Philosophia Vol. 5 No. 4 Pp. 513-514 October 1975

THOU SHALL SAY "THOU SHALL NOT"

CtlARLES F. KIELKOPF

Can we say "Thou shall not kill except in special circumstances CI" by saying "Thou shall kill except in special circumstances C2"? In the question it is intended that somehow the C2 circumstances exempt one from the obligation to kill just when they should not kill.* The negative answer is instructive in at least two ways. It shows the value o f deontic logic because deontic logic perspicuously displays the difference between the two commandments. It also shows that "Thou shall not do A" is a better way of commanding forbearance from an undesirable activity A.

My argument depends upon some assumptions and notation. Assume that the CI circumstances could be given by a finite disjunction. Thus C1 may be: "if you do it in self-defense or do it in war or do it as a legal duty." There is no assumption, though, that we know what the disjunction is; we may need much more experience to know that. But, really, it is not unreasonable to assume that there are only finitely many kinds of excuse for performance of any wrong act. LetClx say "x is a C1 circumstance." Assume that the C2 circumstances could be given by negating the finite disjunction giving CI. Thus C2 would be given by a conjunc- tion containing as its only conjuncts the negation of each disjunct in C/. Thus C2 may be: "if you do not do it in self-defense and do not do it in war and do not do it as a legal duty." With this reading for C2, "Thou shall kill except in special circumstances C2" becomes C below.

C) Thou shall kill except if you do not do it in self-defense and do not do it in war and do not do it as a legal duty.

According to commandment C, a man who kills his wife to save the cost of a divorce had no obligation to kill. But a man who killed in

* The question was raised by my colleague: William Jacobs.

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self-defense, or war, or as a legal duty did what he was obliged to do. Read C2x as "x is a C2 circumstance." With this reading we have C2x as provably equivalent in propositional logic to ~Clx. I assume that provable equivalents are substitutable for one another. Read Kx as "x is a circumstance in which you kill." Read O(pj as "It ought to be that p," and P(p) as "It is permitted that p." I assume that "O("FJ and P(p) are substitutable for one another.

Consider (1) and (2) below. (1) Thou shall not kill except in special circumstances C1 (2) Thou shall kill except in special circumstances C2. If we write "Thou shall not kill" as O(~Kx), a symbolization of the exceptive (2) is (3) below. (3) (x ) ( C l x - .,, O(,,.Kx)).

Replacement of ~O("Kx) in (3) with P(Kx) makes (4) symbolize (i). (4) Ix) (Clx - P(Kx)).

Formula (4) shows us that (1) tells us that an excusing condition for killing gives us permission to kill. When we write "Thou shall kill" as O(Kx) the exceptive (2) is symbolized as (5).

(5) :x) (C2x -- '- 'O(Kx)).

Now in (5) substitute "-,C1 x.for C2x to get (x) ("Clx = ~O(Kx)) and use propositional logic to get the final version of (2) which is (6). (6) (x) (Clx = O(Kx) ). Formula (6) is dramatically different from (4). Formula (6) tells us that having an excusing condition for killing is equivalent to having an obligation to kill.

The difference between formulae (4) and (6) perspicuously reveals the felt difference between the commandments (1) and (2). A bit of reflection shows that (1) is better than (2). If killing, on the whole, is undesirable we do not want to obligate people to exercise their right to kill even when they have that right.

I can close by noting that nothing in the argument that (4) symbolized (1) and (6) symbolized (2) depended upon talk of killing. So 1 have shown that there is a difference between all commandments of the type of (1) and the type of (2).

THE OHIO STATE UNIVERSITY COLUMBUS, OHIO 43210

USA

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