The following "Informal" or "Material" Fallacies are mistakes of reasoning that depend on the meaning of the words and sentences involved in arguments. They may thus be contrasted with the Formal Fallacies that result from logically invalid deductive arguments. Formal Fallacies are things like affirming the consequent, in which the antecedent of a conditional is inferred from the affirmation of the consequent. The argumentum ad absurdum, or reductio ad absurdum, is itself a valid argument, based on the principle [the Law of Clavius, (-P -> P) -> P] that the introduction of the denial of the conclusion into a valid argument produces a contradiction and establishes the conclusion. This is widely used in mathematics and in natural argument -- though some mathematicians, the "Intuitionists," don't like it.
The first group constitutes "Fallacies of Relevance," i.e. the subject matter of the argument is actually irrelevant to the truth of the conclusion. They are thus the opposite of the argumentum ad rem, which is the relevant appeal to evidence and truth.
While the previous kinds of arguments are all fallacies because they are not relevant to the truth of the conclusion, they are not therefore fallacies in every possible context. Beliefs are not always based on actual evidence of truth, but often on other reasons which may provide grounds for credibility, but not for truth. Thus the argumentum ad hominem and argumentum ab auctoritate are forms of the Genetic Fallacy that, in the context of belief, are not fallacies at all. Impeaching a witness in a legal case is an ad hominem argument, but as the credibility of the witness is reason for believing his testimony, attacking his credibility is relevant to the situation.
The second group constitutes "Fallacies of Ambiguity," i.e. the meanings may be relevant to the conclusion but the force of the argument is lost by differences in meaning or ambiguity, which may confuse, deceive, or even produce arguments that are formally invalid (i.e. the validity depends on one unambiguous term being used).
An argument that turns on an ambiguity would be John Locke's argument for the existence of God. Thus, he first sought to establish that "Something has always existed." This is true because, if there were a time when nothing existed, there would be nothing around to make something come into existence -- an argument from "sufficient reason" first used by Parmenides. Locke then argued that "that something would be God." This argument fails because the first argument only established that something or other must always have existed, not that some particular something always existed. So an ambiguity in the word "something" allows for the apparent inference.
As it happens, Locke's argument was a poor rendering of a similar argument by St. Thomas Aquinas. St. Thomas argued that a necessary being must exist. A "necessary being" is something that cannot not exist. The argument is that if there are only contingent beings, which can possibly not exist, then, in an eternity, every possible thing will have happened. With nothing but contingent beings, one possibility is that they might all not exist at once. But if there is a time when nothing exists, then there is nothing around to make anything exist, so there would be nothing for the rest of time after that. Since in an eternity of time, an eternity would already have passed, there would now already be nothing, if only contingent beings existed. Thus, since things now do exist, there must be an necessary being, which by definition would be God.
If St. Thomas' argument commits a fallacy, it would be that of a "Complex Question" or perhaps simply "Begging the Question," for is it the case that the only "necessary being" would be God? No. Any substance could be a necessary being, since by definition a substance can be that which exists independently and is durable, i.e. persists through time. St. Thomas was using Aristotle's theory of substance, in which substance can come into being and also cease to exist. But the older, indeed the first, conception of substance was that of Parmenides, in which substance can neither come into being nor cease to exist. As it happens, Materialists, like Democritus, applied the Parmenidean conception of substance to matter. The Materialist would say that the "necessary being" is not God but simply matter. This is actually a foundational principle in modern physics, where there are a number of "conservation" laws. So a physicist could simply say that St. Thomas' argument establishes, if anything, the Conservation of Mass/Energy -- Einstein's combination of the previously separate principles of the Conservation of Mass and Conservation of Energy. Thus, the total amount of mass and energy in the universe, related by Einstein's equation, E=mc2, remains constant. Mass/energy has necessary existence. On the other hand, Buddhist metaphysics denies that there are substances, or durable existence, at all, which rules out the independent existence of anything St. Thomas considers, including God.
Religion and Humanism, The Sophists to Secular Humanism
Philosophy 9 Index