This is more of a place holding note-to-self but if anyone has suggestions on some writing that has already be done down this line let me know.
Can we explain the appearance of analyticity by constructing a holistic notion of synonymy?
Lets accept that the body of knowledge confronts experience as a whole.
Knowledge confronts the acceptance of statements as well. Perhaps this is reduced to the experience of “thinking that it is true that snow is white.” Perhaps on some more abstract level. Not sure it matters.
In any case two statements are synonymous if their acceptance causes identical revisions in the body of knowledge.
To accept “John is bachelor” causes identical revision as to accept “John is an unmarried man”
How can we know when revisions are identical? By the test of contradiction:
A statement S has identical revision to a statement Q iff
- The acceptance of S causes revision
- The acceptance of not-Q causes revision
- The atomistic acceptance of [S, not-Q] causes no revision
Example:
I accept that “John is a bachelor” and my body of knowledge adjusts to accommodate this proposition.
I accept that “John is not an unmarried man” and my body of knowledge adjusts to accommodate this proposition.
If I accept “John is a bachelor. John is not an unmarried man” no net adjustment occurs to my body knowledge.
The second acceptance has undone the first acceptance and left no change.
Thus these two statements are contradictory. If a statement is contradictory with the logical inverse of another statement then the two statements are synonymous.
Now analytic statements are simply statements which pick out synonymy.
Example:
We have just discovered that “John is a bachelor” contradicts “John is not an unmarried man”
We can conclude John is a bachelor is synonymous with “ It is not the case that John is not an unmarried man”
Pass through to “John is an unmarried man”
Now, “John is a bachelor” is synonymous with “John is an unmarried man”
Such a condition tells us that the predicates are a two-tuple under analyticity.
So we may write Analytic(“is a bachelor” , “is an unmarried man”)
This is equivalent to saying the statement “A bachelor is an unmarried man” is analytic.
Simple tests seem to confirm:
[S,not-S] always contradicts thus statements are synonymous with themselves.
Logically analytic statements always contradicts thus S and not(not-S) are always synonymous.
Creature with kidney, creature with a heart does not contradict under the above test.
- “John is a creature with a kidney” implies revision
- “John is not a creature with a heart” implies revision
- “John is a creature with a kidney. John is not a creature with a heart” implies revision.
- No contradiction.
Do we have at least the appearance of analyticity?
Note: there is a problem with acceptance and revision but I think this can be cleared up by requiring only one candidate statement to induce revision and then making synonymy reflexive.
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Tuesday ~ May 1st, 2012 at 10:18 am
amaeryllis (@amaeryllis)
I like the revision theory, but I’m not sure how well it can work with our imprecise language. For example, I disagree with: “To accept “John is bachelor” causes identical revision as to accept “John is an unmarried man.”” Unmarried is a much broader word than bachelor–bachelor implies never married, while unmarried includes divorced and widowed. John can be unmarried and not be a bachelor (but not a bachelor and not unmarried). “All bachelors are unmarried” is analytic because bachelor necessarily is included in the set “unmarried.” But I wouldn’t call them synonyms.
Much easier with Ps and ~Ps.
Tuesday ~ May 1st, 2012 at 10:32 am
Jacob Hartog
Ain’t language statistical and approximate rather than logical and analytic? Or do we think there be a Platonic form beneath these shrouds?
Tuesday ~ May 1st, 2012 at 10:37 am
Eli
If you have not already read it, Gödel, Escher, Bach has lots on isomorphisms and meaning.
Tuesday ~ May 1st, 2012 at 11:52 am
BSEconomist
I agree iwth amaeryllis. The problem, it seems to me isn’t so much having to do with compound statements as the fact that language is “coarser” than the world it describes. The act of description is not computable in the Turing/Church sense and that implies that your “revision” function will not be either. In turn that means that analyticity would not either.
The problem here, of course, is not that two statements cannot be synonymous as your example suggests (in fact the coarseness helps with that particular problem), rather it is that you cannot verify that two statments are synonymous. The attempt results in an infinite series of checks.
Tuesday ~ May 1st, 2012 at 12:13 pm
Arthur
Look, i don’t know logic very well, but can you accept P and not-Q if P and Q are synonymous?
Do they cancel each other, or you have a contradiction in your knowledge and now everything is possible?
Sorry if i’m being stupid, as i said, don’t know logic.
Wednesday ~ May 2nd, 2012 at 6:22 am
Karl Smith
The problem is how to know if P and Q are synonymous.
Tuesday ~ May 1st, 2012 at 4:45 pm
Jeff
I’m not sure what your goal is with this. If you want to know about the foundations of logic, there is a great deal of work on that. On the other hand, none of this is remotely realistic as an account of how the human mind works, where beliefs come from or how they change, nor as a theory about how language is anchored in meaning.
