We use logic to structure the system of mathematics. Lord Russell was described as bewildered upon learning that original premises must be accepted on some human's "say so". Since human knowledge is so fragile (it cannot have all conclusions backed up by premises), is the final justification "It works, based on axioms accepted on faith"? In short, where do you recommend that "evidence for evidence" might be found, if such exists in the anterior phases of syllogistic construction. Somewhere I have read (if I can rely upon what little recall I still have) Lord Russell, even to the end, did not desire to rely on inductive reasoning to advance knowledge, preferring to rely on deductive reasoning. Thanks. Your individual and panel contributions make our world better.

I was intrigued that you take human knowledge to be very fragile. The reason you gave was that there's no way for all conclusions to be backed by premises, which I take to be a way of saying that not all of the things we take ourselves to be know can be based on reasoning from other things we take ourselves to know- at least, not if we rule out infinite regresses and circles. But why should that fact of logic (for that's what it seems to be) amount to a reason to think that knowledge is fragile? Most of us - including most philosophers and even most epistemologists - take it for granted that we know a great deal. I know that I just ate lunch; you know that there are people who write answers to questions on askphilosophers.org. More or less all of us know that there are trees and rocks and that 1+1 = 2 and that cheap wine can give you a headache. Some of the things we know call for complicated justifications; others don't call for anything other than what we see when we open our eyes or (as in the...

It seems that certain ethical theories are often criticized for contradiction ordinary ethical thinking, or common moral intuitions. Why should this matter, though? Is there a good reason to believe that ordinary common moral intuitions are infallible, and that more refined ethical systems ought not contradict such intuitions?

You're quite right: ordinary moral intuitions aren't infallible. However, the sort of criticisms you have in mind doesn't really suppose that they are. Start with an extreme case. Suppose someone came up with a moral theory with the consequence that most of our common moral beliefs were wrong. Now ask yourself: what sort of reason could we have to believe this moral theory? The point is that there's no possible way of making sense of this; perhaps there is. But if I'm told that my ordinary moral judgments are massively wrong, there would be a real problem about what sort of reason we could have to accept the very unintuitive theory from which that consequence flowed. Or take a more concrete example. Suppose some moral theory had the consequence that wanton cruelty toward innocent people was a good thing. I don't know about you, but I find it hard to imagine what could possibly make this moral theory more plausible than my ordinary moral belief that wanton cruelty is very wrong indeed. ...

I'm struggling wit the following: I am reading an essay that states (repeatedly) that the following "p, p implies q, therefore q" is valid but that the following: "I judge that p, I judge that p implies q, therefore I judge that q" is "obviously" invalid. There is no explanation; apparently this is supposed to be transparent but I fail to see why this is obviously invalid. Why adding "I judge that" makes it invalid?

One sure way to prove invalidity is to describe a possible case where the premises of an argument are true and the conclusion false. To make things a bit more plausible, let's change the example slightly. The following is valid: "q, not-p implies not-q, therefore p" I pick this example because this argument (closely related to modus ponens ) is one that people have a little more trouble seeing, or so my experience teaching logic suggests. So there could be and likely are cases where a person judges that q, and judges that not-p implies not-q, but has trouble with the logical leap and therefore fails to judge that p. That's a counterexample to the argument you're interested in. We have someone who judges the premises of a valid argument to be true but doesn't judge the conclusion to be true. This isn't surprising. To judge something is (putting it a bit crudely) to be in a certain state of mind toward it. Being in the "judges that" state of mind toward the premises of an...

Is it logical to infer a higher power given how extraordinary human life is?

It's a recurring question, and various versions of it make their way into arguments for God's existence. For the moment, I'll just raise one obvious worry (not original to me.) Let's agree that human life is extraordinary. If we assume that this calls for divine explanation, we run the risk of positing a being who is at least as extraordinary as we are, and therefore at least as much in need of explanation. But in that case, we seem either to be set upon an infinite regress or else it isn't clear that we had to take the first step in the first place. This hardly settle the question of whether there's a God (I'm taking that to be what you men by Higher Power.) But it does point out that some arguments for God's existence are too simple and too quick.

