Descartes and Frege: a Rationalist theme

One central feature of traditional forms of Rationalism has been a commitment to the existence of non-sensory modes of knowing. Thus, for one central example, Descartes’ Meditations can be read, in part, as a set of instructions for recognising in oneself, and then using appropriately, a power of knowing untainted by reliance on sensory experience or imagination. Thus, Descartes writes:

I have been accustomed these past days to detach my mind from my senses, and I have accurately observed that there are very few things that one knows with certainty respecting corporeal objects, that there are many more which are known to us respecting the human mind, and yet more still regarding God Himself; so that I shall now without any difficulty abstract my thoughts from the consideration of sensible or imaginable objects, and carry them to those which, being withdrawn from all contact with matter, are purely intelligible. (Descartes, 1641: Meditation IV: Of the True and the False.)

The same theme can be found in the work of Gottlob Frege. Frege’s fundamental aim was to gain clarity on the nature of mathematics, especially arithmetic. In pursuit of that aim, Frege thought that we had to recognise a Third Realm—in effect, the realm of the purely abstract—inhabited in particular by numbers and by what he called thoughts. Thoughts, on Frege’s view, are the fundamental loci of truth and falsity, and the contents of acts of judgement. Thus, when it’s claimed that it’s true that 2 + 3 = 5, what is said to be true is the thought: that 2 + 3 = 5. And it’s the very same item that one takes to be true in judging that 2 + 3 = 5.

It’s sometimes claimed that Frege held that the study of language must figure centrally in the attempt to gain clarity on the nature of thoughts. And there’s surely some truth to that claim. However, it’s equally important to acknowledge that Frege held that natural languages reflect thoughts only imperfectly. He held that the basic structures made available by natural languages fail adequately to reflect the most basic structures of thought. (That is one consequence of the infamous puzzle raised by the construction “the concept horse”, which on Frege’s principles cannot be used to denote a concept.) Furthermore, Frege held that the perceptible forms of language, and the effects of language on the imagination that are exploited, for example, in poetry (its “pictorial aspects”), serve to cloud our view of thoughts. The latter theme, of the sensible as disruptive, is especially prominent in the following passage, from Frege’s essay “Thoughts”:

I am not here in the happy position of a mineralogist who shows his audience a rock-crystal: I cannot put a thought in the hands of my readers with the request that they should examine it from all sides. Something in itself not perceptible by sense, the thought, is presented to the reader—and I must be content with that—wrapped up in a perceptible linguistic form. The pictorial aspect of language presents difficulties. The sensible always breaks in and makes expressions pictorial and so improper. So one fights against language, and I am compelled to occupy myself with language although it is not my proper concern here. I hope I have succeeded in making clear to my readers what I mean by ‘a thought’. (Frege, 1918–19: 360, fn.6.)


Descartes, R. 1641. Meditations on First Philosophy, E. S. Haldane and G. R. T. Ross trans.. Cambridge: Cambridge University Press.

Frege, G. 1918–19. ‘Thoughts.” In his Collected Papers on Mathematics, Logic, and Philosophy. B. McGuinness ed. M. Black, V. H. Dudman, P. Geach, H. Kaal, E.-H. W. Kluge, B. McGuiness, R. H. Stoothoff trans.. Oxford: Basil Blackwell.

  1. thonyc said:

    Es kommt mir der Gedanke dass Frege viel über Gedänke gedacht hat.

  2. thonyc said:

    My error, I’m even more illiterate in German than English. It should read “über Gedanken” Sorry!

    • Thanks! Yes, he certainly did. Even about thoughts about thoughts. I guess he thought of them as a sort of discovery of his, and the acknowledgement of which is crucial to avoiding various errors.

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