Enough has been said regarding the axiom of internal relations. At this point I wish instead to draw attention to a problem concerning the very communicability of the Relations Thesis. As should be clear from the last sentence of the previous section, involvement itself is a non- symmetric relation. The Relations Thesis appeals to this particular non-symmetric relation in order to make the universal claim about all relations I wish to make, but other non-symmetric relations would have done just as well. My initial informal construal simply had it that relations relate what their relata are. Elsewhere, I have spoken of relations implicating their relata and of relata grounding the pertaining of relations. I have also taken Russell’s claim that relational claims are made true by a corresponding complex object which, among other things, consists of the relevant relata, as tacit endorsement of the Relations Thesis. If I might avail myself of the language of facts without this being taken as indicative of a commitment to the existence of facts qua semantic abstracta, I’d also be just as happy to construe my thesis in terms of supervenience:
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The Relational Facts Supervenience Thesis – All relational facts necessarily supervene either solely upon facts sufficing for it to be the case that there are the relata those relational facts relate, or upon such facts in combination with other facts.
But inasmuch as I invoke any such relations in formulating my theses I might be said to fall short of communicating what I wish to communicate, as it is not my intention to highlight an entailment between all relations and some particular relation, involvement, supervenience or whatever, but rather, to highlight a fact about the structure of relations themselves. The Relations Thesis says an involvement relation necessarily pertains between the pertaining of any relation and stuff that accounts for the being, subsistence, or whatever of its relata. It might be thought possible for someone to agree that this is so but miss the point entirely, thinking the pertaining of the involvement relation itself doesn’t implicate its relata in the manner I intend to claim all relations do. It involves them, as this is supposedly the case with regards to the pertaining of any relation whatsoever, but the relation of involvement itself isn’t relata implicating. Obviously, it won’t do to make a further clause that involvement implicates its relata, as implication is but another relation the pertaining of which might be thought not to incorporate its relata in the manner I intend to convey. The same goes for supervenience. The supervenience relation which the Relational Facts Supervenience Thesis claims holds between all relational facts and the sufficiency facts it cites might be thought not to involve, implicate, incorporate etc, both the relational fact and the sufficiency facts. Every attempted ostension towards features intrinsic to relation instances might instead be taken as saying all such instances possess some incomprehensibly wholly extrinsic relational property. Having said all this, I think it highly unlikely that any of the foregoing formulations have induced any such Bradleyan vertigo. I’m sure every construal of the thesis has been taken in the manner intended. I am sure of this because I think nobody so forlorn a thinker as to think relational facts are thus disunified. It is nonetheless noteworthy that were it the case that
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someone conceived of relations as being other than how I intend the above theses to say they are, there is every chance that no attempted formulation of my thesis would suffice to
communicate what I intend to that person. I might do well to abandon language in favour of some non-discursive form of demonstration, say, hitting him or her with a stick like a Zen master. Perhaps I might thereby show what I cannot say.
There is in fact a case to be made to the effect that the purported communicability issue under discussion hinges upon a distinction between saying and showing. Regarding the
Wittgenstein of the Tractatus, Sellars (1962 p. 12) writes, “If one so uses the term ‘ineffable’ that to eff something is to signify it by using a name, then Wittgenstein’s view would be that what are ordinarily called relations are ineffable”. Claims which, due to our ordinary
language’s lack of grammatical perspicuity, purport to mention them merely “call attention to those features of discourse about what is or is not the case in the world which ‘show
themselves’, i.e. are present in a perspicuous language not as words, but in the manner in which words are combined” (Sellars 1962 p. 9). In Sellars’s perspicuous language, Jumblese, to represent that n objects satisfy an n-adic concept, for any n>1, one simply concatenates their names somehow, without invoking any further signs. To represent that a single object satisfies a monadic concept, one writes the name for that object in some particular style, colour or font. The claims ‘a is higher than b’, ‘a is fat’, ‘a is between b and c’ and ‘a is leaning’ might be respectively expressed as follows:
a
b
a
bac aJumblese’s perspicuity is born of its allegorical structure – with the objects as with their names – and it implicitly shows by way of that structure what I explicitly say with the above theses.
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