## If there could be a counter-argument against a premise, does that make the

If there could be a counter-argument against a premise, does that make the premise false and the argument unsound?

### The mere possibility of a

No. The mere possibility of a counter-argument (i.e., "there could be a counter-argument") doesn't imply that the premise is false or that an argument containing the premise is unsound. The counter-argument itself must have a true conclusion in order to guarantee that the premise against which it's a counter-argument is false.

Every sound argument has a true conclusion (although the converse doesn't hold), so if there exists a sound argument against a particular premise, then the particular premise is false. Often, however, the very soundness of that counter-argument will be a matter of controversy.

## An elementary precept of logic says that where there are two propositions, P and

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

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 possibilities: P&~Q, ~P&Q, and ~P&~Q. The fourth case, P&Q, isn't possible.

Or P and Q might be subcontraries, meaning that they can both be true, but can't both be false. For example: if P is "Paula is under 6 feet tall" and Q is "Paula is over 5 feet tall," then the only possibilities are P&Q, P&~Q and ~P and Q. ~P&~Q isn't possible.

Or P might imply Q. If P is "Paula is over 6 feet tall" and Q is "Paula is over 5 feet tall," then the possibilities are P&Q, ~P&Q, and ~P&~Q. Here, P&~Q isn't possible.

Finally, P and Q might be equivalent. Suppose P is "The temperature is 32 degrees Fahrenheit" and Q is "The temperature is 0 degrees Celsius." In that case, P and Q are in effect the same proposition, expressed by different sentences. They are either both true or both false, leaving P&Q and ~P&~Q as the only possibilities.

All of this applies across the board, and in particular it applies in philosophy. Not all philosophical claims are independent, and so for some philosophical propositions, one or more of the four combinations won't represent possibilities. But at least some philosophical disputes are over the very question of what the logical relationship between two claims actually is. For example: consider "Paula's behavior is determined" and "Paula is responsible for her behavior." One important view is that these are contraries; they can't both be true. Other philosophers deny this, claiming, for example, that responsibility entails determinism, in which case "Paula is responsible, and her behavior is not determined" doesn't represent a genuine possibility. Other philosophers would claim that the two are independent, and so all four combinations represent genuine possibilities.

This kind of disagreement about the logical relations among philosophical claims is common in philosophy. But the larger point is that we can't simply assume in all cases that all four combinations represent genuine possibilities.

## I'm having a difficult time determining if a certain math problem should be

I'm having a difficult time determining if a certain math problem should be classified as using Formal or Informal Logic. Here it is: 1. ALL except 2 of my pets are dogs. 2. ALL except 2 of my pets are cats. 3. ALL except 2 of my pets are birds. Q: How many pets do I own? A: 2 or 3 So, while it's obvious why the answer could be 3, it's not obvious how it could be 2 as well. The reason why is because the phrase "All" could be zero, which would represent an empty set. And, of course, I could own pets other than the ones mentioned (fish / lizards). So, knowing that, we can substitute that example back into the original problem as follows: I own two, pets, which are both fish. All except 2 of my pets are dogs, which in this case, is equal to zero. So, the set of dogs can possibly be an empty set. So, anyways, I was wanting to know if the puzzle itself could be considered "formal", or is it informal because most people would mean "All" to at least equal one, and we add that assumption in there?

I interpret you as asking this: Why do we find it puzzling or counterintuitive that statements 1–3 are true in the case in which you own exactly two pets, neither of which is a dog, a cat, or a bird? Is it because we assume that "all" implies "at least one"?

Those are empirical, psychological questions whose answers I don't know. But I do think it's worth distinguishing between what "all" logically implies and what "all" conversationally implies. (You might have a look at the SEP entry on implicature.)

On the one hand, the statement "All intelligent extraterrestrials are extraterrestrials" had better be true, and its truth had better not depend on the existence of intelligent extraterrestrials. So I think there's good reason to deny that "all" logically implies "at least one."

On the other hand, someone who owns no dogs and who says "All my dogs have their shots" has said something odd or misleading, even if true. So I think there's good reason to say that, at least sometimes, "all" conversationally implies "at least one."

## On April 10, 2014, in response to a question, Stephen Maitzen wrote: "I can't

On April 10, 2014, in response to a question, Stephen Maitzen wrote: "I can't see how there could be any law more fundamental than the law of non-contradiction (LNC)." I thought that there were entire logical systems developed in which the law of non-contradiction was assumed not to be valid, and it also seems like "real life" suggests that the law of non-contradiction does not necessarily apply to physical systems. Perhaps I am not understanding the law correctly? Is it that at most one of these statements is true? Either "P is true" or "P is not true"? or is it that at most one of theses statements is true? Either "P is true" or "~P is true"? In physics, if you take filters that polarize light, and place two at right angles to each other, no light gets through. Yet if you take a third filter at a 45 degree angle to the first two, and insert it between the two existing filters, then some light gets through. Based on this experiment, it seems like the law of non-contradiction cannot be true in...

