David Kellogg On Mathematical Equations [3]

David Kellogg wrote to sys-func on 28 April 2023 at 15:27:

This kind of physics does cover Quantum Mechanics, Relativity, Maxwell, Newton, Galileo... The equations are mathematical — i.e. they can be read backwards and forwards, and they are exactly what Yaegan claimed: a different, non-linguistic, semiotic with its own anti-linguistic logic.

Blogger Comments:

[1] To be clear, this is true. In as much as an equation construes the identity of two participants, it can be 'read backwards and forwards'. However, the meanings construed in each case will be different, as demonstrated in the comments of the previous two posts.  

[2] See the comments of the previous two posts for evidence of the misunderstandings on which this conclusion is based.

From the perspective of Systemic Functional Linguistic Theory, mathematics is a field that is realised in (designed) language and (ideographic) pictorial semiotic systems. There are many reasons for interpreting mathematical equations as language rather than as a non-linguistic semiotic system. Two will be provided here.

First, mathematical equations entail a stratified content plane in which wordings realise meanings. On the SFL model, language is the only semiotic system with a stratified content plane (Halliday & Matthiessen 1999: 604):

This deconstrual of the content plane into two strata, referred to in the first chapter, is a unique feature of the post-infancy human semiotic…

The fact that the content plane of mathematical equations is stratified with a lexicogrammar is demonstrated by the fact that, unlike non-linguistic semiotic systems, they can be read aloud. On the SFL model, what is verbally projected is the wording level of content ('locutions').

Second, the only difference between

1. a² + b² = c², and
2. a squared plus b squared equals c squared, and
3. its spoken form

is the mode of expression. All three construe the same wording and the same meaning. If it is claimed that the first is not language, then someone hearing the spoken form (3) would have to ask whether it corresponded to non-language (1) or to language (2), and interpret it differently accordingly.

On the other hand, the claim that mathematical equations are 'a different, non-linguistic, semiotic with its own anti-linguistic logic' goes nowhere in terms of explanatory potential. In contrast, treating mathematical equations as linguistic explains the solving of an equation as the iterated elaboration of an identity relation, and the solution of an equation as the decoding of an unknown Token.

∞

In dismissing all the evidence that invalidates his view, and simply maintaining his original stance, Kellogg has deployed the invincible ignorance fallacy.