Archive for the ‘Existence of God’ Category

The “Third Way” in Syllogistic Format 1: The Introduction and a Review of the First Section

Tuesday, August 10th, 2010

1. I have been engaged in an effort at spelling out, in explicit syllogistic format, the arguments that constitute Aquinas’s “Five Ways” of demonstrating, at least so he thought, the existence of God. In earlier posts, those of June 16th, July 5th, and July 16th below, I have spelled out, in explicit syllogistic format, the first two of the “Ways.” This explicit syllogistic rendering of the argumentation of the “proofs” has made it possible to see rather clearly that (a) it is evident that the two arguments are valid, on the one hand, and (b) it is not evident that they are sound, on the other.

In this post I am turning my attention to his “Third Way.” This attempt at proving the existence of God is, however, quite a bit more complex than the previous two and I do not yet fully understand the core of the argument. So this post is but a first step in my effort at spelling the “Third Way” out in explicit syllogistic format.

2. I begin with the observation that the “Third Way” can be divided into three sections, each of which can be further subdivided into subsections. The first section, dealing with contingent beings, beings which are, as Aquinas puts it, “possible not to be,” concludes that they cannot always exist. It reads as follows:

The third way is taken from possibility and necessity, and runs thus. We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist, for that which is possible not to be at some time is not.
(http://dhspriory.org/thomas/summa/FP/FP002.html#FPQ2A3THEP1)

The second section of the “Third Way,” the core which I do not yet fully understand, concludes that “there must exist something the existence of which is necessary.” It reads as follows:

Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence—which is absurd. Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary.
(Ibid.)

The third section of the “Third Way” concludes that there must exist “a being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity.” It reads as follows:

But every necessary thing either has its necessity caused by another, or not. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes. Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God.
(Ibid.)

3. In today’s post I will only deal with the first section, leaving the other two to be taken up in later posts. I’ll start by noting that the first section can be divided into two subsections, each one a relatively informal expression of an argument. The first subsection reads:

The third way is taken from possibility and necessity, and runs thus. We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be.

The argument the first subsection gives expression to reads, in its explicitly syllogistic format:

All beings which are generated and which corrupt are beings which are possible to be and not to be.

Some beings are beings which are generated and which corrupt.

Therefore, some beings are beings which are possible to be and not to be.

The argument is obviously valid and nearly as obviously sound.

4. Aquinas’s exposition continues:

But it is impossible for these always to exist, for that which is possible not to be at some time is not.

Now, we can see that Aquinas has here distinguished “beings which are possible not to be” from “beings which are possible to be” and left the former alone as the focus of the argument. That is, though he has not explicitly given either formal or informal expression to it, he has implicitly, and rightly, assumed the following argument to be sound:

All beings which are possible to be and not to be are beings which are possible not to be.

Some beings are beings which are possible to be and not to be.

Therefore, some beings are beings which are possible not to be.

5. It is to the beings designated by the “some beings” of that conclusion, the beings “which are possible to be,” that the “these” of “it is impossible for these always to exist” refers. In an explicitly syllogistic format the argument of the last bit of quoted text reads (trying to remain relatively close to the way Aquinas, or at least the translation, puts things):

No beings which are at some time non-existent are beings which are at all times existent.

All beings which are possible not to be are beings which are at some time non-existent.

Therefore, no beings which are possible not to be are beings which are at all times existent.

This argument, of course, is patently valid. Further, the first premise, that “no beings which are at some time non-existent are beings which are at all times existent,” is patently true. It is not, however, at all evident that the second premise, that “all beings which are possible not to be are beings which are at some time non-existent,” i.e., that “that which is possible not to be at some time is not,” is true. It follows that it is not evident that the argument is sound.

6. Aquinas has here, that is, identified modal “logic” with temporal “logic.” More explicitly, he has identified the theory or science of the modal, i.e., of the possible and the necessary, with the theory or science of the temporal, i.e., of the “at some time” and the “at all times.” He has done this by, in effect, postulating alongside the evident proposition that:

All beings which are at some time non-existent are beings which are possible not to be.

the non-equivalent and rather less evident converse proposition that:

All beings which are possible not to be are beings which are at some time non-existent.

Together the two imply that the beings which are possible not to be and the beings which are at some time non-existent coincide completely.

