Broad on Theological Arguments. I. The Ontological Argument

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1 Broad on God Broad on Theological Arguments I. The Ontological Argument Sample Ontological Argument: Suppose that God is the most perfect or most excellent being. Consider two things: (1)An entity that possesses all perfections or all excellent qualities to the highest degree, (2) An entity that possesses all perfections or all excellent qualities to the highest degree except that it does not exist. Clearly entity (1) is superior to entity (2), so entity (2) can t be God. But there is by hypothesis no perfection or excellence that entity (1) lacks, and it possesses all these perfections and excellences to the highest degree. Entity (1) then, is the most perfect or most excellent being and so is, by definition, God. Therefore, God exists. Broad s Version: Anything that lacked existence would lack a positive property which it might conceivably have had. Nothing which lacked a positive property which it might conceivably have had would be a most perfect being; for it is logically possible that there should be something superior to it, viz. a being which resembled it in all other

2 respects but had the additional property of existence. Therefore no most perfect being would lack existence. Therefore all most perfect beings exist. (21) Broad considers two ways that one entity may be superior to another: 3. A is extensively superior to B iff A has all the positive powers and qualities that B has and, in addition, it has some which B lacks. 4. A is intensively superior to B iff (i) A is at least extensively equal to B, and (ii) some of the positive qualities or powers that are common to both are present in A to a higher degree of intensity than in B, and (ii) none of them are present in B to a higher degree of intensity than in A. [Why doesn t Broad just say in (i) that A is extensively equal to B and use intensive superiority as a tiebreaker?] These two criteria do not let us rank entities in a single scale of perfection. For instance, A and B might be extensively equal, but A possesses some some perfections with greater intensity than B does while B possesses other perfections with greater intensity than A does. Broad s example: some minds possess mathematical genius and some musical genius. 2

3 If we cannot rank all entities on a single scale of perfection, then it is not clear that the expression the most perfect being has a reference, that it picks out or denotes anything. Now let us go back to the argument as Broad formulated it: He says that it falls into two steps or parts: I. Anything that lacked existence would lack a positive property which it might conceivably have had. Nothing which lacked a positive property which it might conceivably have had would be a most perfect being; for it is logically possible that there should be something superior to it, viz. a being which resembled it in all other respects but had the additional property of existence. Therefore no most perfect being would lack existence. II. Therefore all most perfect beings exist. Broad says that part I is a valid deductive argument. (He uses the older term syllogism.) But the inference from I to II is tricky, because, according to Broad, the sentence in II, which has the logical form All S is P, is ambiguous. 3

4 Conditional Interpretation. All S is P is understood as If anything were S, it would be P. This interpretation is neutral as to whether anything is in fact S, as to whether there are any Ss. Instantial Interpretation. All S is P is understood as There are some Ss, and none of them lack P. Both premises in part I are conditional, so the conclusion must be conditional as well. Then, if II is to follow from I, it must be conditional as well. But on this reading II is perfectly innocuous. If anything were a most perfect being, it would exist. The instantial interpretation of II is: There are most perfect beings, and none of them lack existence. This sentence is redundant or pleonastic, but, such as it is, in this interpretation it does not follow from the conclusion of I. As far as I can see, this version of the ontological argument is stone dead at this point, but Broad tries to drive a stake through its heart. The argument, he points out, requires the comparison of a nonexistent object to an existent object in respect to the presence or absence of existence. Such a comparison, Broad says, is not possible. No comparison can be made between a non-existent term and anything else except on the hypothesis that it exists. (22) But why, aside from mere assertion, should one think this is so? Broad seems to provide no reason or argument to justify his claim, but 4

5 perhaps one emerges from Broad s reflections on why this lame argument has seemed plausible to some unquestionably great philosophers. Broad s first observation is that, although existential propositions and characterizing propositions look alike grammatically, they are actually quite different beneath the grammatical surface. That is, S exists or S is real looks like S eats or S is red, but the logic of the two pairs is quite different. Look, for instance, at the negations Cats do not bark and Dragons do not exist. The first sentence is about cats, but the second can t be about dragons. There aren t any for it to be about. [But how can I say something different, if I do, when I say Centaurs do not exist?] The first makes sense on either the conditional or instantial interpretation. The second makes sense on neither. But it does make sense, so it is in some way different from the first sentence. We also discover a difference if we try to interpret Cats scratch and Cats exist conditionally and instantially. Finally, if we render Cats scratch in modern logic, we have (x)(cx Sx), whereas Cats exist 5

