by JLS
for the GC.
From wiki, 'therefore' entry:
"[the horseshoe is] part of a mathematical formula, and [is] not considered to be punctuation. In contrast, the therefore sign is traditionally used as a punctuation mark, and does not form part of a formula."
which allows for it getting dropped. There is a conversational oddity about this. To use Grice's example:
"Jack is an Englishman and he is, therefore, brave"
----
I submit, along with D. Frederick, that dropping 'therefore' just does not do for us:
"Jack is an Englishman and he is brave."
----
Why?
Various explanations. But none of them would make 'therefore' TOO analogous with 'if p, q'. In "if p, q" you don't assert either p or q. In "p; therefore, q" you assert both. "if" is a subordinating particle; 'therefore' is an inferential otiosity (unless it isn't).
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I agree that "therefore" (conjunctive adverb, right) indicates an inference, or conclusion really; therefore, "therefore" serves a purpose, and lacking it, the sentence is a mere assertion, not inferential. As a rhetorical device "therefore" (and most con. adverbs) may become trite, however, and seems a trifle "undergraduate-y"--though many a writing teacher would be pleased to have students make it to even Strunk-White hack competency, and use the transition words and inferences correctly (along with the sentence structure and punct.). So it's another contextual thing. You probably won't note too many "therefores" in the prose of FS Fitzgerald, but will see 'em a plenty in a Roger Scrutonizer.
ReplyDeleteYes. It is a trick. On top of that, as Kramer may testify, lawyers use 'therefor' sans the 'e' with yet another conventional implicature in mind. "Give me your watch, and I'll give you my cell-phone therefor".
ReplyDeleteYes, 'therefore' is hardly used by F. S. Fitzgerald. I tend to see the 'therefore' as too interjectional.
As in:
"Jack is an Englishma, he is -- therefore! -- brave."
I suppose the 'there' HAS an explicit element to it -- the thing cannot JUST mean via conventional IMPLICA-ture and be vacuous at the EXPLICA-ture level --. The 'there' may compare with:
"There was a house on the hill", where it seems to have meant, "There -- out there -- over there -- a house on the hill existed."
---
So that accoutns for 'there'. The 'for' is trickier. It must mean 'on account of'. "She cried because it hurt". "She cried for it hurt".
"There, she cried for it hurt".
This would render the syllogism:
It hurt
---
Therefore she cried.
---
Ryle thinks that 'so' has the same function:
"Today is Monday; so, tomorrow is Tuesday -- right?"
Ryle in his "If, so, and because" -- this is the GRICE club, not the Ryle club -- so there is a mandatory critical notice on him -- he fails to amuse me -- considers that what he calls
a "so" sentence or a "therefore" sentence (he does mention 'therefore') are NOT assertions. I think Grice would say that they are second-floor assertions (in Strand 5 of WoW).
"Jack is an Englishman; he is, therefore, brave".
I asserted that Jack is an Englishman.
I asserted that Jack is brave
---- (D. Frederick objects those two points and thinks that 'therefore' is merely 'echoic' of an argument).
BUT:
I do "NOT" assert that his courage follows from his country of origin. I implicate it, says Grice.
Oddly, if we do say:
"Jack is an Englishman, and Jack is brave; and the latter follows from the former", or "... and the former entails the latter", we DO say it and assert it.
But Ryle says that players of the game of logic do NOT use 'follows from' or 'entails' -- spectators of the game of logic do. (He was so-antilogic it hurt).
So, "p; so, q" may be MORE than the assertion of p and q, but it does include such assertions, in a normal, non-echoic, use, rather than mention, scenario.
The 'so' is a polite-marker, like is 'therefore'. It's there to please your logic instructor.
My guess is that "therefore" does not appear in formal logic because it is properly considered a relationship, but appears as something like an operator.
ReplyDeleteThe relationship in question is what we now have as "|-" or "|=" and have discussed elsewhere, and the use of those symbols may therefore account for the lack of "therefore"s.
There is another notation for rules, particularly in sequent calculi.
|- A, |- A ) B
=============
|- B
(the "horseshoe" for JL)
so we have a multiplicity of modern upstarts stealing
the role of "therefore".
RBJ
.
ReplyDeleteWell, . . works just as well for the conclusion, as -> does for the horseshoe, and first order logic worked quite well (er, as long as you don't self-referential-ize...Church-ize) lacking the latest tarskian or Steinford notation. The point is that logic often enters rhetoric at some point--many points--and "therefore" thus serves to indicate a conclusion, even if it's not "necessary in all possible worlds".
that's ∴
ReplyDeleteBoth J and R. B. Jones are right. It would seem, as if, to echo Grice, first paragraph of "Logic and Conversation" we would have him say:
ReplyDelete"It is a commonplace in logic that there is a diverence between 'not' and ~ and 'and' and /\ and 'or' and \/ and 'if' and ) and 'all' and (x) and 'some' or 'at least one' and (Ex) and 'the' and (ix)"
"and ... "therefore" and '/-'.
It's good he stuck with the seven devices as he did which already ARE a mixed bag: ~ is unary truth functor, /\, \/ and ) are truth fucntors, (x), (Ex) and (ix) are quantifiers. But they ALL belong in a molecular formula. We want use 'logical' constant because the phrase hurts!
-- But what about 'therefore' and '/-'? While I agree with Jones that logicians don't use 'therefore' because they use '/-', or as J adds, the 'three dots' ∴, one may still wonder.
I would think -- D. Frederick was aiming a Fregean reply to this elsewhere -- a contrast seems to be between Grice on 'therefore' which merely implicates conventionally something (an inference, no less) AND '/-' or "∴" which do not merely implicate that. In fact, they do NOT implicate that. They 'say' it. They assert it.
One problem is that when we want to talk 'c follows from p' or 'p entails q', or 'p ent q', we get the cry from Ryle: "Formal lingo not allowed", or rather "Meta-lingo not allowed" for Ryle argues that 'so' and 'therefore' are good particles, like 'because' -- used by players of the game of logic. Whereas he argues and he HAS some point to this, that 'follows from' and 'entails' belong elsewhere -- the jury at the grand stand and general spectators of the game of logic he has it in the online essay on "If, so, and because" repr. in Black.