7. I find that Aquinas’s difficulty becomes a little more evident if we vary the argument seen above, that:

All beings which are possible to be and not to be are beings which are possible not to be.

Some beings are beings which are possible to be and not to be.

Therefore, some beings are beings which are possible not to be.

but this time leaving “beings which are possible to be” rather than “beings which are possible not to be” as the focus of the argument, thus:

All beings which are possible to be and not to be are beings which are possible to be.

Some beings are beings which are possible to be and not to be.

Therefore, some beings are beings which are possible to be.

We can next, following a logic parallel to that which Aquinas used when drawing his inference about the “beings which are possible not to be,” draw the following inference about the “beings which are possible to be”:

No beings which are at some time existent are beings which are at all times non-existent.

All beings which are possible to be are beings which are at some time existent.

Therefore, no beings which are possible to be are beings which are at all times non-existent.

Here again the argument is patently valid. Further, the first premise, that “no beings which are at some time existent are beings which are at all times non-existent,” is patently true. It is not, however, at all evident that the second premise, that “all beings which are possible to be are beings which are at some time existent,” i.e., that “that which is possible to be at some time is,” is true. It follows that it is not evident that the argument is sound.

8. Aquinas’s argumentation in the first section of the “Third Way” is, then, though evidently valid, not evidently sound.

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Aquinas’s “Second Way” in Syllogistic Format

Friday, July 16th, 2010

(1) I said in my last post, “A Non-evident and Key Premise of Aquinas’s ‘First Way’”, that in this one I would set forth the second of Aquinas’s “Five Ways” of demonstrating that God exists in an explicitly syllogistic format. The aims are three: that of making its parallelism with the “First Way” evident; that of making it evident that the argument is perfectly valid; and that of showing that it is not evident that the argument is sound by isolating a key premise the truth of which is not evident.

(2) The thesis that the two ways are in principle parallel does need some defense, for the initial descriptions Aquinas gives of them in the Summa Theologiae obscure rather than highlight the parallelism. The first lines of his exposition of the “First Way” identify it as an “argument from motion,” from, that is, an effect, that of a mover:

The first and more manifest way is the argument from motion. It is certain, and evident to our senses, that in the world some things are in motion. Now whatever is in motion is put in motion by another….
(http://dhspriory.org/thomas/summa/FP/FP002.html#FPQ2A3THEP1)

The first lines of his exposition of the “Second Way,” on the other hand, identify it as an “argument from the nature of the efficient cause,” drawing attention to the cause rather than the effect:

The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes.
(Ibid.)

In the post before last, “Gnosis and Noesis Returns: the ‘First Way’ of Aquinas,” in speaking about the critique that Paul Edwards offered of the “Second Way,” I provided a partial justification of the parallelism claim, that of a similarity in focus:

[W]hile the “First Way” has as its focus the change [i.e., in Aquinas’s vocabulary, the motion] that some beings undergo and the causation upon which that change depends, the “Second Way” has as its focus the caused existence of some beings and the causation upon which that existence depends. The causality, however, is in both cases, an “efficient causality.” This is, in the Aristotelian terminology, the activity of an agent, and is thus to be distinguished from, say, “final causality,” the causality of an end or goal. As far as I am aware, the causal series upon which Edwards’ critique bears is, in all relevant respects, exactly similar to Aquinas’s mover/moved series.

(3) Additional justification for the parallelism claim can be found by noting the presence of two sets of two parallel premises. As for the first set of parallel premises, Aquinas, as we have read just above, gives expression to a key premise of his “First Way” in the second sentence of his exposition of the argument. I isolate that premise as:

Some things are in motion.

He does not, in his “Second way,” thus early and explicitly present the analogous premise, i.e.:

Some things are caused.

(For the duration of this post and for the sake of simplicity, I will use “cause” to abbreviate “efficient cause,” “caused” to abbreviate “beings the existence of which depends upon the activity of an efficient cause,” etc. So abbreviating the terms not only makes for easier inspection of the premises and arguments at hand, it also provides the collateral benefit that parallel arguments bearing upon the other modes of causality identified by Aristotle and Aquinas, final, formal, and material causality, are thereby also set forth for logical evaluation in one fell swoop.)

