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Is the positing of an infinite regress a legitimate explanation in philosophy

Is the positing of an infinite regress a legitimate explanation in philosophy respectively are infinite regresses logically possible?

Are infinite regresses logically possible?

Surely it's logically possible for infinitely many positive or negative integers to exist, and they represent a kind of infinite regress: for every negative integer, there's a smaller one; for every positive integer, there's a larger one. Even those who say that only potentially infinite collections (and not actually infinite collections) are possible must admit the possibility of infinite regresses of this numerical kind.

Is the positing of an infinite regress a legitimate explanation in philosophy?

I don't see why it couldn't be. It seems to me that the burden rests with whoever denies the acceptability of an infinite regress of explanations. Indeed, I think infinite regresses of explanations are unavoidable given some highly plausible assumptions.

How does one determine which side in an argument must shoulder the burden of

How does one determine which side in an argument must shoulder the burden of proof?

The other guy has the burden of proof. And yes, I'm serious. It's that bad.

But, to elaborate a little bit, I despise burden of proof type arguments. I do not know of any reasonable way of telling who "ought" to have the burden of proof, and I'm not sure I understand what is supposed to follow from someone's having it. People often end arguments saying something like, "Since they have the burden of proof and haven't met it, it is reasonable for us to believe my view". But this seems to me an odd way of thinking about philosophy.

I mean, I do hope that some of the philosophical views I hold will have some influence and help us understand certain sorts of things better than we do. But whether any of my views might actually be true I very much doubt. And the fact that the other guy hasn't been able to knock my view down doesn't seem like good reason to believe it, even if my view is more common-sensical than his (a common test). Philosophy seems to me to be much more a hunt for understanding than it is one for truth, and I'm not sure "burden of proof" has much to do with understanding.

A very common retort when critizising somebody for a reprehensible action (like

A very common retort when critizising somebody for a reprehensible action (like selling drugs) is that "If I don't do it, somebody else will". Does this kind of bad reasoning fall into any of the classical categories of argument fallacies?

I could be wrong, but I am not aware of a formal or informal term that gets at precisely that defense of reprehensible action, but one could see it as what may informally be called a Red Herring or a case of what may be called "Two Wrongs Make a Right." Arguably whether one person's act is unethical does not rest on the grounds that if the person did not do something wrong, another person would do the wrong act. The actions of others is thus irrelevant or distracting, as in a Red Herring. This might be slightly qualified, however, when the wrongful acts of others may make it excessively dangerous for one to obey the law. Imagine that you are on a highway in which all the cars around you are exceeding the speed limit by 30mph, and that if you were to drive the prescribed speed limit, you would endanger your own life and those of others. In terms of drugs, I believe it is illegal for you to sell or give a drug that has been prescribed for you to another person. Imagine you are seated next to a person on a plane who is gripped by a terrifying fear of flying. The person next to him is about to sell him some illegal narcotics that will indeed calm his fears but it will also mean that the money goes to a drug cartel known to be responsible for the deaths of hundreds of innocent persons. You, on the other hand, can give or sell him some of your safe and efficient anti-anxiety medicine. If there is no other course of action and you gave him your drugs and a flight attendant asked why you did it, I can see offering the reply "If I hadn't do it, that passenger would have contributed to a nasty, murderous drug cartel.

I am confused about how a conditional statement is necessarily true, and not

I am confused about how a conditional statement is necessarily true, and not false or unknown, when the antecedent and consequent are both false. According to the truth table, the sentence "If Bill Clinton is Cambodian, then George Bush is Angolan" is true. How can such an absurd sentence be true? It seems initially like the sentence could just as easily, or more easily, be false or unknown.

The truth-table for the material conditional says that any material conditional with a false antecedent is true. If we construe the conditional you gave as a material conditional, then (because it has a false antecedent) it comes out true. But the material conditional doesn't come out necessarily true unless it's not just false but impossible that Clinton is Cambodian (or else it's necessarily true that Bush is Angolan).

The material conditional has the advantage of being tidy, and a true material conditional will never let you infer a falsehood from a truth. Still, for the reason you gave (and for other reasons too) many philosophers say that the material conditional does a bad job of translating the conditionals we assert in everyday language. You'll find lots more information in this excellent SEP entry.

I am learning about the principle of noncontradiction ~(p^~p). I can see that

I am learning about the principle of noncontradiction ~(p^~p). I can see that this would work if we assume that 'p' can only be true or false. Why should I make this assumption. I can see a lot instances where we need more than 2 truth values (how people feel about the temperature of a room, for instance could have an infinite number of responses, and all would be true because the proposition is based on subjective experiences). What is this type of logic called? If this is a possible logic then can't someone argue that everything is this way?

Your example about the room temperature doesn't seem to support the idea that we need more than two truth-values, because you classify everyone's responses as true. Instead, the example raises the question of how to interpret the people in the room: as disagreeing with each other because they're making incompatible claims ("It's cold"; "It's not cold") or as only apparently disagreeing with each other because they're making compatible claims ("It feels cold to me"; "OK, but it doesn't feel cold to me").

Standard logic (often called "classical" logic) has just two truth-values. Many-valued logics are nonstandard logics that contain anywhere from three to infinitely many truth-values -- in the latter case, all of the real numbers in the closed interval [0,1], with '0' for 'completely false' and '1' for 'completely true'. You'll find lots of detailed information in this SEP entry.

