Unavoidable authoritativeness, self-reference and the empowering constraints of science and mathematics

In his Metaphysical Horror (which I reviewed in my previous post) Leszek Kolakowski wrestles with the problems of self-reference: using statements that refer also to the statement itself. He also wrestles with unavoidable authoritativeness (though he does not express it as such). Particularly when the two run together, as they constantly do in philosophy. So any claim about knowledge has an unavoidable authoritativeness to it: hence the problem with claiming to know that we do not know anything. Similarly with the claim that it is true that there is no truth; that there is no objectivity. And so on. Complete scepticism swallows itself due to the problems of self-reference and unavoidable authoritativeness.

The unavoidable authoritativeness of truth comes from the purpose, the intended function, of language. The first point of language is to talk about the world. Language is stuck with a notion of truth because it matters whether we get things correct about the world or not. That is why we have language at all. All the functions of language are derivative of its truth function. Including the very functioning of language itself, since language cannot function at all unless there are commonly understood meanings and references. 'This word' means X is a truth statement. Language will not let us do without truth.

Nor will being thinking beings let us do without knowledge. Building up, at least mostly, correct beliefs about what is, is central to functioning in the world, starting with simple survival. Any belief that is true, where our believing it is directly connected to it being true, is knowledge. The truth function of language is about conveying knowledge. Truth and knowledge are thus inseparable.

The concepts of ‘truth’ and ‘knowledge’ have inescapable authority to them. (Hence the importance in sabotaging such ‘success’ words for certain sorts of scepticism, as David Stove wittily dissects in Anything Goes.) In the face of this inescapable authority, philosophy also has to deal with being self-referential: making claims that cover the claim being made.

A fundamental problem that creeps into much philosophical thought is treating truth as an absolute feature of statements: as if a statement is either completely true or it is false. I call this the “bucket of shit” view of truth (if one has a bucket of shit and adds a teaspoon of wine, one has a bucket of shit: if one has a bucket of wine and adds a teaspoon of shit, one has a bucket of shit) where any degree of falsity makes a statement simply false. This surely does not treat seriously the reality that, when we think, we abstract from the world. There is no reason not to think statements can be partly true. Indeed, in ordinary reasoning, we use the concept of partial truth (and thus partial falsity) all the time.

If we stop treating truth as an absolute feature of statements, then knowledge stops being absolute as well. Knowledge can be partial (in the sense of being incomplete) and thus subject to being superseded by more complete knowledge, yet still be knowledge. We no longer needed to so bothered, for example, by Newtonian physics being superseded by Relativity. Or by our understandings and perceptions of the world being irredeemably incomplete. Newtownian physics is no longer simply false: it is simply more partial than we were previously aware.

If we are no longer attempting to defend a notion of truth as an absolute feature of statements, much of the sceptical urge loses any target on which it can get purchase and so its inherent self-contradictions become more salient. But, if we do not hold on to a notion of truth as an absolute feature, does that also abolish the question of ultimate foundations? Well, does not any answer to that question imply ultimate foundation? To raise the issue of ultimate foundations is to imply some sort of answer that is ultimately authoritative. I may be unimpressed with all the wrestling with the Absolute that Kolakowski sets out in Metaphysical Horror, but that is because I am not convinced that is a good way to conceive of ultimate grounding. The underlying question(s) are surely the inevitable stuff of philosophy.

I agree with Kolakowski that philosophy cannot look to the success of science as a solution to its own problems, for the success of science is precisely because of its constrained nature. Science constrains itself by what sort of questions it asks, what it attends to, and what answering methodologies it will accept. As Kolakowski points out, philosophy attends itself to the entire universe of meaning and reference.

It is in failing to look at the power of science’s constraint—and to grasp the inevitable ambit of philosophy—that creates the problems I have with the use of the mathematical analogy for logic, particularly for constructing symbolic logic. Mathematics constrains itself in what it attends to (numbers and other mathematical objects) in a way logic does not. It is one thing to formalise—in particular, to formalise via symbols—interactions between numbers (however strange some of the numbers involved) and other mathematical objects. This is what mathematics does, and what gives its great power.

It is quite another to attempt to formalise (in both the weaker, but especially, the stronger sense of symbolic logic) the entire universe of reference. Once logic attempts to operate as if it is like mathematics, then the self-reference and unavoidable authoritativeness problems bite. This then leads to logical paradoxes, where authority is claimed for statements that self-refer, or overlap in reference, in ways that are paradoxical.

Hence the problems with formal logic my teacher David Stove drew attention to, particularly his essay “The Myth of Formal Logic”. Mathematics is authoritative about numbers, number-connected things, other mathematical objects and specific sorts of connections between them. It lacks the problems of authoritativeness over an unbounded ambit of reference, which includes problems of self-reference, that logic, and philosophy generally, has.

Philosophy is itself, it is not some larger manifestation of mathematics or science. Nor is it some sort of analogue to either.

ADDENDA This post has been adjusted slightly for clarity.