Post lecture notes for students of IR 6901: (Week 4,a) Frege’s Begriffsschrift and the language of pure thought

By Farish A. Noor ~ March 29th, 2010. Filed under: Lecture Notes.

A. Frege and Analytical Philosophy:

The tradition of Western philosophy which began with Socrates/Plato and Aristotle took off from the starting point of the dialectic and the questioning of the world around us. From the pre-Hellenic philosophers to the early modern philosophers of the 17th century (Descartes, Hobbes and Locke) the aim of philosophy was to pose questions about the nature of the world around us and to question the basis to all claims to knowledge/epistemology. By the time of Descartes and Hobbes, the suspicion of sensory knowledge pushed them towards subjective nominalism and solipsism, sometimes in the most extreme and narrow forms. However philosophy kept apace with the developments in natural sciences, and by the time of Gottlob Frege and Bertrand Russell, philosophers were posing questions not only about the world, but crucially about the language that we use to describe the world.

Russell and Frege began to objective turn to the world as objects to be discussed and known, but by then were convinced that many of the problems faced by philosophers derived from the very language they used to describe the world around them. Accepting the nominalist premises of Hobbes and Locke, they accepted that our knowledge/experience of the world was framed through language, but also insisted that everyday language was flawed for a number of reasons:

1. The grammar and syntax of ordinary language had evolved historically with the societies that used them, but the rules of grammar and syntax were thus also historically and socially-determined and were laid down as a result of custom and practice. Some (if not all) of these grammatical norms were responsible for leading philosophers to false conclusions about relations in the world, which Frege and Russell argued had nothing to do with the logical relations of things in the world per se, but rather were the result of norms of language-use.

2. As a result of the grammatical biases and norms above, language as it is used in the everyday context actually prevented us from seeing the world as it is, and as such language ‘dressed up’ reality in such a way that language provides us with embellishments of/on reality rather than reality itself.

Rejecting everyday historically-evolved language on the grounds of its anthropomorphism, subjectivism and perspectivism, Frege argued that ‘the thought is something impersonal’, and that the real task of analytical philosophy was to free us from the subjective constraints of language. For Frege and the first generation of analytical philosophers, this was the real task of philosophy: to focus on the logical structures of things in the world by clarifying the use of language so that language may reflect and analyse these logical relations clearly and precisely.

Frege’s background was that of a mathematician. For much of his early life he focused on the problem of logic and logical relations in mathematics and found that in mathematics one could develop a mode of logical annotation that addressed problems of pure thought, that were not encumbered by any subjective attachments. As he developed his project he also began to address the questions that had been posed by successive generations of philosophers but found that their mode of doing philosophy was constantly slipping into illogical and nonsensical propositions and problems thanks to the language they used. His attempt to invent a new logical formulation – which he called the Begriffsschrift – was an attempt to rectify that problem by creating a new language of logical annotation that was free of such subjective biases and nonsensical concepts/entities.

B. The Begriffsschrift as Logical Calculus:

Frege’s Begriffsschrift was first published in 1879 and it was presented as a novel form of logical calculus inspired by mathematical calculus. Its striking features were:

1. It was a form of notation where general signs/symbols (a,b,c) replaced proper names/nouns and symbols were also used to signify qualities/predicates;

2. It did not conform to conventional modes of written script in the manner in which it appeared more geometrical in form – i.e. it did not conform to conventional modes of linear writing/proposition-construction.

3. It was economic in its use of symbols and governed by logical rules of representation that were simplified to suit general propositions.

The first point was already a convention among logicians during Frege’s time, who were already accustomed to substituting symbols for proper names/nouns and whose logical systems were modelled on mathematical equations.

The second point is of interest as Frege was trying to show that conventional (linear) modes of proposition/sentence construction was misleading in the way in which its linearity suggested (and imposed) a certain linearity in thought/thinking too. Frege argued that such linearity did not exist in the world we speak of, and so there was no reason for such linearity to appear in propositions about the world. Furthermore the linearity in written script suggesting a ‘chain of signification’ which superficially conformed to the idealist notion of ‘chain of thoughts’ found in Hobbes and Locke, and that too was misleading he argued. Sluga (1980) notes that Frege’s Begriffsschrift was meant to be a logical language that was written, and not spoken. (pg. 71)

This was a radical break from the traditional of logic that went back to Aristotle and as Sluga (1980) notes ‘post-Aristotelian logic begins only with Frege’. (pg. 65)

