbols. The question will give you the English sentence, and the answer—often at the end of the chapter—will give the symbolic version. But if you look at the answer and trace it back to the question, you have just what you want. The question might ask you to put "No man is his own brother" into symbols. The answer might look like this:           ~∃x(Mx ∧ Bxx) But if you are given the answer and you know what question it answered, then you have your translation. Bear in mind that for this to work, you have to know what the letters stand for; that's often given in the question....

Is there a name for a logical fallacy where person A criticizes X, and person B fallaciously assumes that because A criticizes X he must therefore subscribe to position Y, the presumed opposition of X, although A does not, in fact, take that position? For example, if A criticizes a Republican policy then B assumes that A must be a Democrat and staunch Obama-supporter,even though A is in fact a Republican himself, or else an Undeclared who regularly criticizes Obama as well.

It seems to be a special case of a fallacy with many names: 'false dichotomy,' 'false dilemma,' 'black-and-white thinking' and 'either/or fallacy' are among the more common. When someone commits the fallacy of the false dichotomy, they overlook alternatives. Schematically, they assume that either X or Y must be true, and therefore that if X is false, Y must be true. The fallacy is in failing to notice that X and Y aren't the only alternatives. Your example makes the point. You've imagined someone assuming that either I accept a particular Republican policy X or I am a Democrat, when -- as you point out -- there are other possibilities. The situation you describe is a little more specific: the fallacious reasoner is making an inference from what someone is prepared to criticize. As far as I know, there's no special name for this special case, but the mistake is the same: overlooking relevant alternatives.

If the sentence "q because p" is true, must the sentence "If p then q" also be true? For example, "the streets are wet because it is raining," and the sentence "if it is raining, then the streets are wet." Are there any counter-examples where "q because p" could be true while "If p then q" could be false?

I agree with my co-panelist: "q because p" implies that "q" and "p" are both true. And on more than one reading of "if.. then" sentences, it will follow that "if p than q" as well as "if q then p" are true. It may be worth noting, though: not everyone agrees that when "p" and "q" are both true, so are "if p then q" and "if q then p." There's a different sort of point that may be relevant to your worry. Suppose Peter's smoking caused his emphysema. We can't conclude that if Petra smokes, she'll develop emphysema. Causes needn't be fail-proof. A bit more formally: Qa because Pa (which says, more or less that a has property Q because a has property P) doesn't allow us to conclude ∀x(If Px then Qx) (that is, for every thing x, if x has property P then x has property Q.) The truth of a "because" statement doesn't require the truth of a generalized "if...then" statement.

Is there a logical explanation for why one ought to be altruistic? Someone tried to logically prove to me why one ought to be altruistic. I found a list of logical fallacies here http://en.wikipedia.org/wiki/List_of_fallacies and I'd like to know which one's apply to what he wrote. This is what he wrote... "You should be altruistic because in the long run it will be beneficial not only to society, but also to yourself. Being altruistic fosters and encourages a society in which people help those in need of help, which ultimately means you will be helped when you need it. Conversely, altruism also encourages a society where negative acts against others are discouraged, meaning for yourself that you are less likely to be attacked, stolen from, killed, raped, etc. On the evolutionary level it means that a society that protects and helps each other, and does not ransack his fellow man whenever he deems it beneficial to himself in the short run, has a greater chance of survival, both for the group as a...

There are lots of questions we can ask about this argument, but I'd suggest that trying to shoehorn the issues into specific named fallacies isn't as helpful as just looking for places where the argument raises questions.. (It's interesting that in my experience, at least, philosophers invoke the names of fallacies only slightly more often than the average educated person does.) That said, here are a couple of quick thoughts. The first sentence offers two broad reasons for being altruistic: because in the long run it benefits both society and yourself. Take the first bit: if someone didn't already think they should be altruistic, how persuasive would they find being told "You should be altruistic because it benefits society"? If you want to turn to fallacy lists, is this a case of begging the question? (Don't be too quick just to answer yes. Think about the ways in which wanting to benefit society and acting altruistically might differ.) Turning to the next reason, is it incoherent to think someone...

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