Gottlob Frege:

Begriffsschrift

What is the meaning of a word?

Background

Gottlob Frege (1848 - 1925) was a German philosopher, logician, and mathematician. He is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Frege essentially reconceived the discipline of logic by constructing a formal system: a propositional and later predicate calculus.

Frege’s project

Frege believed that words were often misleading and led to confusions. His approach to the philosophy of language was based on his interest in arithmetic and maths. He thought he could bring the precision of maths to logic and language.

If it is one of the tasks of philosophy to break the domination of the word over the human spirit by laying bare the misconceptions that through the use of language often almost unavoidably arise concerning the relations between concepts and by freeing thought from that with which only the means of expression of ordinary language, constituted as they are, saddle it, then my ideography, further developed for these purposes, can become a useful tool for the philosopher...

Frege, Begriffsschrift, preface

Frege thought that his ideography, as he called it, would be useful for science. He thought his precise language to ordinary language what a microscope is to the naked eye:

I believe that I can best make the relation of my ideography to ordinary language clear if I compare it to that which the microscope has to the eye. Because of the range of its possible uses and the versatility with which it can adapt to the most diverse circumstances, the eye is far superior to the microscope. Considered as an optical instrument, to be sure, it exhibits many imperfections, which ordinarily remain unnoticed only on account of its intimate connection with our mental life. But, as soon as scientific goals demand great sharpness of resolution, the eye proves to be insufficient. The microscope, on the other hand, is perfectly suited to precisely such goals, but that is just why it is useless for all others.

Frege, Begriffsschrift, preface

Against Locke’s conception of language:

Frege contrasted his approach to the analysis of language with that of John Locke. The key features of Locke’s views of language were the following:

Language is primarily for the communication of private ideas
Words are the names of ideas.
Sentences are combinations of ideas.
The meaning of a word is given by a checklist of descriptions of nominal essences. Locke believed that we could never really know the object because we can’t directly perceive atoms (so we cannot know an object’s real essence).
This checklist of ideas is improved over time as we discover the meaning of words. The nominal essences will gradually converge on the real essences of things.

Frege was critical of what he saw as the psychologism of Locke’s approach, that is Locke’s tendency to reduce everything down to psychological and subjective experience. In a different work, The Foundations of Arithmetic, he laid out three very important principles (which, we will see, marked a real change in teh way philosophy was done).

In the enquiry that follows, I have kept to three fundamental principles:

always to separate sharply the psychological from the logical, the subjective from the objective;
never to ask for the meaning of a word in isolation, but only in the context of a proposition
never to lose sight of the distinction between concept and object.

The Foundations of Arithmetic (1884/1980)

We will look at each of the three in turn:

Always to separate sharply the psychological from the logical, the subjective from the objective

For Locke, sentences are ways to transmit private ideas. For Frege, truths are public. 1+1=2 is essentially a public idea. When someone understands 1+1=2 they are partaking in something public.

Frege thought that Locke failed to distinguish between different types of proposition. Frege’s new concept script relied upon developing a distinction which was described by David Hume:

… we divide all truths that require justification into two kinds, those for which the proof can be carried out purely by means of logic and those for which it must be supported by facts of experience.

Frege, Begriffsschrift, preface

Never to ask for the meaning of a word in isolation, but only in the context of a proposition

Locke thinks that words are names for ideas, but as Frege makes clear, words in isolation, don’t make sense. If someone on the street randomly shouts ‘cheese!’ at you, it won’t necessarily make you think of cheese but it may make you wonder why someone is shouting random words at you.

It is fairly obvious that the context matters to the meaning of a word. The word 'man' means quite different things in these two sentences:

He is a horrible man
Be a man!

(I'm not endorsing the second use! Just using it as an example.)

Discussion

Words may have a meaning only in a context, but does it have to be in a proposition?

For Frege, instead of a proposition being a combination of ideas, he viewed a proposition in terms of an argument and function.

For example, the following formula is an expression of the area of a circle as a function of the radius:

A = πr2

Similarly, we could write something like

Q(x, y)

And this could mean x is the father of y.

The mere invention of this ideography has, it seems to me, advanced logic. ... In particular, I believe that the replacement of the concepts subject and predicate by argument and function, respectively, will stand the test of time.

Frege, Begriffsschrift, preface

never to lose sight of the distinction between concept and object.

Frege thinks that Locke doesn’t distinguish between an idea and the object for which it is an idea. Mill, for example, wrote,

When I say, ‘the sun is the cause of the day’, I do not mean that my idea of the sun causes or excites in me the idea of day

Mill, A System of Logic Ratiocinative and Inductive, bk 1, ch. 2, § 1)

Frege thought that his argument and function approach to logic helps to demonstrate how concepts come about.

A concept is what Locke probably would have called an idea, though a concept is different from an idea in that it is something public, not private. According to the psychological representationalists like Locke, an idea was something private which was identified through a kind of inner-perception.

It is easy to see how regarding a content as a function of an argument leads to the formation of concepts. Furthermore, the demonstration of the connection between the meanings of the words if, and, not, or, there is, some, all, and so forth, deserves attention.

Frege, Begriffsschrift, preface

This is an example of the concept script that Frege produced:

Tasks

Explain and demonstrate what Frege meant by each of the following:
- always to separate sharply the psychological from the logical, the subjective from the objective;
- never to ask for the meaning of a word in isolation, but only in the context of a proposition
- never to lose sight of the distinction between concept and object.
Do you agree with Frege's conception of language? Explain your answer.

#logic

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