Saturday, May 19, 2012

A brief history of existence

Yesterday’s post caught a few people by surprise. What is the background to all that? What is the ‘thin’ conception of being? Etc. Of course there is a background to this, and it is large, and it should be part of the baggage of anyone studying modern analytic philosophy. So here is a brief history of the subject.

We start in the fourth century B.C. with Aristotle and his Perihermenias, his treatise on the second operation of the understanding, where two simple concepts are combined to form a proposition. In the tenth chapter he has an obscure paragraph about the verb ‘is’ being predicated as a ‘third elements’. In the scholastic Latin which was used to translate Aristotle’s Greek, this is rendered as tertium adiecens, literally third adjoinment or third adjective. What on earth does that mean? Thomas (in the middle of the thirteenth century) makes a valiant attempt to explain it in his commentary on the work. He says that sometimes the verb ‘is’ is predicated by itself in a proposition, such as in “Socrates is“ i.e. Socrates exists. By this we signify that Socrates really exists. That is predication of ‘is’ as a second element, i.e. existence predicated of itself, existence as a predicate. At other times it is not the main predicate but is joined to the main predicate to connect it to the subject, as in “Socrates is white.” Here we are not asserting that Socrates exists, but rather attributing whiteness to him by the verb ‘is’. Hence, ‘is’ said to be a third element, not because it is a third predicate, but because it is a third element or word in the proposition.

Roll forward to the eleventh century and to Anselm and his so-called ontological argument. This was an argument to prove the existence of God through logic alone, by proving that the concept of God has the concept of existence built into it. He argues as follows
… it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist;. and this being thou art, O Lord, our God. (Proslogion chapter 3).
I won’t go into the tortuous logical details of the argument now, but the argument is generally thought to be invalid, and the reason is generally thought to be treating the verb ‘is’ as a predicate, i.e. as the main predicate in the sentence, rather than as a copula or ‘third element’ which simply joins the real predicate (being wise or being good) to the subject.

The whole issue was extensively discussed in the late thirteenth century, but this is rarely if ever mentioned in modern philosophy courses because of the assumption that all philosophy began in the early modern era as a byproduct of the glorious enlightenment process. Thus students tend to hear about the ontological argument in the context of Descartes, rather than Anselm or thirteenth century philosophers. Descartes writes in his Meditation V:
… the existence can no more be separated from the essence of God, than the idea of a mountain from that of a valley, or the equality of its three angles to two right angles, from the essence of a [rectilinear] triangle; so that it is not less impossible to conceive a God, that is, a being supremely perfect, to whom existence is awanting, or who is devoid of a certain perfection, than to conceive a mountain without a valley.
Note that Descartes was writing in Latin, another fact that is sometimes overlooked. This is because we associate the enlightenment process with the modern romance languages rather than Latin, which belongs to the dark ages before the early enlightenment.

Roll forward again to Kant, the glorious eighteenth century philosopher of the high enlightenment, who famously tells us (in The Critique of Pure Reason, A 598/B626) that existence is not a ‘real predicate’. This was a period when all good philosophers wrote in German (Sein* ist offenbar kein reales Praedikat).  'Existence' is not a determining predicate which enlarges the concept of the subject to which it is added, in the way that ‘white’ enlarges the concept ‘man’ by increasing its intension but reducing its extension. When philosophers talk about existence not being a predicate, it is usually Kant’s discussion they have in mind. (Maverick has strong views about this, but I’ll pass over those for now).

Kant had little influence on modern logic, however. The main development of the question whether ‘existence is a predicate’ comes in the middle of the nineteenth century. I have a bit about the history in a discussion of Brentano here, and see also this contemporary paper here. Brentano argued that we can always translate any sentence containing the verb ‘exists’ into one that does not contain it. Thus ‘a sick man exists’ translates to ‘some man is sick’. This idea is the direct ancestor of the modern view, often associates with Quine, that existence is what the existential quantifier expresses. It is uncertain how it got into modern predicate logic, as there are at least three contenders, namely Brentano, Frege and the American Charles Peirce. Probably it was Peirce via the German logician Ernst Schroeder. I wrote a short piece on this for Wikipedia years ago, which is still there (permalink).

So the issue of detail is whether the verb ‘is’ is simply a copula that joins subject to predicate. This is essentially the view embedded into modern predicate calculus and the use of ‘existential’ quantifier. The general and important position that it underlies is whether we can prove the existence of God, or not. If existence is merely ‘someness’, i.e. if ‘existing thing’ is equivalent to ‘something’, the ontological argument does not get off the ground. But if it is something larger or ‘thicker’, the argument at least stands a chance. Thus large things sometimes hang on small things.

One day I should write this history up properly. Every discussion I see has some part of the history, without taking a view of the whole.

*I literally just noticed that Kant is using the German 'sein', which is the infinitive of the German verb 'to be'.  English philosophy tends to follow Latin philosophy in using the distinct verbs 'to be' (esse) and 'to exist' (existere). That distinction is a subject in its own right, which I will pass over for now.

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Blogger Jason Hills said...

Thanks, Ed.

I am familiar with this history. You have clarified for me what is being discussed, existential instantiation in formal predicate logic. In that case, I do not have much to say, as logic is a place a non-specialist dare not tread.

I would comment that historically-focused programs do teach the history, but those programs are usually not analytic programs. I met a student the other day who told me that her institution requires students not to take history until they are seniors, which I found rather odd.

2:58 pm  

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