Principles of Validity: What Logic Is and Isn’t

Speaking as someone who has taught logic professionally, at the college level, for over two decades, I thought it might be helpful to enlighten these would-be debaters on what logic is and what it is not, what it can do and what it can’t.

Before it is possible to understand what logic is and does, it is first necessary to understand the nature of argument. An argument is not a fight or a quarrel; ideally, all argument would be completely dispassionate…

although this often seems quite challenging for mere mortals. The purpose of argument is to persuade the arguee to believe or to act in some way desired by the arguer. All advertisements are arguments because they are trying to persuade you to spend money.

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An argument, therefore, consists of a body of statements which are divided into two classes: 1) premises, of which there may be many, or they may be left unstated [the enthymeme], and 2) conclusions, of which there is only one (although it may be compound; I shall ignore details in this introductory survey).

The conclusion is the statement that the arguer wants the arguee to accept; the premises are the reasons given why the arguee should accept the conclusion. Premises usually present evidence of some sort.

Notice that the relationship of the premises to the conclusion can be considered a relation of “support,” much as we might imagine certain beams and posts supporting a house. The point of the argument, therefore, is to show that the premises support the conclusion of the argument, and, unless the arguee or the counter-arguer have very good evidence to the contrary, the arguee ought to accept the conclusion. There are two ways in which this relationship of support can go wrong.

The first way that the support-relation between premises and conclusions can go wrong occurs if one or more of the premises are not true. If one or more premises of the argument are false, then of course they provide no support for the conclusion.

At a minimum then, we must be certain that the evidence presented in the premises is true, and there are some more-or-less reliable ways to do this: empirical perception, scientific research, accredited authority, etc. How we determine the truth of the premises is a question for that branch of philosophy known as “epistemology” (theory of knowledge), and has no direct bearing on the nature of logic itself.

The second way in which the support-relation within an argument can go wrong occurs when the premises of the argument are in fact uncontroversially true, but they nevertheless fail to provide any support for the conclusion.

Consider this example:

P1. All cabbages are vegetables (T)
P2. All carrots are vegetables (T)

C. Therefore, all cabbages are carrots. (F)

Both premises (P1 and P2) are true, but the conclusion (C) is nonetheless false. What happened here?
It is at this point, that we first enter the realm of logic. What has happened to the argument above is that it is “invalid.” An argument is invalid when the truth of the premises is insufficient to establish the truth of the conclusion.

Conversely, an argument is “valid” when the premises, if true, are in fact sufficient to support the truth of the conclusion. But how do we know whether an argument is valid or invalid? The answer is sometimes hard for beginners to accept; validity is entirely a matter of form, i.e., the structure of the argument apart from its content.

In logic, statements (the premises and conclusion of the argument) can be drained of all meaningful content and represented by symbols like ‘P’ and ‘Q.’ The logician then examines the way that P relates to Q, and whether it obeys or violates certain rules which can be spelled out in great detail and at some length, but which I will not attempt to do here.

If a given argument is valid, then the truth of the premises (if they are true) does indeed “flow through” to the conclusion; if the argument is invalid, it does not matter whether the premises are true, because they do not support the conclusion.

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Logic, then, is a rather complex relationship which holds (or fails to hold) between the premises and conclusions of arguments. I often think of these support relations as wiring, and I’m the electrician trying to figure out whether a current introduced at one end will come out where I’d like it to at the other end. Just because electricity is introduced at one end, there is no guarantee that it will come out as I’d planned, unless the wires connect correctly.

The logician is like the electrician, trying to determine whether all the wires of the argument are connected properly before electrifying the system, which may, or may never, be electrified.

I think that is about as clear as I can be on the nature of logic in a microessay, but there is one vital point I should make before closing: “validity” and “truth” are often used as if they were interchangeable synonyms, but strictly speaking, this is a serious mistake.

Truth is a relation between statements and the world; if the statement adequately reflects the current condition of the world, it is true. Validity, on the other hand, is a relation between statements in an argument; if the argument is valid it will properly conduct truth from the premises to the conclusion – assuming that the premises are indeed true, a matter to be settled by unrelated epistemic means.

Where an argument fails to be logical, i.e., where the argument is invalid, it does not follow that the conclusion of the argument is false. It follows only that the premises do not support the conclusion; in other words, the argument is not convincing.

Fallacies (both formal and informal, a distinction we need not examine here) never “prove” that an argument’s conclusion is false; fallacies prove only that the conclusion of the argument is unsupported by the premises, and hence the argument fails to persuade.

The 5 fundamental skills of Philosophy: 1. Reflection (impulse control) 2. Skepticism (methodological doubt) 3. Analysis (conceptual reverse engineering) 4. Free variation (considering alternatives) 5. Synthesis (what works and what doesn’t)

James Pearce

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