On an Argument Due to Arthur Collier


In the sorely underappreciated tract Clavis Universalis (1713), Arthur Collier seems to have been the first to find in the old shopworn antinomies of metaphysics an obvious and natural resolution for all such aporias, worth quoting at length:

As for instance, suppose a man should advance the notion of a triangular square. Or suppose two persons contending about the attributes of this strange idea: the one arguing from the idea of a triangle, that it has but three angles; and the other contending that it must have four, from the idea of a square; what could any reasonable stander-by conclude from this, but that the thing they are disputing about is nothing at all, even an impossibility or a contradiction? Nay, these disputants themselves must needs close in with this manner of arguing, and that on two accounts. First, in that this manner of arguing accomodates the difference between them, and salves the honor of both. For by this, both appear to be in the right in the precise points they are contending for; and wrong only in something which they are both equally concerned for, viz., the supposition of the being of the triangular square, which is the thing supposed by consent between them. But chiefly, secondly, in that the person who argues in this manner must be compelled to have the law of reason on his side, and may compel them, on their own principles, to assent to his conclusion. This is done by granting to each party his point, namely, that a triangular square is both triangular and quadrangular. This done, they have nothing to do but to answer each other’s arguments, which it is here supposed that they cannot do. By this, therefore, each grants the other to be in the right. So that for a stander-by to grant both to be in the right is, in this case, a demonstration that they are both in the wrong; or in other words, that the thing they are disputing about is nothing at all.’

The argument is disarmingly cute, but it cuts: he applies it in short order to resolve two ancient disputes over the finite or infinite extent of the world, and the infinite or finite divisibility of matter. Most attempts at resolving these since Zeno’s day have sought the way out by scrutinizing the concept of the infinite, but since they haven’t gone away by Collier’s day he avoids this fruitless strategy, and instead moves directly to the entirely legal conclusion that if we admit both of these predicates to apply to their respective subjects, the subjects must be nothing at all. One could not apply the term deflationist’ with more justice to any other form of argument in the history of the world.

What I want to note about it is that it operates on the logical level to an ontological conclusion, by a principle that you might call ontological commitment for two’: we can’t allow anything into our ontology whose properties we can’t agree on, and in default of any impossibility proof ruling out the one or the other of the conflicting properties, reason arbitrates that the hypostasis must go. Everything worth preserving is preserved: we agree on what triangularity is, we agree on what squareness is, and we agree than a triangular square must have three angles and Omust have four angles, and we agree that something can’t have both numbers of angles. Therefore, logically, we are both bound to agree that there is no triangular square, and we can all go home happy.

Easy in this case, harder in others: the same argument leads him directly to banish the notion of an external world. Note the qualifier: Collier is at pains to point out that his argument does no violence to everyday empirical reality or the existence of physical things, but only banishes absolutely a transcendental reality which is absolutely external to experience. The point is put much more clearly and directly than it ever is in Berkeley, and therefore with fewer undesirable side effects.

What is striking about this argument from a historical point of view is that it anticipates Kant’s exactly parallel argument by nearly seventy years, and given that it had been translated into German in 1756, it is not out of the question that he had read it. What’s interesting about it from a philosophical point of view is that it treats Kant’s doctrine of transcendental illusion in a much more homely, dialectical way: the source of the difficulty in all dogmatic philosophizing turns out always to lie in what both sides of a dispute have already supposed by consent’, and if we drop the absolute presupposition held in common by both partisans that such a thing is, the argument dissolves. The argument begins over what everybody knows to be’, and concludes only when both parties retreat to maintaining only what each of them can assent to. By this via negativa, we can all avoid error together.

Further Reading:

Arthur Collier, Clavis Universalis

Arthur Lovejoy, Kant and the English Platonists