Indirect Proof and Necessary Evils

April 4, 2009

In most fields of philosophy, a set of propositions that entails a contradiction is held inconsistent, following the law of non-contradiction.1 Where one can rank the support for the various propositions, this allows the figure of indirect proof: if adding a proposition to a set of beliefs singly better supported than it produces a contradiction, the proposition added must be considered false.2

In one field of philosophy, however, most people seem to hold this method of reasoning invalid: ethics. Many proposed ethical systems place upon people burdens to two or more incompatible actions. Elsewhere, such a system would be held inconsistent, and in need of alteration. In ethics, however, the law of non-contradiction does not seem to apply: an actor faced with contradictory obligations should follow one, considering his violation of the other a necessary evil, regrettable but not fatal to the system.3

This strikes me as exceedingly sloppy reasoning. We do not hold that although Newtonian physics and relativity are contradictory, they are both true and we should follow one, considering our denial of the other necessary to avoid indeterminacy; we hold that the contradiction renders any belief in both necessarily false. So it should be in ethics. There are no necessary evils; only false ethical systems that produce them. The true ethical system will at no time obligate an actor to two incompatible actions. This does not mean, of course, that I believe that, a priori, if an ethical system is to prohibit, for example, lying, it must do so in all circumstances; that prohibition may have exceptions (“One may not lie except to criminals”, or even “One may not lie except when doing so is commanded by a higher principle”, with the precedence established).4 However, these exceptions must be inherent to the original ordinance, and not produced from the conflict of absolute ordinances.

Law being a subset of ethics governing enforceable interpersonal interactions, rights are also subject to this prohibition of contradiction. No right may be justly violated at the instigation of any other ethical principle. Thus, long lists of “human rights” such as those of the UN are necessarily false, for they place agents under competing ethical claims. Even the rights to free speech and freedom of property are inconsistent, as in the stock case of crying “fire”. Traditionally, it has been held that in this case the latter right overrides the former. I say, on the other hand, that this instead means that one of these rights is not a true right, but rather a manifestation of something else. Legal questions must be solved by argument from sound principles, not by weighing of incompatible principles in incommensurate units.

1: A strong contradiction is, however, necessary. A set of propositions that produces a paradox is not inconsistent unless the addition of other certain premises produces a strong contradiction.

2: Note, however, that this also applies to the better-supported premises; their contradiction of a supported premise lowers their support correspondingly, even though from the assumption that they are better supported than the new proposition their support remains positive. Thus, one cannot use a set of propositions to disprove a large number of propositions only slightly less-well supported; even though it is more plausible that any one of the introduced propositions be false, it is more plausible that some proposition in the original set be false than that all of the introduced propositions be false. Thus, the set of propositions believed true should be the set that minimizes the combined evidence in favor of propositions believed false.

3: And it is not clear to me why he should do one instead of the other. If government is a necessary evil, unjust but necessary to prevent other injustices, why should we not hold that the injustices consequent on the absence of government are a necessary evil, unjust but irremediable without other injustice?

4: This is ultimately the problem with Kantian ethics and rule utilitarianism. Kant’s categorical imperative may be valid in principle (and is a necessary consequence of moral absolutism), but his use of it to obtain, for example, an absolute prohibition on lying ignores that the true rule of behaviour is not necessarily “lying is acceptable”, but rather “lying is acceptable in this situation”, which one could wish to be a universal principle of action without the consequences attending permission of lying in general. Similarly, for any proposed rule under rule utilitarianism one could propose the modified rule that the previous rule is to be followed except when violations of it would improve utility. The rule utilitarian would then have to say that there is no such instance, which requires much stronger support (and, arguably, moves rule utilitarianism indistinguishably close to deontology, merely approaching from the opposite side (assuming the consistency principle)).


Circular Reasoning

February 28, 2009

I used to think that circular reasoning should be one of the rarest of fallacies. Would not someone notice that their argument demands the conclusion as a premise? Since then, two things have surprised me: the prevalence of circular reasoning, and the difficulty of its definition. Here I shall restrict myself to practical reasoning,1 under the definition of “using a premise not granted by one’s opponent to demonstrate to him the falsity of his beliefs”. Thus, while a circular argument may be valid, it has (or should have) no persuasive value.

