Making Arguments vs. Manipulating Symbols

There is still another problem with Spinoza’s manner of argumentation. Spinoza is trying to get geometrical certainty about metaphysics by a logical arrangement of his claims. But this cannot work even in principle. If you take the rules of logic and the forms of the syllogisms, and fit sentences into them using their mere verbal patterns, without thinking about what you are saying, what it means and in what sense it is true or untrue, then you are manipulating symbols, not actually making arguments, and it may well mean that your conclusion is false, whether or not each of your premises is true in some way.

Alexander Pruss, in a recent blog post, argues for the existence of God from certain facts about language:

This argument is valid:

  1. All semantic truths are knowable to members of the community of language users.
  2. There are semantic truths that are not knowable to human language users.
  3. Therefore, there is at least one non-human language user.

There is some reason to accept (1) in light of the conventionality of language. Premise (2) is going to be quite controversial. I justify it by means of a standard argument for epistemicism. Consider Queen Elizabeth II. There are 88 statements of the form:

  • Elizabeth was not old at age n but she was old at age n+1

where n ranges from 1 to 88. It’s a straightforward matter of classical logic to show that if all 88 statements are false, then:

  1. Elizabeth was old at age 1 or Elizabeth is not old at age 89.

But (4) is clearly false: Her Majesty is old now at age 89, and she surely wasn’t old at age one. So, at least one of the 88 statements is false. This means that there is a sharp transition from being not old to being old. But it is clear that no matter what we find out about our behavior, biology and other relevant things, we can’t know exactly where that transition lies. It seems very plausible that the relevant unknowable fact about the transition is a semantic fact. Hence, (2) is true.

The most plausible candidate for the non-human language user who is capable of knowing such semantic facts is God. God could institute the fundamental semantic facts of human language and thereby know them.

(“So, at least one of the 88 statements is false” should be “So, at least one of the 88 statements is true.”) I would consider this to be more a case of manipulating symbols than of making a serious argument.

An atheist is likely to say about this argument, “Wait a minute. Maybe it’s not obvious to me what is wrong with your argument. But there’s just no way you can prove the existence of God from simple facts about how words are used. So there must be something wrong with the argument.”

I agree with the hypothetical atheist that reasonable intuitions would say that you cannot prove the existence of God in such a way, and that this is a reason for doubting the argument even if you cannot formally point out what is wrong with it.

But in fact I think there are two basic problems with it. In the first place, Pruss seems to be failing to consider the actual meaning of his premises. He says, “There is some reason to accept (1) in light of the conventionality of language.” What does this mean? A semantic fact is a fact about the meaning of words or sentences. Pruss is arguing that all facts about the meanings of words or sentences should be knowable to members of the community of language users, and that we should accept this because language is conventional. In other words, human beings make up the meanings of words and sentences. So they can know these meanings; whatever they cannot know about the meaning is not a part of the meaning, since they have not invented it.

But later Pruss says:

This means that there is a sharp transition from being not old to being old. But it is clear that no matter what we find out about our behavior, biology and other relevant things, we can’t know exactly where that transition lies. It seems very plausible that the relevant unknowable fact about the transition is a semantic fact. Hence, (2) is true.

But if this is right, it undercuts the justification for believing the first premise. For the only reason we had to believe that all of the semantic facts are knowable to the community of language users, was a reason to believe that they were knowable to human beings. If they are not knowable to human beings, we no longer have a reason to believe that they are knowable to anyone, or at any rate not a reason that Pruss has given.

This illustrates my point about the necessity of considering the meaning of what you are saying. The argument for the first premise is in fact an argument that human beings can know all of the semantic facts; thus if they cannot, we no longer have a good reason to accept the first premise. We cannot simply say, “This argument is logically valid, we’ve given a reason for the first and a reason for the second, that gives us reason to accept the conclusion.” We need to think about what those reasons are and how they fit together.

The second problem with this argument is that the “standard argument for epistemicism” is just wrong. And likewise, the argument consists of precisely nothing but manipulating words, without thinking about the meaning behind them. It is a “a straightforward matter of classical logic” in the sense that we can fit these words into the logical forms, but this does not mean that this process is telling us anything about reality.

To see this, consider this new word that we can construct by convention, namely “zold.” A person who is between 80 and 90 years old is said to be zold; a person who is between 1 and 10 years old is said not to be zold.

Now consider the 88 statements of the form, “Elizabeth was not zold at age n but she was zold at age n+1.” It’s a straightforward matter of classical logic to show that if all 88 statements are false, then either Elizabeth was zold at age 1, or she was not zold at age 89. But this is clearly false according to the conventions already defined. So at least one of the statements must be true, and there is a sharp transition from being not zold to being zold. It is obvious that no matter what we find out about human beings, that will not tell us where the transition is; the transition must be a semantic fact, a fact about the meaning of the word “zold.”

Obviously, in reality there is no such semantic fact. The convention that we used to define the word simply does not suffice to generate a sharp transition. The problem with the argument for the sharp transition is that the rules of logic presuppose perfectly well defined terms, and this term is not perfectly well defined.

And it is not difficult to see that the word “old” does not differ in a meaningful way from the word “zold.” In reality the two come to have meaning in very similar ways, and in a such a way that there cannot be a sharply defined transition, nor can classical logic force there to be such a sharp transition.

It is not enough to fit your sentences into a logical form. If you want the truth, the hard work of thinking about reality cannot be avoided.

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2 thoughts on “Making Arguments vs. Manipulating Symbols

  1. […] Alexander Pruss argues that all words are sharply defined, at least in the mind of God.  He makes the argument, “Words are part of the world, so if there is vagueness in words, there is vagueness in the world.” This is no different, of course, from arguing that since words are part of reality, and some words are universal, there are universal things. There are universal things, if we mean by that universal terms or concepts, and there are vague things, if we mean by that vague words or concepts. But there are no universal cats or dogs, nor are there vague cats or dogs, despite the words “cat” and “dog” being vague. […]

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