Analytic a posteriori truths

According to Wikipedia, many philosophers starting with Kant (who invented the terminology) have rejected the category of analytic a posteriori truths. In tonight's post, I wish to discuss the likelihood that all propositions that we consider analytic do indeed fall into this category and do so because language is learnt. This post follows on from a previous post I wrote titled 'The analytic-synthetic distinction". I shall also discuss the possibility that regret is an evolutionary adaption and say something more about my own life. I fear that this blog is no longer as interesting as it once was, that I no longer write as well as I once did, but I have insightful thoughts in my head and I want to get them down in written form. I hope that the reader will take the time to read a somewhat stylistically unflashy essay and engage with the argument it makes even if you find the subject matter a little abstruse.

We need to start with some definitions. We need to define a priori, a posteriori, analytic, and synthetic. One standard definition of an a priori truth is that such a truth is known independent of experience. A posteriori truths are known by virtue of experience. The distinction between a priori truths and a posteriori truths is epistemological. Analytic truths are propositions that are true by virtue of the meanings of the words they contain while synthetic truths are propositions that are true by virtue of the way they relate or correspond to facts in the outside world. The distinction between analytic and synthetic propositions is linguistic. All interesting propositions are synthetic; analytically true propositions don't tell us anything we don't already know. Combining these two distinctions, we arrive at four possible categories of proposition:

1. Analytic a priori truths. These are in essence tautologies.
2. Analytic a posteriori truths. Kant rejected this category as being self contradictory.
3. Synthetic a priori truths. These are interesting truths that we know without recourse to evidence from the real world.
4. Synthetic a posteriori truths. These are truths which tell us something we didn't know about the world in which we live in, based on empirical evidence.

Because Kant rejected the second category, in his view all truths are analytic a priori, synthetic a posteriori, or synthetic a priori. The empiricists, such as Hume, had believed that all knowledge is acquired from experience and would thus have rejected the idea of synthetic a priori knowledge if they had known this term for it; Kant however devotes much of his great work The Critique of Pure Reason to defending the idea that we are born with innate knowledge, that we possess faculties that yield true interesting true beliefs independently of experience. In particular, Kant argued that we are born with an understanding of space, time, and causality that is nontrivial, interesting. Kant also argues that the truths of mathematics are synthetic a priori truths. I shall come back to mathematics later in this essay.

A simple way to clarify the distinction between analytic a priori truths and synthetic a posteriori truths is through a famous, classic example. Consider the proposition, "All bachelors are unmarried".  This statement cannot be refuted, is true in all possible worlds, because the word "bachelor" means "an unmarried man". It is also uninteresting because it can be re-expressed as the tautology, "All unmarried men are unmarried." This proposition, according to Kant and those who followed him, is an analytic a priori truth. Now, suppose I carry out interviews with one hundred bachelors and, based on these interviews, state, "All bachelors are lonely." This proposition is interesting, tells us something we didn't already know, and is based on empirical evidence. Accordingly, we describe it as synthetic a posteriori. Unlike the first proposition, the second can be refuted. If we find a single bachelor who isn't lonely, it will have proved the second proposition to be false.

At the opening of this essay, I signalled that I was going to argue in favour of a completely different position, that the propositions (or beliefs or units of knowledge) we describe as analytic are all known a posteriori. To justify this highly unorthodox opinion, I wish to talk about speech acts and definitions.

The theory of speech acts was most famously first presented by J.L. Austin, who also called them performative utterances. Speech acts come in an enormous number of flavours, from requests, questions, and answers, to promises, declarations, and much more. Speech acts do not describe the world but are intended to change the world or themselves bring about change. It is the second sort, the speech acts that themselves change the world, that I am interested in. Suppose a marriage celebrant says, "I now pronounce you man and wife". This speech acts changes the world – two people who were formally single are now wedded. Suppose a judge says, "I find you guilty and sentence you to ten years hard labour." Again this speech act changes the world – the accused is now a criminal and a prisoner. Suppose a boss says, "I now promote you to head of the human resources division" – the nature of his employee's job has now changed. Somewhat controversially I believe that when a psychiatrist says, "I now diagnose you schizophrenic" this similarly changes the world. The patient is now subject to a completely different legal and social discourse than he did previously, including the expectation that he or she will need to take medication for the rest of his or her life.

