Frege’s argument for platonism

0. Introduction

Contemporary platonism (with a small ‘p’) can trace its roots back to Frege, in particular to his 1918 paper Thought. There are many fascinating arguments and proposals in this paper, which is one of the richest in the early analytic tradition. In particular, I want to look at one argument, which is broadly contained within pages 298 and 302. The argument is basically that communication (and science generally) would be impossible if platonism were not true; and clearly communication is possible, so platonism is true. What needs to be defended is the first premise, which links the possibility of communication with platonism. This is what Frege explains in the section I want to focus on.

  1. Thoughts and Propositions 

Frege is setting the scene for 20th century philosophy of language by giving us a very vivid account of a the notion of a proposition. Frege does not use this word however, but uses the term ‘thought’ for this task. Here is how he introduces the notion:

“Without wishing to give a definition, I call a thought something for which the question of truth arises. So I ascribe what is false to a thought just as much as what is true. … The thought, in itself immaterial, clothes itself in the material garment of a sentence and thereby becomes comprehensible to us. We say a sentence expresses a thought.” (p. 292)

Thus a ‘thought’ is what is true or false (something for which “the question of truth arises”), and is what is expressed by sentences. He is quite clear on page 293 that only are declarative sentences express ‘thoughts’ (“Only those sentences in which we communicate or state something”). He goes on over the pages up to 298 to explain how the same ‘thought’ can be expressed by multiple synonymous sentences, (“It makes no difference to the thought whether I use the word ‘horse’ or  ‘steed’ or ‘cart-horse’ or ‘mare’ “), and that indexical sentences can express the same ‘thoughts’. Frege’s example of the latter is that the thoughts expressed when Dr. Gustav Lauben says “I have been wounded”, and when Leo Peter hears this and remarks some days later, “Dr. Gustav Lauben has been wounded”. In each case, different sentences express the same ‘thoughts’.

Thus, by ‘thoughts’, Frege means what contemporary analytic philosophers mean by ‘propositions’, and from now on I will refer to them as the latter.

The question then is what type of things these propositions are. Frege argues that there are two candidate types of thing for propositions to be, before rejecting both of them and proposing a third way.

2. The Outer World

Firstly, propositions might be thought to be ordinary material objects of some sort:

“A person who is still untouched by philosophy knows first of all things which he can see and touch, in short, perceive with the senses, such as trees, stones and houses, and he is convinced that another person equally can see and touch the same tree and the same stone which he himself sees and touches. Obviously no thought belongs to these things” (p. 298-299)

Propositions, like ‘Donald Trump is the president’, clearly often involve material objects (such as the man Donald Trump), but the propositions are not themselves objects. The proposition that Trump is president is not one of those things out there in the world alongside Donald Trump. Thus, propositions are of a different kind than ordinary material objects.

3. The Inner World

Having dismissed propositions being part of the ‘outer world’ of material objects, he considers a a second realm; the ‘inner world’. This second realm is introduced to us by Frege as follows:

“Even an unphilosophical person soon finds it necessary to recognise an inner world distinct from the outer world, a world of sense-impressions, of creations of his imagination, of sensations, of feelings and moods, a world of inclinations, wishes and decisions. For brevity I want to collect all these, with the exception of decisions, under the word ‘idea’.” (p. 299).

Thus, ‘idea’ is a technical term which refers to all the various aspects of experience, such as sensations, feelings, desires, etc. Frege then considers the question of whether propositions could be ideas or not. To do this, he outlines some distinctive features of ideas.

Firstly, in contrast to material objects, ideas are had by bearers. Take some aspect of experiential inner life, such as a desire to eat a cake. It makes no sense to consider this desire existing apart from a bearer who has the desire, such as my desire to eat this cake. It is a metaphysical impossibility for there to be an ‘unaccompanied desire’, i.e. a desire to eat cake somehow drifting through the world without someone who has the desire; desires, just like all ideas, are had by bearers. In contrast, a material object, like a cake, can perfectly easily be considered without any bearer. Indeed, there is no contradiction in imagining the cake being the only thing in existence; an unaccompanied cake is metaphysically possible.

