Advanced Search

Consider the following:

Consider the following: "If we lower the standards we lower the results, so if we raise the standards we raise the results" (in passing this is about education). I have the impression that there is a fallacy in this - even if I assume the first part of the inference, I suppose we could raise educational standards and just watch everybody fail miserably), but I cannot phrase clearly why/how this is a fallacious claim. Am I right? Is this fallacious and if so, is there a technical term for it?

Let's assume it's true that "If P, then Q". The conditional claim that you imagine being inferred from this has the structure "If not-P, then not-Q". [Not quite: I don't think the negation of "we lower standards" is "we raise standards". One way in which we might fail to lower standards is to keep them fixed.] This is indeed an incorrect inference. The first conditional claims that P is a sufficient condition for Q. While the second claims that P is a necessary condition for Q. And the latter claim simply doesn't follow from the former. For instance, it's true that if Rex is a dog, then Rex is a mammal. (Being a dog is a sufficient condition for being a mammal.) But this does not imply the false claim that if Rex is not a dog, then Rex is not a mammal. (Being a dog is not a necessary condition for being a mammal.) This fallacy is sometimes called The Fallacy of Denying the Antecedent. ("P" is called the antecedent of the first conditional claim above.)

Is this a valid argument? If not, what is the fallacy committed?

Is this a valid argument? If not, what is the fallacy committed? (1) A hypocritical agent is one that says one thing, but does another. (2) The government kills people. (Through wars, the death penalty, etc.) (3) The government tells us not to kill. (By making it a law to not murder. Murder is a form of killing, thus making it a law to not murder is a form of making it a law to not kill.) __________________________________________________ Therefore, (4) The government is hypocritical.

I think your argument is logically valid--that is, IF the premises were true, then the conclusion would be true. And I don't think it commits any formal or informal fallacies (except perhaps equivocation in the sense I'll explain shortly).

The problem is that it is unsound, because it has at least one false premise; hence the conclusion is not "made true" by the premises. Premise 3 is false. The government does not tell us not to kill no matter what. As you point out, it tells us not to break specific laws against specific types of killing. Typically, citizens are not breaking the law (and are morally justified) in killing in self-defense or to protect others from an immediate and deadly threat. And (legal) killing in war and use of the death penalty (where it is legal) are also not forms of killing the government tells us not to commit.

Now, we may have reasons to think that some or even all killing in war is morally problematic and even more reasons to think the death penalty is morally wrong. And we have greatly narrowed the scope of such legalized killings over time (in the U.S. and even more so, in other industrialized nations, most of which, for instance, have made the death penalty illegal). And we may believe that it is hypocritical to say some killing is OK but not others (though almost no one, perhaps Jesus excluded, suggests that you cannot kill, if necessary, in self-defense). But I don't think that the government is "saying one thing but doing another" in these cases, because the government, just like most of us, does not treat all killings as the same thing (hence the equivocation in the use of "killing").


Hi, I'm having an argument with my pal. He argues since logic prescribes (creates a standard) what is a good/bad inference (valid/invalid) it is normative. On the other hand, I think Logic is like mathematics or physics - there are laws of logic, but they are not normative (they only describe). Can you help us settle this beef? Thank you, Miko

I don't know that I can settle anything. The dispute you are having is one philosophers today have generally. Some people think logic is normative, in that it prescribes rules concerning how one should think, or reason; other people think logic is purely descriptive, and that it simply tells us something about the notion of implication or validity.

One reason people often given against the normative interpretation is that the norms logic provides just seem like bad ones. For example, it was once argued that, since logic tells us that A and ~A imply anything you like, then logic would be telling us that, if you reach a contradiction, you should infer that the moon is made of cheese; but, of course, what you should actually do is figure out what went wrong and give up one of the contradictory beliefs. The obvious reply, though, is that this is too simple a conception of what the norms logic prescribes are. It assumes, in particular, that if A implies B, then it is a norm that, if one thinks A, one should infer B. But maybe the norm is that, if one thinks A, then one ought either to infer B or to give up A. Logic won't tell you which one to do, but it demands you do one or the other.

A deeper concern is that reasoning itself might be more involved with probability than logic allows. In that case, the norms of reasoning would presumably come from probability theory, and classical two valued logic would have the wrong subject matter. (Let me insert a plug here for my colleague David Christensen's book Putting Logic in Its Place and suggest you read the entry on Bayesian epistemology at the Stanford Encyclopedia.) On the other hand, however, there are known ways of essentially deriving probability theories from logical theories, so two-valued logic would represent a sort of idealization to the case of absolute certainty of the norms that govern reasoning, which actually proceeds, most always, under uncertainty.