It has been a long time since I read Austin or his most important follower John Searle but, from what I can remember, they do not discuss what I believe to be the most important kind of speech act – definitions. Suppose I say, "I define the adjective 'clugy' as designating people who experienced psychosis but recovered." My utterance does not describe the world and is neither true nor false – but if you accept my definition we can then talk meaningfully about people who are clugy and people who are not in ways that will be true or false. Although my act of definition is neither true nor false, if you accept my definition, a statement like "That clugy woman recovered" will then be analytically true. If a doctor says, "I define schizophrenia as a lifelong condition that requires daily medication (like diabetes)" and another person says, "Sue recovered from schizophrenia", that second statement is analytically false, because it contradicts the definition of schizophrenia established by the doctor. All analytic propositions are derived from definitions that are learned at some time. Suppose my friend Sally has picked up the belief that the word 'bachelor' means 'a lonely man'. If she says, "All bachelors are lonely" it will be analytically true for her but synthetic, and potentially false, for me; if I say "All bachelors are unmarried" it will be analytically true for me but synthetic, and potentially false, for her. The fact that words can mean different things to different people undermines Kant's whole notion that analytic truths are known a priori without any relation to lived experience.

In my previous post about the analytic-synthetic distinction, I argued that Kant's project fails for three reasons. First, different people define words in different ways. Second, the meanings of words can change over time. And third, language is learnt. Even if we suppose for the moment that everyone in a language group defines all the words in their vocabularies in the same way and always has, language must still be learnt and this requires definitions. We can demarcate out two different types of definition, what I call specific definition and diffuse definition. Specific definition is when a person is told explicitly the definition of a word or looks it up in a dictionary. Diffuse definition is when a person, typically a child, infers the meaning of a word from the way adults are using it. The first type of definition is necessary for big, complex words (like disponible) while the second type of definition is how we typically learn normal, everyday words like 'cat' and 'table'. Because most of the words we know we learn in the second way, the line between synthetic truths and analytic truths becomes vague. According to the dictionary, cats are defined as carnivorous and so the proposition "All cats are carnivorous" is analytically true – but if we tell a ten year old child, a child who has no difficulty distinguishing cats from other animals, that her pet tabby will become unwell if it eats fruit or vegetables, it may well surprise her. The statement, "Cats are carnivorous," will be synthetic for her even though it is analytic for me.

All analytic truths are known a posteriori because we must learn the meanings of words from others in our environment at some time. Kant argued that mathematical truths are a priori synthetic. But I am going to argue that mathematical truths are a posteriori analytic because they also depend on definitions. This is a bold and controversial stance to take but I have been thinking about this for a while and finally want to lay out my theory.

Suppose I define the word 'two' by saying, "I define the word 'two' as being 'one plus one'". This definition is neither true nor false – it is another speech act. I then define the word 'three' by saying, "I define the word 'three' as being 'two plus one'". I go on to define the word 'four' by saying, "I define the word 'four' as being 'three plus one.'" Finally, I define the word' five' by saying, "I define the word 'five' as being 'four plus one." We now consider the question "What is three plus two?" By substitution, "Three plus two" is "Three plus one plus one". By substitution again, "Three plus one plus one" is "Four plus one". And this is "five". Thus "3 + 2 = 5" is a tautology. And thus an analytic truth.

I wish to make three points concerning this theory. First, of course, we don't have a different word for every possible whole number. For numbers bigger than twenty, we use a kind of algorithm to work out their names. We say, for instance, 'one million, twelve thousand and sixty three," sorting the number verbally into groups of different sizes. If we did have an entirely different word for every possible whole number, let alone every rational number, we would be required to have an infinitely large vocabulary, an impossibility. Second, arithmetic doesn't just depend on definitions and substitutions – there are also rules such as the commutative law (a + b = b + a) and the associative law ( a + (b +c) = (a +b) + c ). It may well be that mathematics is like language, that the fundamental axioms of arithmetic are analogous to Noam Chomsky's universal grammar. Finally, people may object that definitions plus rules can't explain geometry, such as the law that the internal angles of a triangle sum to 180 degrees. I admit that I haven't worked out all the details of the theory yet.

I'll finish this post by summarising its main contention. I am arguing that all analytic truths, truths that depend on meaning, are a posteriori rather than a priori because the meanings of words must be learnt. I have argued that even mathematics can be described as analytic a posteriori. When I began writing this essay, I also intended to discuss regret from an evolutionary perspective but this post is long enough already. I'll talk about it in a later post. We'll see down the track.