Wednesday ~ May 2nd, 2012 at 6:29 am
Karl Smith
So, the goal is to account for the appearance of analytic statements, that is things that are true by definition.
On whether or not it is a “realistic” account then that in part depends on what you mean by realistic. It is highly unlikely that this method mirrors what is going on inside the human brain.
However, if what is going on inside the human brain is logically consistent then there should be some way to write it out logically.
The classic example is a pool player. We doubt that the process that goes on in a pool players mind is in fact analogous to trigonometry. Its probably a set of rules of thumb based on angles, lighting, etc. However, if the player actually puts the balls into the pocket there should be someway to describe this in terms of trig.
If we cannot do this then this suggest either pool players are just really lucky or the rules of trig are wrong.
Similarly, somehow it really seems like their are analytic statements. Further, people can reliably pick them out. This suggests there is some logically consistent way to define at least the appearance of analytic statements though Willard Quine casts serious doubt on whether or not there are in fact analytic statements.
Wednesday ~ May 2nd, 2012 at 2:30 pm
Nate W.
I think this is a non-starter, Karl.
First, your definitions seem to be happening at the wrong level. At best, what you’re constructing are definitions of synonymy and analyticity at the level of an idiolect (synonymous-to-John, analytic-for-Susan, etc.), when what you want is definitions at least at the level of a language. (synonymous in English).
Second, I think the prospects of defining the notions of synonymy and analyticity in terms of their causal upshot just isn’t going to work unless you assume what you’re trying to prove. Take two logically equivalent sentences. Say X and not-not-x. Or, better, x and not-not-not-not-not-not-x. These are logically equivalent sentences, but they may not have identical impact on my belief revision because, as it happens, I have a hard time keeping track of the “nots”. So these sentences might, as a contingent, factual matter, have different impacts on my belief revision. “Oh no,” you say, “that can’t happen. If you don’t correctly keep track of the nots, then you aren’t accepting a logically equivalent sentence”. But that’s just a way of admitting that you aren’t interested in all the revisions caused by accepting a sentence, you’re only interested in the revisions caused by its correctly assessed content. But then you can’t take two sentences and determine whether they are synonymous by looking at what revisions they cause, because you don’t know what caused revisions to pay attention to until you know whether the sentences are synonymous.
Third, how do you handle the empirical findings in behavioral economics/psychology that have demonstrated that logically equivalent options elicit different responses when option A is phrased in terms of achieving gains and option B is framed in terms of avoiding losses. These are cases of same content, different logical revisions.
Third, I’d like to hear more about what counts as synonymous here. Are the sentences “Clark Kent is about to open a box of Kryptonite” and “Superman is about to open a box of Kryptonite” synonymous? They would definitely elicit different reactions from Lois Lane, who would be humdrum about the first, but panicked about the second.
Four, “triangular” means having three angles and “trilateral” means having three sides. Not synonymous. Being an angle and being a side are different things, after all. But since all triangles are trilaterals and all trilaterals are triangles, everything true of triangular polygons is true of trilateral ones and vice versa. So the revisionary upshot of incorporating a sentence about triangular polygons should have the same revisionary upshot as a similar sentence about trilateral polygons. But these two sentences are not synonymous.
Sorry, that’s a lot to digest. How familiar are you with the philosophical literature on synonymy and analyticity? The obvious first stop on these issues is Quine’s “Two Dogmas of Empiricism”, but you may already be very familiar with that.
Wednesday ~ May 2nd, 2012 at 2:53 pm
Nate W.
I think I made my second point above, poorly. Here’s another stab.
Assume you have two systems with identical starting beliefs. The systems differ, however, in that the second system has a logical fail rate of 10%. Ten percent of the time, if the systems contains “If A, then B” and receives A as an input, it fails to derive B. The first system has a 0% logical fail rate. If it contains “If A, then B” and it receives A as an input, it always derives B. So these two systems could both receive A as an input (i.e. synonymous inputs), and yet make non-identical revisions. So you obviously want to rule out systems the second type. You want idealized revision systems. But what do you mean by idealized ? It seems to me that “idealized” here just means “treats synonymous inputs identically”. But then you can’t define “synoymous” in terms of such systems’ behavior. It doesn’t move the ball forward to say that synonymous statements are just those that are treated identically by systems that treat synonymous statements identically.
Wednesday ~ May 2nd, 2012 at 3:51 pm
Karl Smith
Nate:
I think all your points are correct.
My thought with this is not that it is an avenue to resurrect analyticity itself but to explain the appearance of analycity.