I'm struggling wit the following: I am reading an essay that states (repeatedly)

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 argument doesn't guarantee that someone will be in the same state of mind toward the conclusion, even if the conclusion happens to follow. Consider some argument with 10 premises P(1), P(2)...P(10) and a conclusion X. And suppose that X really does follow from P(1)... P(10). Your suggestion seems to tell us that anyone who judges the premises to be true will actually judge the conclusion to be true, even though, we'll suppose, the reasoning required to get from premises to conclusion is subtle and complex.

If you think about it, it's not at all unusual for people to miss seeing what their beliefs imply. Math is a particularly obvious case; getting someone to accept the principles of Euclidean geometry doesn't guarantee that they'll simply judge all the theorems to be true. But math is by no means the only case.

Another way to to put it: the problematic argument you judge to be valid needs another premise. A general version of the premise would be something like this:

Whenever an argument is valid and I judge that its premises are true, I always judge that its conclusion is true as well.

That's false for any human "I."

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

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

If by 'logical' you mean 'a decent argument can be constructed of this form' then i would say the answer is yes -- but if you mean 'an absolutely convincing argument ...' then, well, you don't find too many of those anywhere in philosophy -- my favorite version of the kind of argument that Allen Stairs mentions is some version of the fine-tuning argument -- which observes how perfectly fine-tuned features of the universe seem to be, such that they could easily have been otherwise, and yet had they been otherwise then human life (conscious, rational, moral life) would not have been possible -- and goes from there to argue that it is reasonable to think this didn't occur by chance -- a good source on this topic would be any of Paul Davies' recent books ...

best, ap

I know a number of people who subscribe to a particular model of human

I know a number of people who subscribe to a particular model of human development, who often use terms peculiar to this model in premises in arguments. For example, I've heard many variations on this theme: "You and/or your worldview, and thus your view on the issue we're arguing about, are at level or stage x, and because x is not as highly developed as y and me and/or my view is at y, it's obvious that your view is less than adequate [or wrong, etc.]." One could point out that the premises require support, but I've been reluctant to do that in large part because my sense is that the very use of these premises falls in the direction of being a fallacy of relevance. (I've suggested that interjecting such premises into an argument is a conversation stopper, but the term "conversation stopper" doesn't have the same weight as terms like "fallacy of relevance.") I seek clarification, suggestions, advice.

Actually, this sounds like a pretty good example of the 'question begging' fallacy. I can't just assert that 'your view is inferior/not as highly developed'. I have to provide some sort of reasonable evidence for you to think my claim that 'your view is inferior/ not as highly developed' is correct. Without such evidence I'm simply presupposing what I should be proving (this happens A LOT in our culture for some reason).

Is it possible to positively prove a negative?

Is it possible to positively prove a negative?

People often say this and it can be baffling to logicians! Perhaps your use of "positively" hints at what you're getting at though. Let's assume by "prove a negative" you mean something like: establish that something of a particular kind does not exist. For instance, your "negative" statement might be: Martians do not exist. And perhaps by "positively prove" you mean: establish by pointing to a particular thing that does exist. Then an instance of your claim might be that it's not possible to establish that Martians do not exist by displaying any particular non-Martian. And that's right: just because this particular object is not a Martian it doesn't follow that there are no Martians. In general, from the fact that a particular object is not an F we cannot logically infer that there are no Fs. So, if that's what you mean, logicians will agree that it's not possible "to positively prove a negative." However, that does not mean that one cannot logically prove statements of the form: there are no Fs. Those statements can be the conclusions of logically correct arguments.

How can we ever talk about what would be?

How can we ever talk about what would be? If a statement A is assumed, that's not actually true, then anything would follow since a conditional with a false hypothesis is always true. But anything (such as "P and not-P") can't be true. This seems to show that a statement that is not true would never be true to begin with. Thus, we can't talk about what would be, only what is. For example, I'm not driving to the store. But if I were, I'd also be swimming. Of course, though, I can't drive to the store and swim at the same time. This comes to show that so long as I'm not driving to the store, we can't ever discuss the situation where I am driving to the store, since that situation implies a contradiction.

