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
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.
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.