One of the most pervasive examples I have encountered is Hume’s argument against miracles: because a miracle is, by definition, a violation of natural laws, it is of infinitely low probability, and so any explanation consistent with natural laws is of higher probability. Therefore, no report of a miracle can prove their existence, for it is always better explained without resort to miracles. This argument seems to have dominated secular understandings of miracles, but does it actually prove anything? Note the hidden premise: that all violations of natural laws are of infinitely low probability. I, for one, do not grant the premise, and neither, I suspect, do any who believe in miracles (except, perhaps, for Kierkegaard and his followers, but I can make little sense of his intellectual system and thus cannot speak for him): I hold that divine action is unconstrained by the principles that God has chosen to follow in most circumstances, and thus that miracles are not of infinitely low probability. Since the argument thus depends on proof that miracles are of infinitely low probability (which, rather ironically, science cannot demonstrate), it cannot be used independently to discredit reports of miracles.2

The other place I often see such circular reasoning used is in maintaining the necessity of government. I frequently encounter arguments that the credit crisis proves the necessity of government restraints, or that the thalidomide tragedy proves the necessity of the FDA. In neither case was the market free; the banks were regulated in the first case; the FDA existed in the second. Therefore, for the arguments to validly reject the perfectly free market, one must accept the unstated premise that all regulations reduce the probability of problems. Brought to light, this premise should seem absurd to all people, for it is utterly implausible that all government regulation, whatever its form or intention, is beneficial. But even granting that those who make the argument accept that premise, I doubt that very many supporters of the free market would accept it. I would explain the matter differently: each crisis occurred because the government regulation was insufficient (possibly necessarily so) to avert the problem, but was sufficient to cause people to forsake their own responsibilities of monitoring risks. Thus, I would argue the matter in reverse: the existence of such crisis under a regulatory regime indicates the difficulty (although not, prima facie, the impossibility) of effective regulation. These examples only prove the need for government regulation if one assumes its superior effectiveness, which those who would controvert its need would almost certainly deny.

I must note that use of circular arguments (under this definition) is not itself irrational; I think that all people do and even must use them continually to themselves to address challenges to their position. If any challenge to my belief required me to reprove my positions a nihilo, I would never accomplish anything else(actually, I would never accomplish even this). Thus, it is perfectly reasonable to respond to an argument against one’s position with an argument drawing on the position as a premise, thus maintaining the consistency of one’s beliefs even in the face of the counterargument.3 However, what suffices to maintain one’s own position against a counter-argument does not necessarily suffice as an argument against another’s position. Proper form in an informal debate requires basing all of one’s arguments on premises that one’s opponent accepts. If neither can do so, then the debate must remain inconclusive. Above all, one must not declare irrational one who does not agree with one’s conclusions because he does not believe in one’s premises; unless one can object to his premises on some lower common ground,4 one cannot question the rationality or truth of his opinions. However, this seems to be the form of almost all modern debate (from both sides, I must note; this is why I cannot stand Coulter), particularly in religion and politics. It is possible to demonstrate that miracles are impossible, if one assumes that they are impossible; but what does this prove concerning the rationality of those who hold them to be possible?

1 Circular reasoning has no firm place in classical two-truth value logic, most formulations being trivial or proscribing all valid arguments.

2 Does it even prove that much? It seems to me that Aristotle’s dictum that an impossible plausibility is preferable to a plausible possibility applies to life, not merely poetry. Take the example of Christ’s resurrection: to admit the possibility of resurrection seems less momentous than to admit that so many people would lie with expectation of harm. On the other hand, I must acknowledge that this argument is, itself, somewhat circular, for to admit the possibility of resurrection would be far more momentous to an atheist.

3 However, one must be careful to avoid using one’s position to reject the argument: I believe A, P implies not A, therefore not P. Instead, one must either disprove P without reference to A or prove that P is consistent with A. The statist who holds that state regulation of drugs is beneficial can, while maintaining local rationality, state that failures of state regulation do not disprove its utility because it might be worse without the state control (to dispute which would be to commit the nirvana fallacy). However, if it is then demonstrated that conditions would have been better without the state agency, he may not say that because that contradicts his belief in the state system, the demonstration must be false; he must address the demonstration itself.

4 Which will, I believe, always exist, but may be very difficult to find. Of course, one could merely deny all points of agreement to avoid “losing” a debate, but one hopes that one who does so would still question his beliefs. I would also dispute that he has really avoided losing, for the only way to lose a discussion is to fail to aspire to the truth.