Logicians have long distinguished between "indicative" and "subjunctive" conditionals. The terminology reflects a difference, in English, in the grammatical "mood" of the antecedent and consequent. So we have:

  1. If Kennedy was not assassinated, he is living is Columbia.
  2. If Kennedy were not assassinated, he would be living in Columbia.

The view to which you refer, that a conditional with a false antecedent is always true, has certainly been held, but only about indicative conditionals. So (1), on this view, is true if Kennedy was, as we all suppose, assassinated. But it is an entirely different claim that (2) is true simply because Kennedy was assassinated, and I know of no logician who has ever held that view. This is largely because some subjunctive conditionals, such as (2), are precisely intended to report on what would have happened had things been other than we know (or at least presume) they are. Since, as you say, it would be pointless to utter such conditionals, which are known as "counterfactuals", if their truth was always guaranteed by the falsity of the antecedent, we need a different account of what it is for such a conditional to be true.

What is involved in the truth of a counterfactual (or, more generally, subjunctive) conditional is, of course, an entirely different matter, one much discussed and debated. It's probably also worth noting that most logicians, and most linguists, would now reject the claim that natural language conditionals, even indicative ones, are "material", i.e., are true so long as the antecedent is false or the consequent is true.

Fox "news," busily enjoining viewers to mock the idea of wealth redistribution,

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" 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 upshot might be.

Suppose, on the other hand, that we set up a system that smooths GPAs out completely, so that every student gets the same GPA - say, 3.2. Then what we've done amounts to getting rid of GPAs. It gets rid of them because what a GPA does, at least roughly, is tell us how well people did on certain sorts of tasks. For that to be possible, the system for awarding GPAs must allow (though needn't require) that different people can end up with different GPAs.

We've looked at the extreme cases of completely uniform distribution. In practice, the reply might be, no one has anything that extreme in mind. But the point of looking at the extremes was to draw attention to a difference between the very logic of the two cases. Redistributing income doesn't as a matter of logic affect the purchasing power of a dollar, even though redistribution schemes raise lots of perfectly good policy and empirical questions. But unless the "redistribution" of grades is a mere matter of relabeling, redistributing GPAs destroys the information that GPAs are intended to convey. It's logically a bit like what we'd have (to borrow Kant's example) if it was understood by everyone that when we say "I promise" there's no real expectation that we'll do what we "promised." That would be a case where promising in any meaningful sense would be impossible.

Real life redistribution schemes would no doubt be less total. But the underlying logical point doesn't go away. GPA redistribution schemes would amount to fuzzing out the information at the core of what a GPA is. Near as I can tell, there's no similar logical problem for wealth redistribution. And so the analogy really is an apples and oranges affair.

Is the doctrine of the trinity illogical?

Is the doctrine of the trinity illogical?

I thought I would add just a tad more.

Here is one argument against the Trinity and a reply:

It has been argued that the Trinity involves Tri-theism or the supposition that there are three Gods (Father, Son, Holy Spirit). There cannot be three Gods for this reason: If there is a God, God is omnipotent. A being is omnipotent if it is maximally powerful; there can be no being more powerful than an omnipotent being. But if the Trinity is true, neither of the persons in the Godhead are omnipotent, because the power of each can be challenged by the power of the other. The Father cannot make a universe, unless the Son or Holy Spirit consent. That is less powerful than if only the Father exists.

Here is a reply: If God exists, God is essentially good. That is, God cannot will that which is not good. If the Father, Son, and Holy Spirit share an essentially good nature, their wills cannot conflict. This seems more plausable when one takes up what I mentioned in my earlier reply: the parichoretic model of the Trinity which understands each Person as interpenetrating or being in a state of co-inherence with mutual, unequaled access to the mind of the other.

Here is one other interesting argument from medieval philosophy, but revived today by Richard Swinburne and Stephen Davis.

If God exists, God is perfect in love. (This might be justified either by an appeal to revelation or some kind of ontological argument to the effect that if God exists, God is maximally excellent)

The three highest loves are: love of self; love of another; and the love of two for a third.

IF God is Triune, God has self-love (each of the Persons possess this), the Father loves the Son, and the Father and the Son love the Holy Spirit.

Why not the love of three for four, etc? Swinburne thinks that is a further love that extends the three highest, so love of three for four or five or... are all goods, but they are not the chief, maximal perfections of love from which the other loves follow. A further point can be made that in classical theism, the love in the Triune Godhead, does lead to the love of more, namely the love of creation.

In any case, check out the reference I gave earlier, starting with the free online Stanford Encyclopedia of Philosophy