Fixing Classical Arguments

In my last post, I wrote about how the premises of classical deductive arguments could be construed as either statements of logical definition or of observed fact. I argued that philosophers often confound the two and, as a result, either draw the conclusion that matters of fact can be “proven” by pure reason or else that some factual premises are “basic” and need no support.

Some philosophers use this approach to tag certain premises, such as “Other minds exist” or “God exists”, as part of the basic foundation of a rational worldview. Such basic premises, they maintain, can be rationally embraced without any need for evidence or observation to back them up.

But instead of embracing foundationalism, philosophers can turn instead to the scientific method and learn from it. Let’s take a closer look at what I have in mind.

Science relies on making inferences and then devising tests to see if those inferences are reliable. Philosophy, traditionally, relies on deductive reasoning, as in

Premise: All men are mortal
Premise: Socrates is a man
Conclusion: Socrates is mortal

But the premises are recognized as needing to be buttressed by arguments of their own. Such as

Premise: Only men engage in the use of complex tools and language
Premise: Socrates engages in the use of complex tools and language
Conclusion: Socrates is a man

But even these premises need the support of a logical argument. Thus

Premise: I saw Socrates typing on the computer
Premise: Socrates explained to me in English what he was typing
Premise: A computer is a complex tool
Premise: English is a complex language
Conclusion: Socrates engages in the use of complex tools and language

Eventually we end up with an extremely long string of interlocking arguments in which the conclusion of one becomes the premise of another. But is it enough? Doesn’t each premise always need supporting argument, and each argument need premises which need arguments in a never-ending chain? Not always.

Some premises are different than others. Some premises are true “by agreed upon definition”.

Premise: A triangle is a polygon with 3 sides.
Premise: Figure A is a polygon with 3 sides.
Conclusion: Figure A is a triangle.

We may need a Premise which defines polygon and perhaps one which defines sides. But given an agreed meaning for its words, our first premise defines a triangle. We do not need (and can hardly imagine) a classical argument to support it as a premise. (The best we could do would be to utilize premises which constitute compatible ways of defining a triangle.)

So there are two types of premises: those which define things and those which describe some presumed “fact” about the world. Instead of calling all premises “premises” it would therefore be more useful to call some “definitions” and some “facts”. But there is something a bit odd here. The premises we call “facts” are precisely the ones that seem to need to be the conclusion of prior argument.

The General Semanticists distinguished between “inferences” and “facts” and we will find that distinction useful here. A fact is something that you can observe directly; an inference an assumption you make about things you can’t observe, but which might be observable by someone in the right position. The clock tells you it is 2 PM, so you infer that it is still daylight out. Or you observe sunlight streaming in the window and infer that it is sunny outside. Those are inferences. But only if you see the daylight or the sun directly do they become assertions of fact.

But here we must retreat: even our direct perceptions are not necessarily facts. We infer that the leaf we see on the tree is green because we see it as green—and yet, as we now know scientifically, neither the leaf nor the light reflected from the leaf is green. That the leaf has color is an inference which our brains have evolved to make on our behalf—not because it is “factual” but simply because it is useful. The brain has a built-in inference machine—eyesight—in which it takes hints from detected photons and manufactures colors and shapes from those hints. Sometimes the brain’s built-in inferences are wrong, and we experience an “optical illusion” as a result.

If you observe the way scientists (and other intelligent people) define something as “fact”, what you will observe is that facts are always built on prior, dependable inferences. It is a “fact” that the earth orbits the sun—of course we know that this supposed fact about the sun is built on a complicated framework of inferences about the apparent movement of the sun, planets & stars in the sky. At a lower level of abstraction, we know that our “direct observations” of the sun, planets & stars are themselves inferences—we don’t for example ever experience any of those things “moving” but instead infer that they have moved. And at an even lower level of abstraction, as mentioned earlier, our experience of sight is based on the brain’s inferences about the hints from photons gathered by the sensor cells in our retina. (Of course, that there are such things as “photons” or “sensor cells” are themselves very high level inferences—built upon many levels of inferences treated at each intervening level as facts.)

But back to our classical syllogisms. As we saw, some classical “premises” are “definitions” and others are “inferences.” We might ask, Does it make a difference what we call them? I believe the answer is that it can make a significant difference, and I will argue that the term “premise” ought to be dropped for the terms “inference” and “definition”. Consider the following,

Definition: all bachelors are unmarried.
Inference: John is a bachelor.
Conclusion: therefore John is unmarried.

In the traditional syllogism the first and second statements are merely premises, with the presumption that they are on a par. But by recognizing that the first statement is a definition of terms and the second an inference we have drawn about John, the argument is clarified. The conclusion, of course, is also an inference, since one of the premises it relies on is an inference. This is exactly as it should be, since our conclusion “John is unmarried” may serve as an inference in our next syllogism.

This approach helps us distinguish the following two arguments:

Inference: All men are mortal.
Inference: Jesus is a man.
Conclusion: Jesus is mortal.

Definition: All men are mortal.
Inference: Jesus is a man.
Conclusion: Jesus is mortal.

Per this last argument, there is something “inhuman” about someone who never dies, so that, for example, if Jesus is still alive on the cross 2000 years later he must not be a man after all. Whereas in the case of the prior argument you would not know which inference was false.

Or, taking the Christian doctrine of the trinity as a definition of Jesus, you might have:

Inference: all men are mortal
Definition: Jesus is a man
Conclusion: Jesus is mortal.

In this case if Jesus is still alive on the cross, then the inference “all men are mortal” must be false given the definition of Jesus. (I’m pretending that 2000 years is enough to infer immortality—of course it may not be). At any rate, I hope this shows that distinguishing between premises which are definitions and those which are inferences (even when the wording is identical) is clarifying—and therefore preferable.

Definitions are always tautological (& tautologies are always definitional). In classical syllogisms a premise may sometimes masquerade as an inference but sometimes turns out, on examination, to be tautological in actuality. (Several of the classical arguments for God existence have this flaw.)

There is a lot more that might be written on this topic. But I’ll stop with this: when there is a conflict between an observed inference and a definition, the scientist modifies the definition to fit the inference, whereas the theologian usually denies the inference to preserve the definition (or the basic belief, if they are a foundationalist philosopher). This is why many religions deny the inference of evolution.

It is also why science improves over time, and religion & philosophy do not.

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