The third point gets to the heart of Frege’s contention against language-use in the conventional, everyday context: He argued that much of conventional language consists of grammatical norms that have been normalised to the use of words/signs that were part of language-construction; but which have also become (mistakenly) the objects of philosophical speculation. For instance, the rather simple one-sided predicate sentence ‘The sky is blue’ is misleading for Frege because when the word/sign ‘blue’ is removed we end up with ‘The sky is’, where ‘the/is’ ends up being an object for philosophical speculation (such as in the case of the questions ‘what is the sky’, ‘does the sky exist’ etc – i.e. leading to questions of existentialism and ontology)

Frege insisted that in cases of the sentence above, the only two objects to be signified are ‘sky’ and ‘blue’, and what was needed was a more precise logical annotation that clearly signified the proposition about the blueness of the sky (along the lines of sky=blue).
The aim of the Begriffsschrift was precisely to create such a precise logical annotation that was simple, economic, consistent, clear and logical.

The Begriffsschrift was therefore a simple and logical notation that was meant to be free of the ‘gaps’ in language (word/signs like ‘the’, ‘is’) that allowed for unwarranted suppositions and presuppositions (all deemed subjective and culture/context-bound) to creep in. He hoped that in such a logical and clear notation system there would be no blanks or gaps between objects referred to/signified that would allow for unclear definitions and imprecise meaning/signification; in the same way that mathematical equations left no room for ambiguity. (Frege did refer to his system as ‘a notation based on the formula language of arithmetic’ (Begriffsschrift, pg. vii.)

Frege was also reacting to the older philosophical notion that thinking was a subjective process that required judgement, which in turn was a mental/psychological process that involved the mental apprehension and construction of propositions and their meanings; a sort of manual labour. This was an idea that went back to Hobbes, Descartes and Locke, who held that understanding a proposition meant collecting it together in a chain of signs/words that had to correspond to a chain of thoughts/ideas.

But Frege argued that this was a psychological process and had more to do with psychological states rather than truth-statements and truth-claims. He held the view that understanding propositions/sentences about the world meant ‘grasping the thought’, and that grasping a thought was not the same thing as creating a thought and/or establishing an order among its parts.
He noted, for instance we can still grasp a thought even when denying it: I.e. denying the truth of the proposition ‘Superman can make himself invisible’ amounts to denying the truth-claim of the proposition, but it does not mean that we fail to grasp the meaning of the proposition. (In fact, it is the opposite: it is precisely because we grasp the meaning of ‘superman can make himself invisible’ that we can claim that it is false.)

C. Sense and Reference

Frege’s criticism of conventional everyday language rested on his claim that in the subject-predicate relations of language (as it has been traditionally understood) assumed that intentionality and the intention of the speaker was important. For A to say something to B it was assumed that B had to understand or be able to intuit what A was meaning to say.
This, for Frege, opened up language to a range of ambiguities and uncertainties as it meant that the truth value of some propositions lay in the intention of the speaker A (i.e. what A wanted to convey to B) and that to ascertain that truth value one had to ‘get into the head of A’ so to speak.

Frege’s argument (which would later be taken up by Wittgenstein in his Tractatus Logico-Philosophicus) was that sentences had sense and reference, but that the sense of a sentence lay in what it was trying to depict/picture, and that its function was to be either true or false. These were the two cardinal rules of his logical annotation, that:

All propositions contain sense in what they depicted/represented.

All propositions had only one reference: they were either true or false. Thus the reference of ALL propositions was their truth value.

This then helps us understand the purpose of the logical annotation of the Begreffsschrift: The logical-geometric formulae of the annotation were simplified, clear models of real logical relations (of things in the world) with all traces of subjectivity, perspectivism and bias removed (or so Frege hoped). If we see the logical annotations of Frege as such logical models, then we can understand Wittgenstein’s claim of logical propositions as pictures/models of the world better.

One of the consequences of Frege’s stand of logic and his theory of logical annotation (that was meant to get to what he called ‘the kernel of the logical relations of things in the world’) was its curious form of anti-empiricism.
Frege was not discounting objective reality, but was taking the view that to speak of reality as if its ‘essential’ characteristics could be debated about was a nonsense. The purpose of philosophy was not to get to the essential truths of the world but rather to depict correctly and clearly the logical relations of things in the world as we experience them. To attempt anything further would be (1) one of the errors of grammar (a somewhat odd though bold claim, as if all of speculative philosophy was a huge grammatical mistake!) and (2) be taking language beyond where it could go.

But because ordinary everyday language has historically evolved and the subjective biases of language have become normalised and sedimented, it would be better – he argued – to invent a purely formulaic simple logical annotation that could be made to refer to things and to refer (make truth claims) to the world.

Further reading:

Hans D. Sluga, Gottlob Frege, Routledge, The Arguments of the Philosophers series, Routledge, London, 1980.

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