The Thoughts Of Hume In Systemic Functional Linguistics [7]

Russell (1961: 638):

It is a mistake to suppose, as many philosophers do, that the ideas of mathematics 'must be comprehended by a pure and intellectual view, of which the superior faculties of the soul are alone capable'.  The falsehood of this view is evident, says Hume, as soon as we remember that 'all our ideas are copied from our impressions'.

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From the perspective of Systemic Functional Linguistic Theory, the ideas of mathematics constitute the semantics (meanings) of that field: a domain.  Halliday & Matthiessen (1999: 323):

… the semantic correlate of a contextual field is a domain. When we model the ideational semantics of a particular field, we create a domain model. … Domain models are variants of the general model. A particular domain model specifies which of the semantic systems in the overall model are activated in a particular contextual field: the ideational meanings that are “at risk”. Each field thus has its own semantic profile, which can be seen against the background of the overall semantic potential. … If we then switch our point of vantage, the overall model appears as a generalisation across the full range of such field-specific varieties.

From the perspective of Systemic Functional Linguistic Theory, our ideas are meanings of the semantic system, and these originate from the impact of the environment on the organism.  Halliday & Matthiessen (1999: 17):

The view we are adopting is a constructivist one, familiar from European linguistics in the work of Hjelmslev and Firth. According to this view, it is the grammar itself that construes experience, that constructs for us our world of events and objects. As Hjelmslev (1943) said, reality is unknowable; the only things that are known are our construals of it — that is, meanings. Meanings do not ‘exist’ before the wordings that realise them. They are formed out of the impact between our consciousness and its environment.

Halliday & Matthiessen (1999: 609):

… what is being construed by the brain is not the environment as such, but the impact of that environment on the organism and the ongoing material and semiotic exchange between the two.

Halliday & Matthiessen (1999: 612):

Thus meaning arises out of the impact between the material and the conscious as the two facets of a child's ongoing experience.