² See Malcolm, Norman, The Ontological Argument, Philosophical Review (January, 1960)CrossRefGoogle Scholar, and see Samuelson, Norbert, On Proving God's Existence, Judaism (Winter, 1967)Google Scholar.

There are several possible philosophic traditions for speaking about g and it is not certain that the use of the term “God” in any one of these traditions is consistent with the use of the term “God” in any other tradition. For example, given that there is “a prime mover” and given that there is “something greater than which cannot be conceived,” it is not certain that a single entity could be both the prime mover and something greater than which cannot be conceived. Since I wish to avoid this issue in this paper, I limit my use of the expression “g” solely to that supposed entity whose existence Anselm in the light of Malcolm's commentary claims to be demonstrable.

³ In my statement of these rules I have assumed Russell's doctrine of class levels and I have assumed that positive predicates can be distinguished from negative predicates. However, the rules stated below should be neutral with regard to any theory of predication in the sense that if either or both of the above assumptions are denied, the statement of the rules can be altered to account for the different analysis of predication. In general what the rules state is that all positive predicates are predicable of g with the exception of all members of what are defined as “exclusion” predicates, and all but one member of any class of what are defined as “graded” predicates provided that that class does not entail predicates from a class of nongraded, exclusion predicates. There may be other exceptions to the rules that ought to be noted. For example, g does not exemplify the class of all classes. Also g does not exemplify a predicate P where P is any predicate other than Q in the class of φ predicates where φ is not an exclusion class of predicates which does not entail an exclusion class of predicates and Q is a φ predicate. In this case a proposition of the form “g is P” would be judged not to be well formed. P would be an example of what I here call a “negative predicate” and the rules of predication range only over positive predicates.

⁴ To be blue is not better or greater than to be orange.

⁵ The same thing cannot be blue and orange all over.

⁶ For other reasons, namely Rule 3, it cannot be.

⁷ I leave open the question whether an entity may occupy more than one space at a time. There are certain problems with such a claim. For example, consider Michigan Avenue in Chicago. Presumably this street occupies a single space, but part of this space extends over a bridge that crosses the Chicago River. When that bridge is up, it is not altogether clear what is the space that Michigan Avenue occupies. It might even occupy two spaces, one on each side of the uplifted bridge. The problem arises because it is not clear just what a space is. But this lack of clarity does not affect the dogma that if something occupies all space, then it occupies no space.

⁸ In symbolic language the initial two definitions and the five rules can be stated as follows:

SYMBOLS: Greek letters are used for variables for classes of classes of predicates. English capital letters are first level predicate variables, “g” is the proper name of a being no greater than which can be conceived, a < b means that a is greater than or more perfect than b. a > b means that a is less perfect or less than b.

⁹ Throughout the remainder of this discussion “W” will stand for any predicate relation of “being together with” so that “aWb” reads that a is together with b. This predicate W is based on and similar to but for reasons which shall become clear not identical with the relation W that Goodman, Nelson uses in The Structure of Appearance (Bobbs-Merrill, 1951).Google Scholar

¹⁰ In other words, Wxy = df. (Axy·x/y) where Axy means that a is allied with y and x/y means that x and y are discrete entities.

¹¹ In other words, Axy = df. ((Mry) V (z) ((Mxz·((x + z) = y)) V (Mys·((y + z) = x))) V (Zxy· (xOy))) where Mxy means that x matches y, x + y means the sum of x and y, Zxy means that x and y are equal in size, and xOy means that x and y overlap.

¹² In other words, Mxy = df. ((MS(x + y)) · (QUx) · (QUy)) where MS(x + y) means that x and y constitute a definite sum, and QVx means that x is a quale.

¹³ That is to say, if a is together with b, then b is together with a.

¹⁴ That is to say, nothing is together with itself.

¹⁵ In those instances where the claim is made that a particular instance of a W relation is transitive, Goodman expresses it as follows: (Wx,(y + z)). This case is to be distinguished from (Wxy·Wxz). The former case entails Wyz but the latter case does not.

¹⁶ See section 3.32 below.

¹⁷ See Ethics, Theology, and Occam's Razor, Central Conference of American Rabbis Journal (April, 1966), and The Problem of Free Will in Maimonides, Gerscnides, and Aquinas, Central Conference of American Rabbis Journal (January, 1970) for a more detailed discussion of what I mean by “person.”

¹⁷ It is open to question if temporal continuity is necessary in order to make the claim that the god that I experienced now is the same god that I experienced before.

¹⁸ The term “angel” is ambiguous. Where an “angel” means a disembodied spirit which differs from y in that it is subservient to and a “messenger” of y not associated peculiarly with any body, then angels are gods. In this sense of the term in Greek mythology only Zeus qualifies as a god as distinct from angels. The other inhabitants of Mount Olympus are angels. But as the term was used by the medieval Aristotelians, an angel is an intellect or a soul of a given body or sphere. In this sense of the term angels or “intelligences” are not gods.

²⁰ ZalmanSchachter has correctly argued that belief in God rests more on Contact with Zaddikim (righteous men) than it does on arguments. See Patterns of Good and Evil, by Schachter, Z. in Rediscovering Judaism, edited by Wolf, A.J. (Quadrangle, 1965).Google Scholar

²¹ See Every Event Has A Cause, by Warnock, G. J. in Logic and Language, edited by Flew, A. (Blackwell, 1953).Google Scholar

²² See On Knowing God, by Samueison, N., Judaism (Winter, 1969).Google Scholar

²³ For example, someone trustworthy could say, “I saw Frank shoot Malcolm” or “I read about Malcolm's funeral in the New York Times.”

²⁴ How many years must a man be missing reasonably to be declared dead ? Is the common current legal designation of seven years reasonable or merely conventional?

²⁵ See footnote 7 above.

²⁶ See Individuals (Methuen & Co., 1959), Part One, Sections I and II.

²⁷ That a complete map is not given and in principle cannot be given is as irrelevant in this case as it is in the case of the linear array in which natural numbers are located.

²⁸ Goodman characterizes the relation of “being betwixt” as follows:

It might be objected that the relation of being betwixt is possible only between entities that can be matched and in Goodman's language only qualia and not concreta can be matched. In other words, in Goodman's language qualia are basic units that have no other basic unit as a part of them, where what it means to be a basic unit is to be an individual of which the relation W applies. (See footnote 10.) But a concretum is a complex (rather than a compound) which is not together with any individual. Something is complex rather than compound if each of its discrete parts are together.

In Goodman's terminology, concreta and qualia are defined as follows:

One response to such an objection is that y like other concreta is a complex which is not itself together with anything but is together with other things in virtue of qualia of y matching other qualia which are not parts of y. But if it be replied that y is not complex and it is in fact the case that y is not complex (an issue that lies outside of the scope of this paper), then there is no reason why Goodman's scheme could not be extended to include individuals that have no quale as a part. (In this connection see page 220 of The Structure of Appearance.)