In addition, ideas are metaphysically private. No two people can literally have the same aspects of experience. We can both look at the same lime tree, but the experience each of us has of the lime tree cannot be shared with one another. Frege goes so far as to say that the question of whether two people see the same thing when they both see the same green leaf doesn’t even make sense:

“Now does my companion see the green leaf as red, or does he see the red berry as green, or does he see both as of one colour with which I am not acquainted at all? These are unanswerable, indeed really nonsensical, questions” (p. 299)

These questions are unanswerable, according to Frege, because the term ‘red’ or ‘green’ is being used not to state a property of objects in the outer world of material objects, but to “characterise sense-impressions belonging to my consciousness” and, as such, “it is only applicable within the sphere of my consciousness” (p. 299). When I say ‘red’ I’m referring to a part of my inner sense experience, not an objective property out there in the world. It is metaphysically private.

So ideas are i) had by bearers, and ii) metaphysically private. However, Frege argues that these two properties are not shared by propositions.

If a proposition was an idea, then it would be had by bearers, and it would be metaphysically private. Consider the proposition expressed by the Pythagorean theorem. If that were an idea, then as Frege says:

“…one should not really say ‘the Pythagorean theorem’ but ‘my Pythagorean
theorem’, [and] ‘his Pythagorean theorem’, and these would be different” (p. 301)

The proposition would be had by bearers, just like ideas. In addition, they would be metaphysically private, and this would mean that questions over their truth and falsity would also be metaphysically private. Going back to the example of how colours are private for Frege, this was because a colour, like ‘green’ or ‘red’, is not supposed to be a quality of material objects as such, but a quality of inner mental experience instead. When I see a green field, I have a sensation of ‘greenness’ which is an inner private experience. Thus, it makes no sense to ask whether your experience of greenness is the same or different to mine. Likewise, if the Pythagorean theorem is true-for-me only, then it doesn’t even make sense to wonder if it is false-for-you:

“Then truth would be restricted to the content of my consciousness and it would remain doubtful whether anything at all comparable occurred in the consciousness of others.”  (p. 301).


“If someone takes [propositions] to be ideas, what he then recognises to be true is, on his own view, the content of his consciousness and does not properly concern other people at all. If he were to hear from me the opinion that a [proposition] is not an idea he could not dispute it, for, indeed, it would not now concern him.”” (p. 302)

This leads Frege to make the following conclusion:

“If every [proposition] requires a bearer, to the contents of whose consciousness it belongs, then it would be a [proposition] of this bearer only and there would be no science common to many, on which many could work.” (p. 301)

If propositions were thoughts, then they would be had by bearers, and metaphysically private. If they had those properties, then there could be no possibility of having a common body of science on which many could work together. In short, if propositions were ideas, then science would be impossible.

4. The Third Realm

Here is where Frege draws together the considerations into the positive vision of what a proposition is:

“So the result seems to be: thoughts are neither things of the outer world nor ideas.

A third realm must be recognised. What belongs to this corresponds with ideas, in that it cannot be perceived by the senses, but with things, in that it needs no bearer to the contents of whose consciousness to belong. Thus the thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer. It is not true for the first time when it is discovered, but is like a planet which, already before anyone has seen it, has been in interaction with other planets”

5. Conclusion

This post obviously only just begins to scratch the surface of this idea, but the outline of the argument is hopefully somewhat clear. Frege argues that material objects have the properties of being available publicly and can exist independently of any others, unlike ideas which are metaphysically private and have to be accompanied by bearers to exist. Propositions have aspects of both, being independent of bearers, yet not being ordinary objects in the material world either.

While there are certainly lots of extremely influential attacks on Frege’s basic picture here, most notably by the later Wittgenstein, his position was extremely influential on philosophers throughout the 20th century, such as Russell, (early) Wittgenstein, Husserl, Quine, Gödel, Putnam, Dummett, etc.

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