# What is (∃!e) in Davidson 1967?

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?

• ∃! means "exists and is unique", it is a standard notation, see Uniqueness quantification. Mar 31, 2020 at 0:59
• Answered, thank you. Mar 31, 2020 at 1:17
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– J D
Mar 31, 2020 at 22:46

∃! means "exists and is unique"
• 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" May 26, 2020 at 16:45