# Frequently, one finds the following statment: "You cannot prove a negative." My question is, in this context, what is meant by the word "negative?" I understand how the word is used in mathematics and I "think" I know the meaning when used in logic. I just cannot seem to get a handle on how it is used here. Moreover, does it, perhaps, refer to a total position in the debate over the existence of God? Any comments you would make would be greatly appreciate. I enjoy your application very much and, moreso, since I am so old. Thanks. JH

This is a pretty confusing expression. What's usually meant, I think, is that a negative general proposition -- a proposition asserting that a certain kind never occurs -- requires much more by way of justification from its defender than from its opponent. Take the proposition "there are no black swans," for example. To prove it, you would have to comb through the whole universe, presumably all the way backward and forward in time, to demonstrate conclusively that nothing contained therein is a black swan. To disprove the proposition, by contrast, all you need do is produce a single black swan. Given this asymmetry, it thus makes sense to saddle the opponent, rather than the proponent, of a negative general proposition with the burden of proof. What's confusing here is that the same sort of asymmetry is present with affirmative general propositions as well. Thus the proposition "all elks like mushrooms" requires much more by way of justification from its defender than from its opponent. To...

# Hi, I would like to ask a question about Logic. There is a formal logical fallacy called "Circular Reasoning", are not all argument tho circular? The conclusion is always found in the premises. and then drawn from them into a conclusion.

Drawing conclusions from premises is not circular. You are going in one direction, from the premises to the conclusion. Circularity appears when you also defend your premises by appeal to the conclusion. To illustrate with a somewhat informal but real-world typical example: P1: The government of country A is hell-bent on territorial expansion P2: The government of country A is expanding its military capabilities C: The government of country A is threatening its weaker neighbors. There's nothing circular here, the argument displays a relationship between two premises and one conclusion: the premises, if true, together support the conclusion. To explore whether they are true, and thus actually support the conclusion, we need to examine what evidence can be adduced in their support. Suppose P2 is uncontroversially true so that attention turns to P1. We ask the presenter of the argument how she can support P1. Is A's government really hell-bent on territorial expansion? Suppose she...

# Is there not something disingenuous and disrespectful in claiming that an opponent's views are not sincere or belonging to themselves, but rather unconsciously motivated by psychological insecurities, social power dynamics and ideology?

There is something disrespectful about such a claim alright: one is not engaging with the opponent's expressed view on its merits but is dismissing this view as not based on conscientious, reliable reflection. But then such a claim may be true: some people do indeed hold views that are unconsciously motivated by the kind of factors you mention. In any case, one may conscientiously reach the conclusion that another's view is so motivated, and stating such a conclusion may not then be disingenuous.

# There's a logical scenario which often comes up in discussions around the question of voting. We all know the conversation... Person 1: I don't vote because my vote has no impact on the outcome of the election. Person 2: Not on it's OWN it doesn't, but if everyone thought that, no one would vote, and THEN what would happen?! Person 1: But I don't decide whether all those other people vote, I only have control of my 1 vote! My question here relates not to whether or not one should or shouldn't vote, or to the voting example alone, but rather to the logic of this situation. For this example let us assume (for the sake of the point I am interested in) that it is universally agreed that all people (including Person 1 and 2) agree that nobody voting is an outcome that everyone wishes to avoid. And also assume (despite the conversation above!) that everyone decides privately whether to vote or not, such that their decision cannot influence others decisions) Finally assume that the election involved has...

I don't think there's a named fallacy here, but I do think the principle proposed by Person 2 is unsound. If this principle were sound, then it would be impermissible to remain childless even in a world as overpopulated as ours. The principle can be revised to be more plausible. When many people in some group are making a morally motivated effort to achieve a certain good that would not exist (or to avert a certain harm that would not be averted) without their effort, then one has moral reason to do one's fair share if one is a member of this group. This sort of principle against free-riding on the moral efforts of others can explain why one should generally vote and do so conscientiously -- at least unless one has conclusive reason to judge that enough others are already acting and that one's own effort will therefore add nothing to the outcome. But there is also a more direct explanation of why one ought to vote. As philosopher Derek Parfit has argued, the extremely low probability of one...

# No matter whether one adopts a deontological or consequentialist account of ethics it is apparent that there exists a moral imperative to prevent genocide. To what extent and to what cost this imperative must motivate our actions is, I suppose, a subject of serious debate, however. But how can we define genocide? Surely we can all agree that the murder of 10,000,000 people constitutes genocide. But what if we subtract one fatality? Still genocide, of course. Minus one more? The same is still true. But at some point that logic fails; when we get down to the death of one, a few, or no people we certainly no longer have a case of genocide on our hands. It seems there is a sorites paradox here. If the number of people killed is ultimately arbitrary, how is the concept of genocide meaningful? Surely we can still find moral value in the deaths of millions (or even in the death of an individual), but it seems the label in itself is ultimately kind of subjective and meaningless.

