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My Latest Ponderings: Do Propositions Exist?

December 2, 2019

A typical approach in philosophy tends to take for granted that one central goal in the theory of meaning is to shape our language use so as to be open to truth or falsity. The idea is to make our claims amenable to a logical analysis and deduction for the sake of clarity. The way in which this is usually done is to analyse language relative to some ideal standard of propositional discourse.

In propositional discourse we take from language the assumption that a person is trying to communicate some truth with it and we set about analysing it with this in mind. So lets take someone who utters the sentence: “The world is stationary, because I feel no movement of it.” Firstly we have to forget about the content of the statement and whether we have any agreement, disagreement or emotional feeling towards this content, and focus on its structure alone.

In its pure structure, so says the propositional analysis, we don’t need to think about the context of this statement, who said it, or why, we can isolate the elements into separate claims to make it amenable to a logical calculus of its truth or falsity. So, what we have is a claim that

  1. I feel no movement from the world
  2. If I can feel no movement from the world, then the world is stationary
  3. The world is stationary

We have a premise, that we can determine as true or false, we have an inference that can be true or false, and we have a conclusion that can be three things. True, False or invalid. It is invalid if the inference does not hold from the premises to the conclusion.

In this case, forgetting the content of the claims, the conclusion itself is valid, as formally speaking, 3 follows logically when 1 and 2 are true. The ideal in this direction is a totally extensional approach to meaning, (a project pursued by Quine) so that no semantic issues can muddy the water, and so that logic can be tied tightly with propositional use of language when arguing about truth, philosophy, science and other important subjects.

A couple of critical problems have been found with this approach. On the one side, and the original reaction to this meaning analysis of language as reducible to propositional discourse, was the Wittgensteinian one, which argued a flurry of things together. Firstly, that there is no private language, so meaning is not determined by individuals propositional claims. Secondly, there are in reality no ideal language uses, only a bunch of language games with family resemblances. Thirdly, following from this, meaning as a concept depends on use and context and does not have some transcendent basis to which we can approximate with discourse.

Strawson took up this new linguistic approach with his claim about pursuing descriptive, rather than revisionary metaphysics. The central point he was making with this was to deny a pre given rational privilege to propositional discourse that language should be “revised” to meet up to the standards of, and instead focus on the various everyday and common usages of language and try to navigate through them to analyse the various meanings in context of different language uses. The speech act approach of J.L. Austin is another part of this, and he was the teacher of Strawson.

The other criticism found on the other side of this debate about this approach of an ideal language of propositional discourse, is that it goes too far in trying to separate logic from the content of our claims. The extensional logic cannot be pursued the whole way without taking the meaning out of the whole enterprise. Originally this approach in philosophy of logical analysis had been created by Bertrand Russell as a reaction to the intensional, monistic logic of his predecessors such as Bradley and Bergson. In its place though, Russell offered not a truly extensional system, but what he rather called a plural approach.

A plural approach basically takes it that relations are real and not reducible to identity statements. The hope of the intensional logic, or monistic approach was that all being could be reduced to one subject containing all its predicates as necessary consequences. The problem was that reality was simply not symmetrical in this way. The fundamental asymmetry at the heart of reality and how we represent reality is what was pointed out to them by Bertrand Russell, who noticed that some irreducible relations, such as asymmetrical ones are critical even in basic mathematics and arithmetic. We need these relations to construct mathematics, and so the reality as we have it, simply cannot be reduced to a symmetrical, unified formulation.

The extensional logic goes beyond this unfortunately and takes the meaning out of the irreducible logical relation the whole thing relies on, the notion of implication. When we say something like If A then B, we mean that B is implied by A in some way. There is some inferential connection between the two statements that means something. The problem when we purely extensionalise this is that we have no such connection. For a purely extensional logic, if A then B, is true even when A is false, thus we end up with a world of inferences that are correct and conclusions that are true even though they don’t follow from any given premise.

What we have really here is Not A and Not B, if there is not an A then there can’t also not be a B. Take, if it’s raining, I will get wet. I could get wet for any number of reasons, nothing to do with rain, and it would make this proposition correct and true. The purely extensional propositional claim gives no connection between the conclusion and the premise. In the old fashioned terminology we have a necessary condition for getting wet, but not a sufficient condition.

Of course, we are assuming the correctness of the inference for the sake of argument, it could easily be the case in many circumstance that it rains and I don’t get wet. I could have an umbrella, I could be an inside a house, etc.. But what the general point seems to be here is that an extensional, calculus style approach to logic, makes of the propositional use of language something too ideal and restricted to represent what we mean.

Now, unlike the earlier group of ordinary language philosophers, this groups reaction is not to give up hope and dive into an orgy of language games, but to backtrack and question this extreme extensional analysis of propositional discourse. Perhaps there are propositions and ways to aspire to this type of discourse, but this ideal is not so simple as we had once thought, and will contain some semantic and ontological elements beyond purely formal syntactical, extensional analyses.

Maybe we can continue to pursue a propositional understanding of language. It seems to be the only firm basis for fair and reasonable discussion where both sides are making appeal to an independent arbiter of logic and truth. It seems to me this is a good solid ideal to maintain, even when we discard the puritan extensional framework.

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