(4) The proposition that some things are caused is, however, hard at work in the argument, as is evident when the argument is fully expressed. This can be seen by rendering explicit the argumentation expressed in a truncated manner in the following sentence, the penultimate of Aquinas’s exposition of the “Second Way”:

But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false.

It quite obviously gives a truncated expression to a sequence of several arguments, one of which is:

If the cause/caused series goes back to infinity, there is no first cause.

If there is no first cause, there is no intermediate cause.

Therefore, if the cause/caused series goes back to infinity, there is no intermediate cause.

The second in the sequence of several arguments is:

If the cause/caused series goes back to infinity, there is no intermediate cause.

If there is no intermediate cause, there is no ultimate cause.

Therefore, if the cause/caused series goes back to infinity, there is no ultimate cause.

The third in the sequence of several arguments is:

If the cause/caused series goes back to infinity, there is no ultimate cause.

If there is no ultimate cause, there is no ultimate effect, i.e., no caused.

Therefore, if the cause/caused series goes back to infinity, there is no ultimate effect, i.e., no caused.

This is the point at which the premise, “Some things are caused,” comes in to play, as the premise in a fourth argument, a double negation argument:

Some things are caused.

Therefore, it is not the case that there is no ultimate effect, i.e., no caused.

That conclusion serves as a premise in a fifth argument, a modus ponendo ponens argument, thus:

If the cause/caused series goes back to infinity, there is no ultimate effect, i.e., no caused.

It is not the case that there is no ultimate effect, i.e., no caused.

Therefore, it is not the case that the cause/caused series goes back to infinity.

Taking stock, we can first see that there is, parallel to the explicitly stated premise of the “First Way,” that:

Some things are in motion.

there is also the implicitly present premise of the “Second Way”:

Some things are caused.

Still taking stock, we can second take note that we have just reviewed Aquinas’s argument that it is not the case that the cause/caused series goes back to infinity.

(5) Now, to turn to the second set of parallel premises: after having presented us, in his exposition of the “First Way,” with the first premise of the argument, Aquinas immediately went on to present us with a second premise of the “First Way,” that:

Whatever is in motion is put in motion by another.

In his exposition of the “Second Way,” however, he does not immediately go on to explicitly state an analogous premise. But it is more than merely plausible that it is implicitly present. First, in his “Third Way,” he denies that anything caused is caused by nothing, telling us that:

Now if this [that at one time there was nothing in existence] were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing.

And, in the “Second Way” itself, he rules out self-causation, saying, “There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself.”

These two theses imply the following proposition, able to serve as a second premise operative in the “Second Way” analogous to the one already seen to be operative in the “First Way”:

Whatever is caused is a caused by another.

(6) Continuing in parallel with the approach I took in “Gnosis and Noesis Returns: the ‘First Way’ of Aquinas,” I will observe here that a proposition like the immediately preceding suggests the question of whether or not, when one thing is the cause of another, the former is itself caused. Given that it either is or is not caused, then:

Either the cause is itself caused by another
or the cause is not itself caused by another.

Now if the latter is the case, then it immediately follows that there is an uncaused cause, in which case Aquinas as would, no doubt too optimistically, go on to say, “this everyone understands to be God.” It seems at least possible, that is, for Aquinas to have had the inference from the latter possibility to the existence of an uncaused cause in mind and thought it to have been sufficiently obvious to not require an explicit exposition. But perhaps not.

(7) At any rate, Aquinas went on to deal with the former, and remaining, possibility, that, again, “the cause is itself caused by another.” And, of course, as it did in the “First Way,” the question arises of whether that cause is itself caused by another. We are thus presented with a cause/caused series that goes back, or regresses, from one cause that is caused by a prior one to that prior one and then to that prior one’s cause, etc. This obviously raises the question of whether or not this series goes back or regresses infinitely.

In “Gnosis and Noesis Returns: the ‘First Way’ of Aquinas,” I noted that the arguments in the “First Way” fell into two, as I called them, movements, the first concluding that the mover/moved series does not go back to infinity and the second that there is an unmoved mover. The parallel series of arguments in the “Second Way” also falls into two such movements, the first concluding that the cause/caused series does not go back to infinity and the second that there is an uncaused cause.