The number of victims is not the only consideration entering into the judgments of whether a genocide is taking place. Other relevant factors are the nature and size of the victim group and the motivations and intentions of the perpetrators. Still, we can hold these other factors fixed and ask your question again, for example: hypothetically lowering the number of people killed, maimed, raped, and otherwise brutalized in the Rwanda genocide, when do we reach the point at which the genocide label would no longer be applicable? Or: at what time, in those horrible months of early 1994, did the daily decision of the world's leading governments not to intervene become a decision to ignore a genocide? You're right that there is some vagueness here. But this does not render the term meaningless. As Wittgenstein writes, there may be some unclarity about where exactly the boundary lies between two countries -- say between China and Russia -- but this does not entail that it's unclear on which side Beijing or...

# Theist: We should follow the Bible, and the Bible says that there is a God. Atheist: Why should we follow the Bible? Theist: Because the Bible says we should. Atheist: That’s circular reasoning. But then the Atheist says: We shouldn’t believe in God. Here’s logic to show he doesn't exist. Me: Why should we follow logic? Atheist: We’ve come to the conclusion that logic, and not the Bible, is right by using logic. Me: Is this not also circular reasoning? Someone please tell me why I’m wrong. Also, if I just disproved the validity of logic but used logic to disprove it, does that mean my argument is no longer valid because it’s based on logic, which is no longer valid. But if my claim is no longer valid that disproved logic, does that mean that logic is ok now. But then, that would mean that my argument is still ok, which means that… I think you get the idea. Someone please tell me why I’m wrong before my head explodes.

Fair enough, you cannot support logic by appeal to logic. But this does not disprove logic. It just shows that one attempt to justify logic is unsuccessful. How then do we justify logic, or the Bible for that matter? You seem to think of justification as starting with nothing -- and then it's indeed hard to see how anything can ever be justified. But in real life, when we justify, or question, something we always take other things for granted: other beliefs, modes of inquiry, methods of reasoning, and so on. Each of them can be questioned too, of course, but we cannot question all of them together at once. Nothing justifies our thinking as a whole, though every part of it can be justified (or disqualified) by its fit (or incoherence) with the rest. If logic (or the Bible) makes sense to you and helps you make sense of the world, then you have a good justification for continuing to rely on it. If you find incoherence in logic, or between logic and something else you have been relying on, then you need...

# Are there as many true propositions as false ones? More of one than the other?

Professor George's conclusion is probably true, but the reasoning seems to me invalid. This is so, because the two "pairing" operations produce different pairs. For example, the first operation might create the pair <"Bush is married"; "it is not the case that Bush is married">. The second operation might create the pair <"it is not the case that Bush is married"; "it is not the case that it is not the case that Bush is married">. The first operation finds one unique false claim for every true one -- but some false claims are left over (for example, "3+3=9") . The second operation finds one unique true claim for every false one -- but some true claims are left over (for example, "3+3=6"). Therefore, the argument works only if it can be shown that the two sets of "left-over" claims are equal in number of members. One might try to avoid this problem by redefining Professor George's operations so that any claim that begins with an odd number of iterations of "it is not that case that" gets paired with...

# Logically what is the difference between conceivable and probable or possible?

The common domain these three predicates range over is that of states of affairs consisting of objects that have certain specific properties or stand in certain specific relations. Being conceivable is the easiest condition to meet. It excludes only states of affairs that we cannot think or imagine. We cannot imagine a stone that is green all over and also red all over, a stone that occupies the same space as a clump of metal, a bachelor who is married, a living horse that's not an animal, and so on. While there is a narrow sense of "possible" that coincides with "conceivable," usually being possible is a more demanding condition. To be possible, a state of affairs must not merely be conceivable, but must be consistent with what we know about this world (e.g., the laws of nature). A puddle of water turning into a human being, an animal living forever, a daytrip to another galaxy -- these are conceivable, but not possible. Being probable is more demanding still, requiring not merely that states of...

# Dialetheist: "Some contradictions are true." My question: "Who claims (if any), that some tautologies are false?"

In colloquial speech there are some apparent tautologies that are used to make a substantive point that can be disputed. There is the famous Yogi Berra saying "it's not over till it's over" used to make the (disputable) claim that the team behind can still catch up. And there is "boys are boys" expressing the (very disputable) claim that its pointless to work toward decent behavior by men in matters sexual.

# Referring to propositional logic conditionals, if we say that an antecedent A is a necessary and sufficient condition for consequent B, can we say that A caused B?

No. That A is a necessary condition for B means that B presupposes A, that B cannot hold without A also holding. That A is a sufficient condition for B means that A implies B, that A cannot hold without B also holding. That A is a necessary and sufficient condition for B thus states a symmetrical relation between A and B: Neither can hold without the other, that is, both hold or neither. If A being a necessary and sufficient condition for B indeed implied that A caused B then, given symmetry, it would likewise imply that B caused A. A and B would have caused each other -- a rather odd way for them to come about. An example may help. In this example, A is that you are an unmarried male human adult at some given time t, and B is that you are a bachelor and this same time t. Your being an unmarried male human adult at t is a necessary condition for your being a bachelor at t. (For you to be a bachelor at t, you must be an unmarried male human adult at t. Your being a...