Gottlob Frege · Mathematics
Frege insisted that logic and arithmetic are objective, not descriptions of how anyone happens to think - and he armed this with the <em>context principle</em> (ask for a word’s meaning only within a sentence) and a Platonism of objective <em>thoughts</em>, waging a lifelong war against the ‘psychologism’ that would reduce logical laws to laws of the mind.
In Frege’s day a powerful idea was in the air: that logic is really a branch of psychology. The thought is seductive. Logic concerns thinking, and thinking is a mental process; so surely the laws of logic just describe how the human mind works when it reasons correctly - the natural laws of thought, discoverable, like other mental laws, by observing minds. This position is called psychologism, and Frege regarded it as the single most dangerous confusion in philosophy. His objection is simple and devastating. The laws of logic are not descriptions of how we do think - people constantly reason badly - nor even of how we must think as a matter of mental compulsion. They are laws of truth: they say what follows from what, objectively, whether or not any mind ever grasps it. That the angles of a triangle sum to two right angles was true before any geometer was born and would be true if minds had never evolved. Logic, for Frege, is not about the thinker. It is about the truth the thinker is trying to reach.
Frege’s defence of objectivity was not merely negative; it came with a positive method, crystallised in one of his three governing principles in the Grundlagen: never ask for the meaning of a word in isolation, but only in the context of a sentence. This context principle is aimed squarely at psychologism. When we ask ‘what does “four” mean?’ in isolation, we are tempted to go looking inside ourselves for an accompanying idea or image - and find, of course, that no image is the number four, whereupon meaning seems to dissolve into private mental fog. Frege blocks this at the source. The unit of meaning, he insists, is the sentence: words have meaning only through the contribution they make to the sentences in which they occur. To fix what ‘four’ means, we do not introspect; we explain the truth-conditions of the sentences containing it. Meaning is thereby pulled out of the private mind and located in the objective, shareable content of sentences. The context principle is Frege’s tool for keeping meaning public.
Frege sharpened the case with a distinction between the idea and the thought. An idea (Vorstellung) is a private mental item - a sense-impression, an image, a feeling. Ideas cannot be shared: my visual image of green is mine alone, incomparable in principle with yours, and it comes and goes with me. If the contents of our thinking were ideas in this sense, then when you and I ‘agree’ that two plus two is four we would in fact be entertaining two different private items, and would never really share a single thought at all. Science, disagreement, and even translation would be impossible; there would be as many arithmetics as there are minds. A thought (Gedanke), by contrast, is public: it is the very same content grasped by different people at different times in different languages, which is precisely why we can share knowledge, argue, and build on one another’s work. When a teacher conveys the Pythagorean theorem to a class, she does not implant thirty private images; she directs thirty minds to grasp one objective thought. The whole enterprise of science presupposes that thoughts are common property - and that, Frege argues, is the final refutation of psychologism.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned Frege’s three guiding principles - separate the logical sharply from the psychological, ask for a word’s meaning only in the context of a sentence, and keep the concept-object distinction in view - and his argument that logic concerns objective ‘thoughts’ in a third realm, not the workings of any mind. Exp…
Leads to John Stuart Mill.
Begin this lesson →epoché — a humanities education that remembers you.