Extensions on Peirce's Pragmatic Law

In a previous post I went out on a limb to argue that Peirce's pragmatic maxim is formally identical to Peirce's Law, a form found in many logic textbooks today. In a later post, I went a bit further out by suggesting an avenue for (re-)constructing a logical proof of pragmatism; and still further by stating that pragmatism is basically correct if my shpiel happens to be right.

Today I'm going to inch closer to the leafy edge by making a further conjecture, tediously illustrated.

Ballsy conjecture #4: The development of Peirce's philosophy can be seen to assume the pattern of Peirce's Law. In other words, it thoroughly informs his thinking.

If pragmatism is the rule for right reasoning, as he argues in the 1903 Harvard lectures,[1] and if he duly acts on that, we should be able to discern it in the form of his reasoning.

This may be only of interest to scholars, but it seems to me that it would make sense of the trajectory of his thinking. That's got to count for something. Here's a case I've found so far. In 1902 Peirce criticizes Aristotle's venerable argument for first principles.[2] The Stagirite states that every premiss depends on scientific arguments rest on more general principles; those may well in turn rest on still more general principles. If anything is to be true at all, there must be a stop to the regress - i.e. most general principles. Peirce disagrees. He likens the Achilles paradox except we're going backward in time rather than forward (This would be because thinking takes time. Nope, there are no two ways about it - go ahead, try.)

Reasoning would be like what Lewis Carroll pictures in "What the Tortoise Said to Achilles", first published in Mind in 1895.[3] Suppose, the tortoise says, you argue that premisses A and B lead to conclusion Z: what if he accepts the premisses but refuses the conclusion? Well, Achilles can introduce premiss D: If A and B, then Z must follow.[4] What if the tortoise refuses that? Simple – add premiss E: If A, B, and D, then Z. And so on.

Effectively this is attempting to state that if a rule of inference is accepted, along with certain premisses, the conclusion necessarily follows. It would be equivalent to saying that if the rule is accepted, the consequent follows out of necessity. Formalized, it lo0ks like this:

{(C	→	Z)	→	Z}	→	Z	…
T	T	T	T	T	T	T	…
T	f	f	T	f	f	f	…
f	T	T	T	T	T	T	…
f	T	f	f	f	T	f	…
	⇑		⇑		⇑		…

You can see the pattern that is set into motion here: as long as we are trying to derive the conclusion from the premisses, we will never actually reach it by means of the reasoning alone. The arrows ⇑ at the bottom of the table mark the truth values accruing to the conditionals as each successive ramification is added; one can also see that the alternation will continue infinitely. In posing this paradox, Carroll has questioned the notion of implication.

Peirce would reply that the question is misdirected at the outset. He appeals to the act of thinking things out: in the process of thinking we are so busy focusing on the object under consideration that we cannot attend to the process. Once we have reached a point where we can pause and reflect on the path leading up to this conclusion, we search for propositions that do lead up to this conclusion. But the argument represents the last stage of his thought, not what led up to it: we say X is true if Y and Z are true – it follows, granting the premisses. The key element here is thought: thought is thinking about something, whatever that may be. If we try to clarify this, we find that thought is starting on a percept. But percepts cannot be articulated in propositions, for they are not products of thought; therefore the first logical particles are perceptual judgments or facts. But these are radically different from the percepts themselves, meaning that thought is developing on its own processes. What this means for the tortoise’s challenge is that he is right – but only if his picture of reasoning is right. And this Peirce would deny. We do not employ logical rules in order to reach conclusions, we use them to articulate the conclusions we have reached already. So the form (P → Q) → Q gives an improper picture of how logical rules are applied.

The error lies in supposing that the conclusion Q can follow from the relation P → Q alone. A more fruitful inference to make is this: If a relation of inferences to the conclusion implies that we took the steps leading up to that conclusion, then those steps were taken. In one fell swoop, both the tortoise’s paradox is dissolved and the validity of the premisses affirmed. And in doing that, there is no need to justify implication; it is merely posited hypothetically. That it happens to work every time enables us to say that although there is no reason for granting implication, there is no reason against it. Meanwhile all evidence supports its validity, and it has been astoundingly successful. Therefore, until further notice, we have every reason to accept implication as a valid form of inference

We have seen this sort of reasoning – in Peirce’s Law. Much of Peirce’s argumentation is of the form ((P → Q) → P) → P; indeed, it is arguably the framework of all of his researches. Assuming he takes his own pragmatic maxim to heart – a maxim which bears this form as well – his analysis of conceptions follows this train of reasoning. The form has been proven valid, and it explains the maxim; for an explanation is “the adoption of a simpler supposition to account for a complex state of things”, and the logical form is more general. This suggests, then, that the elusive proof of pragmatism is to be found in the proof of Peirce’s Law. The modifications of the maxim are but refinements of the great project which he maps out in the Popular Science Monthly series.

This is a belabored explanation of a single point. But I'd like to think it's typical of the sort of reasoning Peirce employs throughout his career; at least the conjecture I'm making suggests it. It's actually not so controversial as the next assertion I'm holding out for examination:

Ballsy conjecture #5: Peirce's pragmatism leads to realism, and does so by means of its form.

It's pretty well known that Peirce was a nominalist early on in his career. He eventually adopts a realistic stance, but it takes some time. (To be honest, I'm not so sure it's that simple - my own inclination is that he always was a realist, though his intellectual professions said otherwise. But that's another post.)

Taking the conjecture a step further, it seems to me that it leads to realism of its own accord. Suppose that the things we perceive - percepts, as Charley called them - are effects. This means that where's a cause, there's an effect. If that's the case, then it follows that they're caused by something real. This is exactly how we conceive them: images are caused by something.

Note that I am not saying that the percepts themselves necessarily imply a cause, only that we think them so. So I'm not misapplying the pragmatic maxim here. I'm saying that we conceive percepts as part of a causal relation; this means we suppose that real things cause those percepts. And what holds them together is this relation of cause and effect. It is our link to an external reality, and a refutation of nominalism.

In another post, I wish to show that this realism extends to the broadest conceptions possible: the categories.

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[1] CP 5.196 (1903).

[2] See CP 2.27 (1902), of which this is a boring reiteration.

[3] Mind, N. S. vol. 4 (1895), p. 278

[4] W4,547 (1883–4).