So, its not important that the statements be analytic in English, only that the speaker is making a clear and distinguishable difference between statements that she considers synthetic and statements that she considers analytic.
What I “think” is the useful turn here is that its not the impact of evidence on the belief that matters but the impact of the belief on the entire web of belief.
So, when I say “Unmarried man is just what a bachelor means” implicit there is both a “to me” and what I am saying is that I perform a revision that using these two terms in a contradictory manner.
On Clark Kent, I think the proof is in the pudding as it were. A person who does not distinguish will say no Clark Kent just *is* Superman.
On Triangle and Trilateral. I would have to think on this.
(John is drawing a triangle. John is not drawing a trilateral.)
This actually causes me to pause and attempt to imagine a non-trianglar trilateral. But, I fail. What does that mean. I think it means they fall under synonymy here. But, I am not sure.
Wednesday ~ May 2nd, 2012 at 4:52 pm
Nate W.
Okay, two things. First, it’s not clear there’s anything to explain here. “Analytic” isn’t a term in general use by the population. It’s only in use by a very particular sub-set of academics, and it’s not clear to me that use is uniform even across this (small) set. So it’s not clear to me that there’s much of anything to explain.
But let me grant you that we could introduce the term to a group of non-users, give them a few examples of analytic sentences like “All bachelors are married”, “Everything red is colored”, etc. and this newly initiated set would classify new instances fairly uniformly. So there’s something genuine to explain. But explaining that sort of uniformity of use seems to me pretty easy to account for. They’re most likely just using “analytic” as a proxy for “necessarily true”. Or “statement that I would not give up regardless of the empirical evidence” or “statement I can’t imagine being false”, or “statement whose negation doesn’t make any sense to me”. Why aren’t those perfectly good explanations that do all the work that needs doing?
Wednesday ~ May 2nd, 2012 at 6:02 pm
Karl Smith
The competent user argument is one hook, but more profoundly I think is that we had philosophers going on about analyticty, seemingly communicating with one another and attempting to build a complete philosophical system based on this concept.
Is it plausible that the whole time they were speaking of nothing? Just gibberish?
Now, consider the easy answers to what they were saying
Necessarily true: well, what does that mean? Surely not necessarily linguistically true because then we would have true analyticity.
Would not give up: Ok. But, after Quine wouldn’t many of us say that we would give them up. Yet, has the distinction suddenly blurred? Are we now confused about which statements are and are not analytic? Maybe in a forced sense, but I think most philosophers if pressed could reliably pick out analytic statements.
I cannot imagine being false: Same as above
Whose negation doesn’t make sense to me: What exactly is this supposed to mean. if I say “Some bachelors are married” do you not understand what I am asserting? I suspect that you not only understand it but understand it to be false. As clearly as if I had said “snow is not white”
Thursday ~ May 3rd, 2012 at 12:54 am
reluctant philosopher
Cool idea. Clearly this is a relation on beliefs, and so if only by stipulation a possible synonymy relation. But it may not be one with which you are entirely happy. Let my belief corpus be S, and suppose it includes no belief about object X, does include the belief that ‘For all x, if P(x) then Q(x)’ , but does not include either ‘If ~P(X) then ~Q(x)’ nor any belief that entails this belief when conjoined with ~P(x). Let my belief corpus be S. I then add P(x) to my corpus, which becomes SU{P(X)}, and revise according to modus ponens, to get SU{P(x),Q(x)}. I then add ~P(X) to my corpus, rejecting P(X) to get the new corpus SU{~P(X),Q(x)}. Since I do not believe that ~P(X) implies ~Q(X), I do not retract Q(x). And thus, on your synonymy relation, P(X) is not synonymous with P(X).
Thursday ~ May 3rd, 2012 at 10:49 am
mwnl
Don’t you mean that two sentences are synonymous for a person P at time t, if at time t, for P, the two sentences have identical implications (t or f) for the sentences held true by P?
If you do, you haven’t defined analytically true for P until you have determined for each implication, whether that truth value is analytic or synthetic for P at t, revising as necessary the remaining set. You have an infinite regress.
In short, we can decide at t to hold a sentence true and revise other sentences, or hold a sentence as false and revise a different set of sentences, changing at t the (a or s) status and thus synonymy as required.
That was Quine’s point. We decide synonymy and t or f status for a sentence at t for P at the same t.
Wednesday ~ August 29th, 2012 at 2:06 pm
lph
A book, Analyticity and Substantive Inquiry (by Lucas P Halpin), defines analyticity in terms of acceptance (endorsement) and forced revision, rather than in terms of truth (a semantic notion/correspondence). No appeal to synonymy is made. However, some of the ideas in that book are loosely similar to ideas that appear in the initial post on this blog.