Fox "news," busily enjoining viewers to mock the idea of wealth redistribution, has posted a story entitled "College Students in Favor of Wealth Distribution Are Asked to Pass Their Grade Points to Other Students" http://www.foxnews.com/us/2011/08/17/college-students-in-favor-wealth-distribution-are-asked-to-support-grade/ Their ludicrous point is "if wealth is going to be redistributed, we should do the same with grades." Is this a "fallacy by false analogy?" If not, what would be the most succinct explanation to explain what's wrong with this comparison? Thanks, Tom K.

Thanks for a few moments of idle amusement! Perhaps the best response is "Oy!" But to earn the huge salary in Merely Possible Dollars that the site pays me, a bit more is called for. So yes: it's a case of false analogy, and the analogy goes bad in indefinitely many ways. But one of them has at least some intrinsic logical interest. Suppose that as a matter of social policy, we set up a system that left everyone with a paycheck of the same size at the end of every month. What does that amount to? It amounts to saying that each person can acquire the same quantity of goods as each other person. Maybe that would be a bad idea; maybe the result would be that people would get lazy and less wealth would end up getting produced overall. But that's not built into to very logic of the idea. It's an empirical claim, even if a highly plausible one. There's nothing logical incoherent, as it were, about a system intended to produce completely uniform distribution of wealth, whatever the practical...

I have been teaching philosophy for a year now, and the Paradox of the Stone has come up again and again, boggling my student and me later on. The standard answer is that God cannot create the stone since it would imply a contradiction, and these philosophers say that even God cannot do that. But if He is God, why can He not create a contradiction? Is there something wrong with accepting the conclusion that God can make 2+ 2 = 5, given that God is all-powerful? Or put it another way, why cannot the concept of omnipotence be the ability to do everything, even if that would imply a contradiction?

Voluntarists say just that: God can make contradictions true. And if someone is really prepared to say that contradictions might be true, it's not exactly clear -- to me, at least -- how to answer. But I'll confess that I've never understood the pull of this solution. Here's a way of getting at what bothers me. Suppose, to see if it could make sense, that there's an omnipotent God. (Our goal is to see if the concept is coherent; not whether it fits any actual thing.) Suppose we have a computer screen with 1280 x 720 pixels. (Let them simply be on or off; ignore color.) Suppose we ask God to turn a set of pixels on so that there's a circle on the screen. (We have to allow for a certain amount of approximation, but that won't affect the real point here.) God can easily do that. (So can anyone with a good Paint program.) Now suppose we ask God instead to arrange pixels so that there's an equilateral triangle on the screen. Once again, no difficulty. But now suppose we set God a third task: turn...

The "naturalistic fallacy" states that it is false to appeal to nature or naturalness in order to judge the goodness of something. Yet despite this being a fallacy, we see it crop up all the time in all spheres of life. Saying something isn't "natural" usually carries a negative connotation, and from foodstuffs to building materials to sexual practices, people use appeals to nature in order to condemn things. Since it seems appeals to nature are very popular, I wonder, is there a stream of thought that considers the naturalistic fallacy not to be a fallacy, but to be a proper form of argumentation? Are there philosophers or movements in philosophy which consider goodness to be clearly derivable from naturalness?

First, just a terminological point. The phrase "naturalistic fallacy" is usually used to mean the supposed fallacy of defining a moral term such as "good" in terms of non-moral properties. For example, if someone said that "good" means "produces happiness," they would be accused of committing the naturalistic fallacy. (Note, by that way, that even if "good" doesn't mean "produces happiness," it could still turn out that producing happiness is a genuine good.) The worry you have is of a different sort: deciding whether something is right or wrong by deciding whether it's "natural." The most familiar case is probably homosexuality, which is sometimes said to be wrong because homosexuality isn't "natural." You're right to be suspicious of that sort of reasoning. One problem is that what we see as "natural" is often not a matter of how things are in "nature" but of what we're used to. People have claimed that it's "unnatural" for women to perform certain jobs or for people of different...