### Because the present

Because the present questioner refers to my reply to Question 5536, I'll chime in here to clarify what I said there.

My point was about the fundamentality of LNC. I wrote, "I can't see how there could be any law more fundamental than the law of non-contradiction (LNC)." I gave the following reason: "Let F be any such law. If the claim 'F is more fundamental than LNC' is meaningful (and it may not be), then it conflicts with the claim 'F isn't more fundamental than LNC' -- but that reasoning, of course, depends on LNC." So that's why no law could be more fundamental than LNC, because LNC would need to be true before (in the sense of logical priority) the claim that some other law is more fundamental would even make sense.

If someone can make sense of the claim that some law is more fundamental than LNC, I'm all ears.

## I'm still puzzled by the answers to question 5792, on whether it is true that

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, then that's true. No game is a game she played and lost because no game is a game she played.

It turns out that avoiding this conclusion isn't as easy as it might seem. We usually agree that "No X are Y" and "No Y are X" amount to the same thing. We can also agree that no animals are unicorns, because there aren't any unicorns at all. But if no animals are unicorns, then the principle we just noted entails that no unicorns are animals. which is already starting to sound awkward. Worse, we also usually agree that "No X are Y" amounts to "All X are non-Y," and so we get "All unicorns are non-animals."

There are approaches to logic that find ways around this sort of thing. But the carpet will have to bulge somewhere. Either the rules of inference will be a bit more complicated or we'll have to give up principles that seem appealing or we'll end up with some cases of "correct" inferences that seem peculiar. Different people will see the costs and benefits differently. My own view, which would not win me friends in certain circles, is that there's nothing deeply deep here. But not everyone agrees.

## Are there any books or videos or blogs or anything easily accessible that

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. There are many English sentences that have the same logical form, and therefore look similar or the same when translated into symbols. Notice that our symbolic sentence above could equally well be a way to say "No moose is bigger than itself."

That said, two further comments. The first is that you will get much better at reading the symbols if you spend a lot of time working in the usual order: going from English into symbols. Second, philosophy went through a patch where it was way too quick to use symbols, often without actually making things any clearer.

## Suppose I have never played a game of chess. If I now make the claim that I've

Suppose I have never played a game of chess. If I now make the claim that I've won all the games of chess I've ever played, is that claim true, false, or undefined? A group of friends had an argument over this, and I figured that philosophers are deeply logical thinkers that can give us the answer and also to get a proper understanding of why the answer is what it is.

It would, of course, be equally true that you've lost every game of chess you've ever played. Bad news to go with the good.

## So I'm reading The Power of Logic, 4th edition. While on a section describing

So I'm reading The Power of Logic, 4th edition. While on a section describing Modus Tollen it says that, Not A; If A, then B; So, Not B is an example of Modus Tollen. My question is how can that be if the conclusion of Modus Tollens is suppose to deny the consequent? Am i reading it wrong or just missing something? Keep in mine im still not beyond chapter 1.

There is either a typo in the book you are reading, or else you reported its contents wrong. Modus tollens is: If A, then B; not-B; so not-A. The version you reported is fallacious. It's a version of the fallacy of asserting the consequent.

## I'm developing a rebuttal to Biblical literalists and I'd like to know whether

I'm developing a rebuttal to Biblical literalists and I'd like to know whether the following is a recognized/named type of syllogism or other type of argument (and if so, what it's called): Verse X prophesied that would happen happened in verse Y Therefore, the prophecy was fulfilled (If this is not a recognized/named type of syllogism or other type of argument, could it be made so by adding one or two lines?)

This is still a little confusing to me, but I take it that you may be looking for the term:

Vaticinium ex eventu

This occurs when a writer (whether Biblical or not) offers a prophecy that some event will occur when (it is assumed) that the writer already knows the event has taken place. In the context of the Bible, perhaps the most salient case that is the subject of controversy is the New Testament recording of Jesus predicting that the Temple will be destroyed, which it was some forty years after his death. It is not obvious, though, whether this is a case of writing ex eventu. It is possible that Jesus could have foreseen the destruction of the Temple, especially when you consider the evidence available during Jesus' lifetime of how Rome responds to rebellion and recent past cases of Jewish resistance to Roman imperial power.

This is more a matter of history, than philosophy per se, though philosophers have long had an interest in thinking about the miraculous and whether it can ever be reasonable to believe in miracles. See the Stanford Encyclopedia of Philosophy on Hume and the entry Philosophy of Religion.

## What's the difference between understanding an opponent's argument, and agreeing

What's the difference between understanding an opponent's argument, and agreeing with it? What prevents me from saying that if my opponent disagrees with my argument, he must misunderstand it?

Nothing prevents you from saying that, but then nothing prevents you from being wrong when you say it. If your argument is deductive, you might make progress by asking your opponent which (if any) premise in your argument he/she finds implausible and which (if any) inference in your argument he/she finds invalid. If your opponent rejects your conclusion, try finding out why he/she doesn't regard your argument as persuasive support for your conclusion.