|Universal quantification: an operator, which indicates that the following expression is a statement about all the objects in the considered domain. Notation "(x)" or "∀x". Ex. E.g. (x) (Fx ∧ Gx) everyday language "All Fs are Gs." .- Antonym_____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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All/Negation/"not all"/Millikan: the "not" in "not all A are φ" is not immunizing. If it were, then the fact that e.g. "All Blubbs are gull" is meaningless and would entail that "not all Blubbs are gull" would be true.
So: from the fact that "not all unicorns are white" is not true, should not follow that "all unicorns are white" is true.
Solution: if the word "unicorn" has no meaning (no mapping rule, not to be confused with intension, which the word has very well) then the sentence "All unicorns are white" should also have no meaning!
Representation/non-existence: in a representative sentence, "All A's are φ" should never be true if there are no A's.
Universal Quantification/Existential Quantification/Millikan: "All A's are φ" would always imply "Some A's are φ". ((s) For representative sentences).
Representation/all/Millikan: but is it such that such sentences with "all" always represent? E.g. "Painfully disappointed, Johnny never returned", e.g. "the boy who delivers the newspaper is not very tall": Here "not" does not operate above the logical predicate that is contained in the grammatical subject.
Suppose, it would also be like this in "All A's are φ".
"Not all A's are φ" is equivalent to "Some A are not-φ". So if there is any positive sentence embedded here, then it should also be embedded in the grammatical subject "All A's" E.g. "All red cows are friendly": becomes "Not all red cows are friendly". What is equivalent to...
..."Some red cows are not friendly". The grammatical subject contains an embedded sentence here ""Some" cows are red". And that must also have embedded the original sentence! So if "All A's are f" implies "Some are ..." then the way "not" works here is perfectly compatible with the way it works on other representative sentences and does not need any special comment.
Representation/Millikan: Question: are such sentences representations then? Often yes, but sometimes not!
Stabilization function: what could be the stabilization function of "All A's are φ"? It must at least be that a disposition is evoked in the listener to produce certain types of inferences.
For example, from "x is an A" to "x is φ" and from "x is not φ" to "x is not A". And from "no B is φ" to "no B is an A".
Problem: beyond these elementary functions the functions of "All A's are φ" seem to be separated.
A) Nominal use/all/Millikan: licensed here "All A's are f" is a subjunction (subjunctive inference) of this type:
E.g. "Suppose x is an A, then x would be φ" and
B) "Suppose x should not be φ, then x would better be not an A".
Representation: E.g.: "All students who cheat are exmatriculated". Now everyone is so frightened that no one cheats at all. That is, the students are adapted to this world, simply by the fact that the sentence produces dispositions to inferences which map dispositions in this world.
Intentional Icons: one might think that the dispositions are correct intentional icons because they map potential dispositions.
MillikanVs: but the use is not representative here, but rather nomical! Here nothing has to be mapped so that the eigenfunction is fulfilled, but a disposition is produced. ((s) The disposition is not mapped).
Nomical use/"not"/Millikan: nomical use, however, is very special and always must be marked somehow. Here, e.g. through the use of the future tense.
There remain two questions regarding "all":
1. Why are we tempted to believe that "all A are φ" is true, not despite, but precisely because of the fact that there are no A's?
E.g. "All day-active bats are herbivores" is true, because there are no day-active bats.
2. How do sentences of the form "All A are φ" map the world at all?
If we consider here only the normal and the nominal use, there is no common explanation, only a jointly focused eigenfunction. Namely, a disposition to produce inferences. If there are no A's, it is not a problem to conclude the disposition from A to φ is simply not activated. Also, the inferences from "x is not " to "x is not an A" and...
...from "no B is φ" to "no B is an A" become true. (Here, however, A must have a meaning, that is to say, in this case, a complex term.)
E.g. "All bad apples have been removed from the basket". Here one can conclude that only good apples are in the basket. Whether bad apples have been in it before, does not have any consequences._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
R. G. Millikan
Language, Thought, and Other Biological Categories: New Foundations for Realism Cambridge 1987