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| Today, on foot after a work related meeting |
Please note: Blogger changed some normal font to small, without my permission. Will attempt fix...
Another friendly reminder of who really owns this site...
Langer explains: 'Obviously one cannot introduce any relation, at random, into any universe whatever; for instance once cannot say that 2 is older than 3, or that one house is wiser than another. Such statements would be neither true no false; they would simply be meaningless.' (69-70).
Meaningless philosophy. A logical and reasonable, universe of discourse is a means of preventing philosophical error. This can of course be translated into religious studies and theology work.
'to the North of' (70). This is symbolized by 'nt2''. (70). But a small font 2 is used. Langer adds this one dyadic (mathematical) relation to a previously presented example in the text. This I reason is why a small 2 is added to 'nt'.
We need to be careful not to read anything into the 'nt2' not intended in this context of universal discourse. The use of numbers to letters complicates matters, but then again it serves as a lesson that with propositions and conclusions, terms and terminology must be understood and evaluated in context to avoid error.
'This is the only relation admitted to the formal context; all propositions must be made solely out of elements A, B, C, D and the relation 'nt'. (70).
She calls 'a relation which belongs to the formal context', a 'constituent relation of discourse'. (70)
Basically the propositions in this constituent relation of discourse are considered legitimate. (70).
'K=int 'houses'' (69).
int=identified with
Logicians generally denote the universe of discourse with the letter K. (69).
Cited: 'K (A, B, C, D,)' (69).
'K (A, B, C, D,) nt2' (70-71).
The four houses are north of...
My add:
K (A, B, C, D,) st2
The four houses are south of...
I am a trained philosopher of religion and not a major in mathematics. I did work with statistics with United Kingdom, academic surveys. But this review is as much about my learning as my teaching.
The equations are becoming more complex and I will work through them to make sure I have a correct understanding and then share where relevant.
I put together the possible propositions A nt B, B nt A, etcetera and arrived at twelve, thankfully before seeing that Langer also had twelve. (77). She states that combined with 'nt' there are sixteen propositions. This is not in my opinion adequately explained, but I would gather A nt A, B nt B, C nt C, D nt D are included (71). She points out that these four all fail as not true. Something cannot be north of itself.
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
