David Rose On Symmetrical And Transitive Relations

David Rose wrote to sysfling on 14 Apr 2024, at 12:02:

Later in the chapter, Michael reveals that he is indeed talking to knowers of formal logic...

‘The relations of projection and expansion, which (when combined with parataxis and hypotaxis) constitute the ‘logical’ component of a natural language, are not reducible to elementary logical relations of a non-linguistic kind...’ (p460)

His use of symmetrical and transitive is indeed taken from formal logic...

A symmetric relation is a type of binary relation. An example is the relation "is equal to", because if a = b is true then b = a is also true.

Transitive relation, a binary relation in which if A is related to B and B is related to C, then A is related to C.

This usage is not explained, although the discussion is hard to understand without knowing it. Which makes things a little confusing for us benighted non-knowers. 

So Christian may like to adjust or explain this table and discussion for IFG5. While status and sequence are SFL categories, the use of symmetry and transitivity here are not.

This is pretty significant, as these terms are used to define parataxis and hypotaxis on p452, and a series of caveats on p460. Eg, ‘although each implies the other, they are not identical in meaning, because while parataxis is a symmetrical relationship, expansion is not’. Which is why I suggested to Jing that

My friend, John, ≠ John, my friend, ...

(in my ignorance)

 Blogger Comments:

[1] This is misleading because it is not true. The Halliday quote merely points out to the linguist reader that the logical relations of natural language are not reducible to the logical relations of designed systems.

[2] This is misleading because it is not true. This usage has been explained in all four editions of IFG. For example, Halliday & Matthiessen (2014: 452):

In principle, the paratactic relation is logically (i) symmetrical and (ii) transitive. This can be exemplified with the ‘and’ relation. (i) ‘salt and pepper’ implies ‘pepper and salt’, so the relationship is symmetrical; (ii) ‘salt and pepper’, ‘pepper and mustard’ together imply ‘salt and mustard’, so the relationship is transitive.

[3] This is misleading because it is not true. All four terms are used as properties of taxis in SFL Theory, as the table makes clear.

[4] To be clear, Rose had argued that the two were not equal on the basis of parataxis:

The thing about parataxis is it’s not reversible (realised by sequence), whereas hypotaxis is reversible (realised by status). So these two aren’t equivalent...

My friend John, ≠ John, my friend

but, as his Halliday quote explains, the asymmetry is in the expansion relation, elaboration, not in the paratactic relation.

David Rose On Parataxis

David Rose wrote to sysfling on 13 Apr 2024, at 15:53:

The thing about parataxis is it’s not reversible (realised by sequence), whereas hypotaxis is reversible (realised by status). So these two aren’t equivalent...

My friend John, ≠ John, my friend

and again at 20:11:

Funnily enough I was thinking of another line from the same tea party

they cried out when they saw Alice coming

...which is hypotactic and reversible (though not logically symmetrical). In contrast,

they saw Alice coming and then they cried out

...is paratactic and not reversible (which is what I meant).

Blogger Comments:

[1] This misunderstands the distinction between parataxis and hypotaxis. Because parataxis is symmetrical, my friend, John does imply John, my friend. Halliday & Matthiessen (2014: 452):

Parataxis is the linking of elements of equal status…. Both the initiating and the continuing elements are free, in the sense that each could stand as a functioning whole. In principle, the paratactic relation is logically (i) symmetrical and (ii) transitive. This can be exemplified with the ‘and’ relation. (i) ‘salt and pepper’ implies ‘pepper and salt’, so the relationship is symmetrical; (ii) ‘salt and pepper’, ‘pepper and mustard’ together imply ‘salt and mustard’, so the relationship is transitive.

Hypotaxis is the binding of elements of unequal status… . The dominant element is free, but the dependent element is not. The hypotactic relation is logically (i) non-symmetrical and (ii) non-transitive. For example, ‘whe n’: (i) ‘I breathe when I sleep’ does not imply ‘I sleep when I breathe’; (ii) ‘I fret when I have to drive slowly’ and ‘I have to drive slowly when it’s been raining’ together do not imply ‘I fret when it’s been raining’.

[2] To be clear, in terms of parataxis, they saw Alice coming and they cried out imply they cried out and they saw Alice coming. It is the introduction of the logico-semantic relation of time (then) that backgrounds this paratactic symmetry.

[3] To be clear, this cannot be what Rose originally meant, since there was no temporal relation in his original example of parataxis my friend, John.