I have, of course, already set forth the series of arguments that constitute the first movement; I did this in making the case, in Section 4 above, that the premise that some things are caused is implicitly present in the “Second Way” and in the process presenting the syllogistically formatted version of Aquinas’s argument that it is not the case that the cause/caused series goes back to infinity. In this section, accordingly, I’ll set forth the second movement.

Now, in presenting the first movement, I introduced and put to use the following premise:

If the cause/caused series goes back to infinity, then there is no first cause.

The reverse can also reasonably be assumed true:

If there is no first cause, then the cause/caused series goes back to infinity.

The sixth argument needed, also a modus ponendo ponens argument, has as it first premise the latter proposition and as its second the last of the conclusions arrived at in the first movement.

If there is no first cause, then the cause/caused series goes back to infinity.

It is not the case that the cause/caused series goes back to infinity.

Therefore, it is not the case that there is no first cause.

The seventh argument is, quite obviously, another case of double negation:

It is not the case that there is no first cause.

Therefore, there is a first cause.

Note that the series of arguments thus far set forth have concluded only that there is a first efficient cause, i.e., there is at least one. They have not ruled out there being many. In what follows, I will use the expression “the first cause under consideration” to refer to the one alone the existence of which the arguments would have, if sound, demonstrated, with no assumption, at least not here, that there is also at most one first efficient cause.

That said, we’re not quite done yet, though the remaining steps are obvious. One, our eighth argument, is:

If the first cause under consideration is caused, then it is posterior to a prior cause.

If the first cause under consideration is posterior to a prior cause, it is not a first cause.

Therefore, if the first cause under consideration is caused, then it is not a first cause.

There is no need to prove that:

The first cause under consideration is a first cause.

The pertinent double negation argument, the tenth, is just as obvious:

The first cause under consideration is a first cause.

Therefore, it is not the case that the first cause under consideration is not a first cause.

Next, eleventh, another modus ponendo ponens:

If the first cause under consideration is caused, then it is not a first cause.

It is not the case that the first cause under consideration is not a first cause.

Therefore, the first cause under consideration is not caused.

Twelfth:

If the first cause under consideration is not caused, then it is an uncaused cause.

The first cause under consideration is not caused.

Therefore, the first cause under consideration is an uncaused cause.

Finally, in setting forth in Gnosis and Noesis Returns: the First Way of Aquinas the “First Way” in syllogistic format, I did not go on to spell out the argument that:

There is a first mover (i.e., the first mover under consideration).

That first mover (the first mover under consideration) is an unmoved mover.

Therefore, there is an unmoved mover.

I probably should have. In this post, however, I will spell out the parallel argument of the “Second Way,” thus:

There is a first cause (i.e., the first cause under consideration).

That first cause (the first cause under consideration) is an uncaused cause.

Therefore, there is an uncaused cause.

(8) It is quite evident that all of the foregoing arguments are perfectly valid. That is, if their premises are true, then their conclusions must also be true. It is not, however, evident that all of the foregoing arguments are perfectly sound. That is, it is not fully evident that all of the premises invoked are true and it is therefore not fully evident that all of the conclusions arrived at are true.

In “A Non-evident and Key Premise of Aquinas’s ‘First Way’”, I recalled Paul Edwards’ critique, by implication of the following premise of Aquinas’s “First Way”:

If there is no first mover, then there are no other, subsequent, movers.

and directly of the parallel premise of his “Second Way”:

If there is no first cause, then there are no intermediate causes.

(The difference between the “other, subsequent” of the former, stemming from Aquinas’s wording in the “First Way,” and the “intermediate” of the latter, stemming from Aquinas’s wording in the “Second Way,” is of no consequence for the current analysis. Subsequent causes, that is, surely include both intermediate and ultimate causes. The exposition I have given of the “First Way” in syllogistic format can easily be revised to make use of the more specific “intermediate causes” and “ultimate causes” instead of the “subsequent” that I in fact used.)

As far as I know Edwards’ critique is still unanswered. In particular, as I pointed out in “A Non-evident and Key Premise of Aquinas’s ‘First Way,’” Edward Feser’s The Last Superstition. A Refutation of the New Atheism (South Bend, Indiana: St. Augustine’s Press, 2008) does not mention it, much less reply to it.

