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I'm writing an essay on a (very old) functional exposition of judgement. I note that two functions of the mind respectively provide what is functionally equivalent to the statements

'If a particular, P, bears the mark, M, then P is an instance of the universal, U'.

and

'P bears the mark M'.

which collectively constitute the input of another function, which outputs the propositional judgement

'P is an instance of U'

Put simply: the first two propositions are only analogous to representations which do not need to be, and likely aren't, explicit (i.e. they're not something we're necessarily cognizant of having). However, the third one isn't meant to be analogous. It's exactly the sort of thing we could hear ourselves thinking (e.g. 'That thing is a tree').

Are there delimiters (parentheses, fonts, etc.) that convey that what they delimit is a proposition? Alternatively, are there delimiters that convey that what they delimit is functional, or analogous to something else, or otherwise able to convey the difference between the first two statements and the third statement?

The easiest thing to do would just be to state the difference. However, my professor's a big of using notation wherever there's a convention for it (even a weak convention). I'm also asking for the sake of my own curiosity.

(I acknowledge that this question straddles cognitive science and linguistics, but given the close relationship of the two disciplines to each other, and that the question is about the notation related to a linguistic object (a proposition), it seemed appropriate to ask it here.)

Thank you

-Hal

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    This would actually be better on Philosophy SE, since it's basically about conventions in philosophy of language (a proposition is not a linguistic object, it's a logical / philosophical one). – user6726 May 11 '17 at 16:19
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Are there delimiters (parentheses, fonts, etc.)
- that convey
-      that                         is a proposition?
-           what they delimit

Yes, there are, and you used three of them in your question.
They're called Complementizers, and they serve to introduce various kinds of subordinate clauses. Almost all of these clauses represent propositions, hence are abstract noun phrases.

Note that this is English grammar, not logical notation. If you want formalization, you need look no further than composition of functions. Your third sentence is a straightforward y = f(x), but the first two together are y = f(g(x)). I.e, there's a hidden variable (and a function g producing it) that's involved in choosing y, given only f and x.

It's always possible to posit a hidden property; otherwise metaphors would be impossible.

As for your specific formulations, obviously there are special meanings attached to terms like individual, universal, mark, bear, and instance, so I can't say anything about them. I'm curious about whether bearing the mark M refers to an actual identifiable mark, or merely a nonterminal node in a decision tree.

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