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Davidson proposes a causal law for singular event causation. Here is one example of a backward-looking part of such a law (changed slightly for clarity and to avoid copyright infringement):

(e)(u)((Ge & (t(e) = u + ε)) -> (∃!q)(Fq & (t(q) = n) & C(q,e)))

Notes:

  • e, q are event variables
  • G, F are event predicate variables
  • u is a time
  • let me know if anything else is unclear

Problem:

What is "(∃!q)"? I wasn't able to find this notation on google, nor in an article on Davidson's theory of causation (e.g. Wirderker 1985).

My gut instinct is that this has to be simply (∃q). Then much of the formalism makes sense.

Yet obviously "!" is often used for negation. But in a law-denoting conditional, why would a universally quantified statement over events lead to the negation of a statement that an event exists that caused it?

Edit: answered.

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    ∃! means "exists and is unique", it is a standard notation, see Uniqueness quantification.
    – Conifold
    Mar 31 '20 at 0:59
  • Answered, thank you.
    – user45910
    Mar 31 '20 at 1:17
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    – J D
    Mar 31 '20 at 22:46
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Stack Exchange user Conifold left their answer as a comment.

I will re-post Conifold's comment as an official answer to question:

∃! means "exists and is unique"

There is a Wikipedia page on Uniqueness Quantification for reference here:

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  • It is really awesome that my answer keeps getting downv-oted even though the answer is correct. For most questions on this website, what the the correct answer is very uncertain. However, this time, it is not up for debate. in Davidson (1967) used ∃! x to say "there exists unique x"
    – Samuel Muldoon
    May 26 '20 at 16:45

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