(Part 2) Collingwood’s Revolution in Logic

In a previous post I looked at Collingwood’s attempted revolution in logic and its anti-realist implications. Sam Lebens raised the interesting question of how the proposed revolution in the Autobiography connects with the more radical line pushed in the Essay on Metaphysics.

The theory in the Autobiography is, if I interpreted it rightly, relatively simple. Truth-bearers become question-answer complexes rather than propositions. Their truth-values depend on the answer’s being the right answer to the question, defined in terms of justifiability. The Essay on Metaphysics presents a much more complex structure, involving propositions, questions to which propositions are answers, and presuppositions giving rise to questions. “Logicians”, Collingwood opines, “have paid a great deal of attention to some kinds of connexion between thoughts, but to other kinds not so much.” (23)

Collingwood lays out his theory more geometrico, in a series of propositions and definitions (don’t confuse yourself yet by asking what questions these propositions are answers to). Life is short, so I’ll only list the propositions here, except for two definitions within Proposition 3, which are important:

1. Every statement that anybody ever makes is made in answer to a question.
2. Every question involves a presupposition.
3. A presupposition is either relative or absolute.

Def.: By a relative presupposition I mean one which stands relatively to one question as its presupposition and relatively to another question as its answer.

Def.: An absolute presupposition is one which stands, relatively to all questions to which it is related, as a presupposition, never as an answer.

4. Absolute presuppositions are not propositions.

I find Collingwood’s own examples unhelpful for making much sense out of this structure. What is clear enough is that we can’t hold onto the neat structure of question-functions yielding truth or falsity with answers as arguments. Collingwood tells us that “A question that ‘does not arise’ is … a nonsense question” (26), and a question’s not arising is a matter of its involving a presupposition that is not in fact being made.

Here is a tentative attempt at a semi-formalisation. Start with the question-functions I discussed in the previous post. A question-function can be placed into another function — a presupposition-function. This generates a presupposition-question-function if the presupposition is in fact made; it generates nothing but nonsense if the presupposition is not made. Thus we begin with the question-function: Q?*. This is then given as the argument in the presupposition-function A!*, yielding the function A!Q?*. This again is then placed in a new function, C(*), yielding: C(A!Q?*). This will be meaningful — that is, it will yield truth-values when various answers are substituted for *, if the presupposition is in fact made.

An example of a meaningful function might then be: C([All men have mothers]![Who is Nero’s mother]?*). This might be called (following Aristotle’s terminology regarding syllogisms) an imperfect function, since more information than is actually stated is needed to show how the question arises from the proposition, for instance that Nero is a man. But Collingwood does not seem particularly bothered about formal imperfection of this sort; probably he thinks (and probably rightly) that any actually presented complex will have some degree of imperfection. In this case, at any rate, various answers can be taken for * to yield truth or falsity. C([All men have mothers]![Who is Nero’s mother]?[Agripinna the Younger is Nero’s mother]) will yield truth, since the answer is right (in the sense explained in my previous post).

A meaningless complex might be: C([All dogs are cats]![Which cat is Fido the dog]?*). No answers substituted for * will produce either true or false complexes; C([All dogs are cats]![Which cat is Fido the dog]?[Fido the dog is Tibbles the cat]) is nonsense rather than a false identity statement, as it might appear to be if we attend only to the answer and not to the complex of which it is a part. A false identity statement would have to exist in a different sort of complex, e.g.: C([Some names refer to the same animal]![Do “Fido” and “Tibbles” refer to the same animal]?[“Fido” and “Tibbles” refer to the same animal]).

Collingwood wants to present metaphysics as the science of absolute presuppositions: those presuppositions which do no stand as answers to any question. In our example above, “All men have mothers” does not seem to be an absolute presupposition, since it can readily stand as the answer to a question: “Do all men have mothers?”. This is a meaningful question: we can wonder, e.g., about whether Frankenstein’s creature, having no mother, is therefore not a man.

What presupposition, actually made, gives rise to the question? This, according to Collingwood, is a matter of historical investigation into the path of inquiry taken by whoever asks the question. Perhaps the presupposition was: “Either all men have mothers or this is not the case”, in which case it looks like a candidate for an absolute presupposition. It might, however, be: “I have a mother” — supposing this, the poser of the question was, let’s say, led to an inquiry into generality. That presupposition certainly is not a candidate for an absolute presupposition; “Do I have a mother?” is a perfectly meaningful question, arising perhaps from the presupposition: “Some men have mothers”.