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A Non-evident and Key Premise of Aquinas’s “First Way”

Monday, July 5th, 2010

(1) In my last post, “Gnosis and Noesis Returns: the ‘First Way’ of Aquinas,” I laid out in an explicitly syllogistic format the sequence of the several arguments that together constitute the first of the “Five Ways” in which Thomas Aquinas thought we could demonstrate the existence of God. When the several arguments are set out in that format, it becomes evident, as I noted, that they are all valid arguments; that is, if their premises are true, then their conclusions must also be true. As I also noted, however, it is not “quite as evident that all of the foregoing arguments are perfectly sound. That is, it is not fully evident that all of the premises invoked are true and it is therefore not fully evident that all of the conclusions arrived at are true.” This is therefore the case for the key culminating conclusions of the “First Way,” that:

There is a first mover.

And:

The first mover … is an unmoved mover.

(Though I did not, I could have and perhaps should have gone on to take note of the inference that passes from the two propositions just given to the conclusion that:

There is an unmoved mover.)

I promised, at the end of that post, that this post would be devoted to showing that the following absolutely critical premise is not evidently true.

If there is no first mover, then there are no other, subsequent, movers.

That is, on the one hand, the premise is not self-evidently true. On the other, Aquinas did not demonstrate its truth.

(2) I am not, of course, the first person to have seen that this premise is not evidently true. That it was not evidently true was shown decades ago by Paul Edwards in his “A Critique of the Cosmological Argument” (first published in The Rationalist Annual, 1959 (London: Pemberton Publishing Co., Ltd.) and available online, at least as of the time of this writing, at:

http://mind.ucsd.edu/syllabi/02-03/01w/readings/edwards.html.)

Before getting into the heart of the matter, it may well be worth our while to take the time to address one minor point that could lead one to miss the force of Edwards’ argument against Aquinas’s “First Way,” that Edwards was dealing explicitly, not with the “First Way,” but rather, as he himself says, with Aquinas’s “Second Way.” Now it is true that, while the “First Way” has as its focus the change that some beings undergo and the causation upon which that change depends, the “Second Way” has as its focus the caused existence of some beings and the causation upon which that existence depends. The causality, however, is in both cases, an “efficient causality.” This is, in the Aristotelian terminology, the activity of an agent, and is thus to be distinguished from, say, “final causality,” the causality of an end or goal. As far as I am aware, the causal series upon which Edwards’ critique bears is, in all relevant respects, exactly similar to Aquinas’s mover/moved series.

(By the way, I intend in the near future to post a presentation of the second of Aquinas’s “Five Ways,” in an explicitly syllogistic format, with the aim of making the parallelism of the two arguments fully evident. And, to anticipate the obvious questions, I will at some time thereafter take up the third and the fifth of the “Five Ways,” which feature some similarities and some significant differences from the first two; I currently, however, do not know what to make of the fourth.)

(3) Edwards summarizes Aquinas’s argument as follows:

Let us take some causal series and refer to its members by the letters of the alphabet:

A -> … X -> Y -> Z

[6] Z stands here for something presently existing, e.g. Margaret Truman. Y represents the cause or part of the cause of Z, say Harry Truman. X designates the cause or part of the cause of Y, say Harry Truman’s father, etc. Now, Aquinas reasons, whenever we take away the cause, we also take away the effect: if Harry Truman had never lived, Margaret Truman would never have been born. If Harry Truman’s father had never lived, Harry Truman and Margaret Truman would never have been born. If A had never existed, none of the subsequent members of the series would have come into existence. But it is precisely A that the believer in the infinite series is “taking away.” For in maintaining that the series is infinite he is denying that it has a first member; he is denying that there is such a thing as a first cause; he is in other words denying the existence of A. Since without A, Z could not have existed, his position implies that Z does not exist now; and that is plainly false.

Edwards goes on to offer the criticism that:

[7] This argument fails to do justice to the supporter of the infinite series of causes. Aquinas has failed to distinguish between the two statements:

(1) A did not exist, and
(2) A is not uncaused.