Hi, I'm a German student in physics. something i noticed is that in every theory we start with a few postulates and conclude predictions about the behaviour of uninlevend objects. Even in quantum- mechanics we can make declarations about things our mind can't even imagine (like electrons). We do all this with math or let's say logic. and here is my question. Why does the universe behave in a logical way? is logic something humans have learned from the universe and only exists in this universe or is logic something that would exist even if this universe wouldn 't exist? Greetings Tobias D. and excuse my bad grammar

There are several questions in what you've asked, all of them interesting. I'm going to single out one of them. If I read you correctly, one thing you're asking is why we can describe the universe using math and logic -- why the universe "fits" our rules of math and logic. We can begin our stab at an answer by noticing that this fact -- that the universe can be described using math and logic -- is weaker than it might seem. Imagine a computer screen of 1024 by 768 pixels, for a total of 786,432 pixels. For simplicity, imagine that each pixel is simply ether off or on; ignore color. Then there are 2 786,432 possible patterns that could show up on the screen. Most of those are a jumble -- not "logical" or orderly in any interesting way. However, each can, in principle, be described. An exhaustive list stating for each pixel whether it's off or on would do. So the fact that the screen can be described using math/logic doesn't really constrain things much at all. Some number of pixels will be on...

Do all things exist? Nonexistence is the absence of existence, by definition. So, nonexistence does not exist. Therefore there is no such thing as nonexistence. To say that something does not exist thus seems to be a fallacy, since NOTHING does not exist. Everything, therefore, must exist. Is this right? If not, what is wrong with the argument?

Of course, in a perfectly good sense of "exist", existence doesn't exist either. Existence isn't a thing, and so there is no such thing as existence, though of course, bears, bells and BMWs exist, to mention but a few. And yes: there is no such thing as non-existence, because "non-existence" isn't way of referring to a thing. But unicorns don't exist. Neither do square circles. And, according to some, neither do free lunches. No fallacy there. Does everything exist? Well, if "everything" means "all the things that exist," then everything exists. (Though of course, this doesn't mean that there is a special thing, namely everything , that exists.) But since, as noted, unicorns don't exist, it's not true that "everything" in the sense of "everything that might have existed" actually exists. It's likewise not true that that every description (e.g., "round square") picks out something that exists. The conclusion of the argument comes partly from trading on ambiguity. Related: ...

Do false statements imply contradictions? Consider the truth table for logical implication. P...........Q.............P-> Q T...........T.............. T T...........F...............F F...........T...............T F...........F...............T Notice that for a false statement P, the last two rows of the truth table, both Q and ~Q follow. No matter what Q is, it's truth follows from false statement P, as the third row shows. We can therefore take Q to be "P is true." From here it follows that a false statement P implies it's own truth, as the third row shows. Do false statements really imply their own truth? Do they really imply contradictions? Are false statements also true?

Imagine that someone finds it useful to define a new term -- "mimp," say. The newly-defined term is a conjunction, i.e., it's used to link sentences together, and it works this way: "P mimp Q" is false when "P" is true and "Q" is false. Otherwise it's true. With this definition in hand, consider the sentence "New York city has fewer than 150,000 resident mimp the next US president will come from New York." Give our definition, this is true. Our definition of "mimp" guarantees that whenever "P" is false, "P mimp Q" is true. Looking at "→" this way may help with your puzzle. The symbol "→" (alternatively "⊃" ) is one that logicians found useful to define, and its definition is given by the rule above. Whether it matches any connective in natural language is open to doubt, and in particular, it does not mean what we mean by the phrase "logically implies." After all, "New York City has fewer than 150,000 residents" does not logically imply that the next US President will be from New York. It...

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