The logical form of the action sentences

The logical form of action sentences (English. Original title The Logical Form of Action Sentences ) is an essay of the American analytical philosopher Donald Davidson from the field of action theory (see. Event semantics ). It was presented at a 1966 convention on "The Logic of Decision and Action" at the University of Pittsburgh . It deals with a problem that arises when statements about actions are formalized, that is, when they are transferred into a predicate logic notation . According to Davidson, the British philosopher Anthony Kenny was the first to raise awareness of this problem. Davidson's solution to this problem has the ontological consequence that actions must be counted as objects . This fits in with ontological considerations developed elsewhere in Davidson's: He regards actions as special cases of events and these in turn as objects (cf. in particular his essays "Causal Relationships" and "On the Individuation of Events").

The problem

Davidson examines the following example sentence:

(1) Müller smeared the bun in the bathroom with a knife at midnight.

According to Davidson, "most philosophers today would initially analyze this sentence [...] as if it contained a five-digit predicate whose argument positions are evidently filled in by singular terms or bound variables ." A common translation in predicate logic would look something like this:

(1a)

{\ displaystyle S_ {1} (m, b, n, d, s)}

Here "S" stands for the five-digit relation "smear", m is a singular term for miller, b for the bread roll, n for midnight, d for the bathroom and s for the knife. The problem here is the adverbial terms "at midnight", "in the bathroom" and "with the knife". For this we consider:

(2) Müller smeared the bun.

Analogous to the above, this sentence could be analyzed as follows:

(2a)

{\ displaystyle S_ {2} (m, b)}

With this analysis, Davidson says, "we blur the logical relationships between these sentences," namely that (2) follows from (1) . In contrast to this, (2a) does not follow from (1a), this is due to the fact that the two-digit predicate has no logical relationships to the five-digit predicate , and there is therefore no predicate-logic inference rule which leads the conclusion from (1a) to (2a) allowed. ${\ displaystyle S_ {2}}$ ${\ displaystyle S_ {1}}$

There is a second possibility to formalize (2), in which the sentence "would be interpreted as an elliptical formulation for" Müller smeared the bun somewhere with something at some point "":

(2 B)

{\ displaystyle \ exists x \ exists y \ exists zS_ {1} (m, b, x, y, z)}

With this formalization, the corollary relation between (1) and (2) is retained, because (2b) follows from (1a), especially because the same predicate ( ) is used in both formalizations . The problem with this approach, however, is "that we could never be sure how many reserve positions would have to be supplied with each action predicate." It is possible to add further adverbial terms to (1) (such as the term "by holding it between the toes of his left foot"). For a uniform formalization, the predicate that is supposed to formalize "smear" would have to have an additional place for each such adverbial determination, and it appears problematic to state the exact number of all possible determinations. ${\ displaystyle S_ {1}}$

Davidson's solution

Davidson observes that there is no analogous problem, "[w] hen I say I bought a house in the city center that has four bedrooms, two open fireplaces and a glass chandelier in the kitchen," apparently one can "always add more details". The logical form of this sentence is: "There is a house such that I bought it, it is in the city center, it has four bedrooms ..." so:

(3)

{\ displaystyle \ exists x (H (x) \ land G (x, k) \ land I (x))}

where H stands for "... is a house", "G" for "--- has ... bought", k for me and I for "... is in the city center". The individual relative clauses appear here as conjuncts in the statement of existence and here it is allowed to add as many as required.

It therefore makes sense to formalize the problematic sentence analogously:

(1b)

{\ displaystyle \ exists x (S (x, m, b) \ land Z (x, n) \ land O (x, d) \ land I (x, s))}

S stands for "... is a smear of --- a ___", Z for "the time of ... is ---", O for "the place of ... is ---" I for "... is executed with ---". (1b) can thus be read roughly as follows: "There is an x such that x is a smear from Müller of the bun and x took place at midnight and the location of x is the bathroom and x was executed with the knife". Theorem (2) would then be formalized as follows:

(2c)

{\ displaystyle \ exists xS (x, m, b)}

This analysis maintains the corollary relation between (1) and (2), and the adverbial determinations (similar to (3)) are now represented as conjuncts, so it is not necessary to commit to a maximum number of such determinations.

In analysis (1b), actions must be counted among the values of the variable x in so that the proposition can be true. According to Quine (cf. his essay " What there is "), Davidson has entered into an "ontological obligation" that there are actions as independent objects. Davidson therefore tries to provide arguments, which are independent of the analysis (1b), for the fact that actions are objects:

Actions (like things) can be referred to with pronouns , as in "Müller did it with a knife." - "Please tell me more about it". "it" and "about it" refer to what Müller did.
According to Davidson, excuses are based on describing a particular deed in different ways: once as a "deplorable act" (that I shot a certain person) and once as an "excusable act" (that I believe the gun was unloaded) the person put on and pulled the trigger). The excuse lies in the claim that these two acts are identical . If this analysis is correct, then deeds (or more specifically, actions) must be objects, otherwise they cannot be called identical.
Explanations of actions work similarly to apologies: the action of "writing a check" can be explained by describing it as "paying one's debts". Here, too, the explanation is based on the fact that the two action descriptions refer to the same action, so it is again a statement of identity.

Footnotes / Sources

↑ ^a ^b ^c ^d ^e cf. P. 158. (Here and in the following the page numbers refer to the Suhrkamp edition.)
↑ p. 159
↑ p. 160
↑ p. 160 f
↑ p. 160

literature

Donald Davidson "The Logical Form of Action Sentences" in: Nicholas Rescher ( ed. ): The Logic of Decision and Action , University of Pittsburgh Press, Pittsburgh, 1967. Dt. Translated: "The logical form of action sentences" in: Donald Davidson: "Action and event". Suhrkamp, Frankfurt am Main 1985. ISBN 978-3-518-06428-3

[S158-1] ↑ ^a ^b ^c ^d ^e cf. P. 158. (Here and in the following the page numbers refer to the Suhrkamp edition.)

[2] . 159

[3] . 160

[4] . 160 f

[5] . 160