I know affirming the consequent is a fallacy, so that any argument with that

I know affirming the consequent is a fallacy, so that any argument with that pattern is invalid. But what what about analytically true premises, or causal premises? Are these not really instances of the fallacy? They seem to take its form, but they don't seem wrong. For example: 1. If John is a bachelor, he is an unmarried man. 2. John’s an unmarried man. 3. Therefore he’s a bachelor. How can 1 and 2 be true, and 3 be false? Yet it looks like affirming the consequent. 1. X is needed to cause Y. 2. We’ve got Y. 3. Therefore there must have been X. Again, it seems like the truth of 1 and 2 guarantee the truth of 3. What am I missing?

You asked, "How can 1 and 2 be true, and 3 be false?" Suppose that John is divorced and not remarried; he'd be unmarried but not a bachelor. You can patch up the argument by changing (1) to (1*) "If John is a bachelor, he is a never-married man" and changing (2) to (2*) "John is a never-married man." The argument still wouldn't be formally valid, which is the sense of "valid" that Prof. George uses in his reply. But it would be valid in that the premises couldn't be true unless the conclusion were true, because (2*) by itself implies that John is a bachelor. An argument that isn't formally valid -- i.e., an argument whose form alone doesn't guarantee its validity -- can be valid in the sense that the truth of its premises guarantees the truth of its conclusion.

The last sentence of Prof. George's reply suggests that definitions are crucial in enabling conclusions to follow from premises. I think that suggestion is true only if logical implication is a relation holding between items of language such as sentences rather than (as I prefer to say) a relation holding between non-linguistic propositions. The proposition that my car is red implies the proposition that my car exists, and the implication holds regardless of how we define words.

How, if at all, is the following paradox resolved?

How, if at all, is the following paradox resolved? You hand someone a card. On one side is printed "The statement on the other side of this card is true." On the other side is printed, "The statement on the other side of this card is false." Thanks for consideration!

You've asked about one version of an ancient paradox called the "Liar paradox" or the "Epimenides paradox." One good place to start looking, then, is the SEP entry on the Liar paradox, available here. Philosophers are all over the map on how to solve paradoxes of this kind, and their proposed solutions are sometimes awfully complicated! Best of luck.

Here's a quote from Hume: "Nothing, that is distinctly conceivable, implies a

Here's a quote from Hume: "Nothing, that is distinctly conceivable, implies a contradiction." My question is this: what is the difference between something that is logically a contradiction and something that happens to not be instantiated? For example, ghosts do not exist. Could you explain how the concept of a ghost is not a contradiction? Thanks ^^

What is the difference between something that is logically a contradiction and something that happens to not be instantiated?

As I think you already suspect, it's the difference between (1) a concept whose instantiation is contrary to the laws of logic or contrary to the logical relations that obtain among concepts; and (2) a concept whose instantiation isn't contrary to logic but only contrary to fact. Examples of (1) include the concepts colorless red object and quadrilateral triangle. Examples of (2) include the concept child of Elizabeth I of England. Concepts of type (1) are unsatisfiable in the strongest sense; concepts of type (2) are merely unsatisfied.

Could you explain how the concept of a ghost is not a contradiction?

Good question. I'm not sure the concept isn't internally contradictory. Can ghosts, by their very nature, interact with matter? Some stories seem to want to answer yes and no. If I recall correctly (it's been a while) the movie Ghost (1990) depicts the rookie ghost struggling to interact with matter well enough to move just a penny, despite the fact that he has no trouble standing on the floor rather than passing right through it. It's as if he can interact with matter only when he's not consciously trying to. I seem to recall that Field of Dreams (1989) has similar inconsistencies. But it may be that both movies can be interpreted as internally consistent if we import enough ad hoc principles of ghostly metaphysics.

Is it true that anything can be concluded from a contradiction? Can you explain?

Is it true that anything can be concluded from a contradiction? Can you explain? It's seems like its a tautology if taken figuratively because we can indeed conclude anything if we suspend the rules of reasoning, but there is nothing especially interesting in that fact in my humble opinion.

Stephen Maitzen has given a syntactic response, showing how formal rules of logic can be used to derive any conclusion Q from a contradiction P & not-P. It might be worthwhile to point out that one can also give a semantic explanation of why Q follows from P & not-P--that is, an explanation based on the truth or falsity of the premise and conclusion, rather than on rules for manipulating logical symbols.

The semantic definition of logical consequence is this: We say that a conclusion follows from a collection of premises if, in every situation in which the premises are all true, the conclusion is also true. To put it another way: the conclusion fails to follow from the premises if (and only if) there is some situation in which all the premises are true, but the conclusion is false. For example, the conclusion "It is snowing" does not follow from the premise "It is either raining or snowing," because there is a situation in which the premise is true but the conclusion is false--namely, if it is raining.

Now, let's apply this definition to Stephen's example. The only way that the conclusion Q could fail to follow from the premise P & not-P is if there is some situation in which P & not-P is true but Q is false. But there is no such situation, for the simple reason that there is no situation in which P & not-P is true. So the conclusion Q does follow from the premise P & not-P, according to the semantic definition of logical consequence.

By the way, in your question you suggest that this kind of reasoning involves some sort of suspension of the rules of reasoning. But that is not true. The point of Stephen's response is to show that according to the rules of reasoning, Q follows from P & not-P. No rules of reasoning have been suspended or changed in any way. Similarly, the point of my explanation is to show that according to the usual semantic definition of logical consequence, Q is a consequence of P & not-P.

If the sentence "q because p" is true, must the sentence "If p then q" also be

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.

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