At any rate, Collingwood proposes that if we dig deep enough into the chain of questions and presuppositions leading up to any proposition, we will get to an absolute presupposition. Thus we end up with a complex like: A0!Q1?A1!Q2?A2!Q3?A3. The absolute presupposition A0 (I use bold font to indicate absoluteness) gives rise to question Q1, whose answer, A1, gives rise to question Q2, etc. When this whole complex is placed into the function C(*), it yields truth if the questions indeed arise from the answers, the answers are right, and the ultimate presupposition is in fact made. If C(A2!Q3?A3) yields truth, then there must be something involving an absolute presupposition, of the form C(A0!Q1?A1!Q2?A2!Q3?A3), that also yields truth.

Collingwood’s reasoning is not entirely explicit, but there seems to be a decent argument that absolute presuppositions cannot be the answers to any questions.

In standard logic there is room for debate concerning the degree to which logical deductions must begin from asserted axioms; thus the trade-off between axiomatic systems and natural deduction methods. But in the logic of question and answer, it is clear that for any question to arise at all something must be presupposed. Every chain of thought thus begins ultimately from an absolute presupposition.

But a chain of thought must presumably also end if it is to be a complete thought. Suppose, in the above example, that A3 gives rise to a new question, Q4, whose answer is A0. A0 then gives rise to Q1, whose answer gives rise to Q2, etc., until we find ourselves again at Q4. To this the answer is A0 and we begin the whole cycle again. What is happening here is that a function is taking itself as an argument: A0!Q1?A1!Q2?A2!Q3?A3!Q4?* is being taken as an argument in A0!Q1?A1!Q2?A2!Q3?A3!Q4?*. This leads to a nightmare of recursion akin to Borges’s variation on the 1001 Nights, where one fateful night Scheherezade begins to tell the tale of the 1001 Nights.

This may not lead to any formal contradiction. But I think it’s safe to say that it’s not a great look. An absolute presupposition can give rise to a series of questions and answers, which, terminating in a final answer, form a complex that can then be placed into the function C(*), to yield truth or falsity under the right conditions. If the chain turns into a nightmare recursion we never get to anything we can place into C(*).

It appears that Collingwood abandons his own principles when he states that “Every metaphysical question either is simply the question what absolute presuppositions were made on a certain occasion” (49). But in fact this is the basis of Collingwood’s argument that metaphysics — the science of absolute presuppositions — can only be an historical science. We cannot begin from our own absolute presuppositions to form chains that lead to questions to which our own absolute presuppositions are the answer. But we can form chains that lead to questions to which the absolute presuppositions of people in the past were answers.

If, e.g., A4 was an absolute presupposition that was made in the past, then the chain A0!Q1?A1!Q2?A2!Q3?A3!Q4?A4 does not have to become nightmarishly recursive; here, for us, A4 is not functioning as an absolute presupposition (though it had better not lead to a question whose answer is A4). Once we get to A4 we can follow the chain of thought followed by those who took it as an absolute presupposition.

Suppose A4 to be “every event has a cause” — something that, according to Collingwood, was generally presupposed in Kant’s time but is no longer generally presupposed. Once we get to A4we can then follow the Kantian questions and answers that bloom from it: …![So there can be no primary event]?[There can be no primary event]![So the universe has no beginning in time]?[The universe has no beginning in time]![But doesn’t this lead to a contradiction, since it can also be shown that the universe must have a beginning — First Antinomy Thesis argument]?[The only possible resolution is found in Transcendental Idealism]. The last statement is the right answer to the question asked, and so the whole complex is true, but this does not mean that the last statement is itself true. A different chain, involving a question about the absolute presuppositions of a different period, would form a false complex if it terminated in the same statement.

Thus Collingwood finds it naive when historians of philosophy (or philosophers doing amateur history of philosophy) ask whether the statements made by philosophers in the past are true or false without examining the complexes in which those statements are parts. To assess a statement, one must (as Collingwood would come to say) ‘reenact’ the chain of thinking that led up to it.

Collingwood’s other conclusion is interesting: we can identify the absolute presuppositions of past ages, but not those of our own. We can’t state our own absolute presuppositions, since “every statement that anybody ever makes is made in answer to a question”, and our own absolute presuppositions can’t be answers to any of our own questions for fear of nightmarish recursion. Unlike those who will come after us, we have no hope of knowing what our absolute presuppositions are. But we can know by Collingwoodian logic that we must have some, and we can gain some insight into what they might be like by studying history.