6 is (Ex)Cx. The two have quite distinct logical forms, as philosophers are wont to say. What emerges from this last comparison is that, whereas is a cat and scratches are properties (represented by predicates in modern logic), existence is not represented by a predicate but by a quantifier. If this is so, then existence should not be thought of as a property, quality, or characteristic that a thing, or class of things, may have or lack. This observation, to go back to Broad s claim on page 22, certainly undermines the idea that one can compare two entities that differ only in that one possesses the property of existing or existence while the other does not. Cautionary note. Nowadays, logic has gone pluralistic. There are many, many logics. In some of them (e.g., quantified tense logic with a single domain) an existence predicate is at least useful and probably even essential. II. The Cosmological Argument Explanations in terms of ordinary causation are explanations of the occurrence of an event or the existence of an object in terms of initial conditions (the existence or disposition of other events and objects) and general laws. [This is another way of saying that the states of systems evolve according to laws.] Such explanations are valuable, but may be 6

7 unsatisfying insofar as either the initial conditions or the laws in the explanans are themselves unexplained. From these unquestionable facts, it is supposed that one can draw the following remarkable conclusions: [T]here must be a substance which is neither part of nature nor nature as a collective whole. And there is another kind of dependence, which is not the ordinary dependence of a later state of affairs on an earlier one in accordance with de facto rules of sequence. The existence of this nonnatural substance must be intrinsically necessary. And the existence of all natural events and substances must be dependent upon the existence of this non-natural substance by this non-natural kind of dependence. (25) (i) Broad agrees that a fully satisfying explanation is one in which the premises are (in some sense or other) necessary and the conclusions follow from the premises by the use of rules of inference that preserve this necessity. One can see such explanations in mathematics, where they are called proofs. 7

8 (ii) But is our universe such that this sort of intellectual satisfaction is in principle obtainable? I do not see the least reason to believe this. Plainly it is not the kind of premiss for which there is or could be any empirical evidence. Nor is it self-evident or deducible from any premisses which are self-evident. Wherever we have this kind of completely satisfactory insight we are dealing with the formal relations of abstract entities, such as numbers or propositions, and not with the existence or the non-formal properties of particulars. There is no reason whatever to think that this kind of rational insight is possible in the latter case. (27) (iii) But Broad thinks that the conclusion is worse than unproved. He thinks it is false. And he thinks so because he can t make sense of the attribution of necessity to an existential proposition. But nowadays one would say that (Ex)(x=a) iff a exists in all (logically) possible worlds. I am inclined (along with Broad) to think that a world without an Ultimate Ground is at least logically consistent, in which case (Ex)(x=UG) is indeed false, but it might be argued (for instance, by someone who believed that the Principle of Sufficient Reason was a presupposition of reason) that my claim (and Broad s) is questionbegging. 8

9 So let s grant the claim. Then Broad points out that it is perfectly obvious that the necessary consequences of facts which are necessary are themselves necessary, (28) but our world seems to be chock-a-block with contingent facts. If so, this is a reductio ad absurdum of a conclusion which is unproven and probably false on other grounds. Broad s specific example is interesting. Necessary truths or facts are, he says, timeless. But specific events occur and objects begin or cease to be at definite times. How could this be explained in any way in terms of the existence or nature of a timeless or non-temporal Ultimate Ground? Why, then, did so many great philosophers (Aristotle, St. Thomas, Descartes, Spinoza, Leibniz, and Locke) endorse this argument? One reason is the same old one as above--failure to distinguish existential from characterizing propositions. But a second reason is more interesting: A second cause is the very peculiar position which Euclidean geometry enjoyed for so many centuries. Here we have a science which seems to consist of propositions which necessarily follow from intrinsically necessary premisses, and yet give us synthetic and categorical information 9

10 about a certain important aspect of nature. This suggested the ideal of a completely rational knowledge of every aspect and every fact of nature; and it made this ideal appear to be intelligible even if the de facto limitations of the human intellect should forbid its being ever realized in detail. We know now that the necessity of Euclidean geometry, like all other necessity, is only conditional. The theorems follow necessarily from the axioms; but the axioms themselves are not intrinsically necessary, and therefore their necessary consequences are not themselves necessary propositions. So we are exempt from this temptation to which so many of our betters succumbed. (30) 10

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