[8] To say that the series is infinite implies (2), but it does not imply (1). The following parallel may be helpful here: Suppose Captain Spaulding had said, “I am the greatest explorer who ever lived,” and somebody replied, “No, you are not.” This answer would be denying that the Captain possessed the exalted attribute he had claimed for himself, but it would not be denying his existence. It would not be “taking him away.” Similarly, the believer in the infinite series is not “taking A away.” He is taking away the privileged status of A; he is taking away its “first causiness.” He does not deny the existence of A or of any particular member of the series. He denies that A or anything else is the first member of the series. Since he is not taking A away, he is not taking B away, and thus he is also not taking X, Y, or Z away.

Let me add my own parallel. Suppose I were to say, “I am the first one to have offered this critique of Aquinas’s argument.” Suppose then that someone were to object, “No, you are not; Edwards beat you to it.” The objection would not be a claim that I am not one who has offered this critique of Aquinas’s argument. It would simply be a denial that I am the first one.

(4) Now defenders of Aquinas’s argument have brought in a distinction here, one they evidently believe to be telling, between, as Edward Feser identifies them, “two kinds of series of causes and effects, namely, ‘accidentally ordered’ and ‘essentially ordered’ series (or causal series per accidens and per se, for you fans of Scholastic Latin).” Feser explains:

To take a stock example, consider a father who begets a son, who in turn begets another. If the father dies after begetting his son, the son can still beget a son of his own, for once in existence, the son has the power to do this all by himself. He doesn’t need his father to remain in existence for him to be able to do it. If we were to imagine an ongoing series of fathers begetting sons who in turn beget others – and of course such series really do exist all around us – then we can observe that in every case, each son has the power to beget a son of his own (and thus become a father) even if his own father, or any previous father in the series, goes out of existence. Considered as a “causer” of sons, each member of the series is in this sense independent of the previous members. Hence this series is “accidentally ordered” in the sense that it is not essential to the continuation of the series that any earlier member of it remain in existence. And in the same way, the potter’s curving his hand in making the pot occurs even though the girlfriend’s request [that he make a pot for her] happened a week ago. The causal link between the request and the hand’s curving is also “accidental” insofar as the latter exists in the absence of the former.

(Edward Feser, The Last Superstition. A Refutation of the New Atheism (South Bend, Indiana: St. Augustine’s Press, 2008), p. 92)

In an “essentially ordered” causal series things are different (Ibid.):

But it [the hand’s curving] would not exist in the absence of the firing of the motor neurons [in the arm]. Here we have an “essentially ordered” causal series, and we have one precisely because the cause in this case is (unlike the girlfriend’s request) simultaneous with the effect. The hand is held in the position it is in only because the motor neurons are firing in such-and-such a way; take away the neural activity, and the hand goes limp. Or, once again to make use of a stock example, if we think of a hand which is pushing a stone by means of a stick, the motion of the stone occurs only insofar as the stick is moving it, and the stick is moving only insofar as it is being used by the hand to do so. At every moment in which the last part of the series (viz. the motion of the stone) exists, the earlier parts (the motion of the hand and of the stick) exist as well.

Let’s pause for a moment over the characteristic of an essentially ordered causal series identified here as that which makes it an essentially ordered causal series: it is such a series “precisely because the cause in this case is (unlike the girlfriend’s request) simultaneous with the effect.” Let’s further identify this, for future reference, as the Feser’s first characterization of an essentially ordered causal series.

Now, to pick up where we left off, the importance of the distinction is that the two different kinds of series differ, at least Feser so believes, with respect to the necessity of there being a first member. On the one hand (Ibid., p. 93):

Now, an accidentally ordered series, like the fathers begetting sons who beget more sons (and indeed like the countless other causal series familiar from everyday experience that extend backwards in time), could, in Aquinas’s view, in theory go back forever into the past. He doesn’t think any such series does in fact go back forever, but he also doesn’t think it can be proved through philosophical arguments that they don’t. That is to say, he doesn’t think it can be proved, and doesn’t try to prove, that the universe had a beginning. The reason is that, since in an accidentally ordered series the members of the series have their causal powers independently of the operation or even existence of earlier members, there is nothing about the activity of the members existing here and now that requires that we trace it back to some first member existing in the past.

On the other hand (Ibid.):

But things are very different with essentially ordered causal series. These sorts of series paradigmatically trace, not backwards in time, but rather “downwards” in the present moment, since they are series in which each member depends simultaneously on other members which simultaneously depend on yet others and so on. In this sort of series, the later members have no independent causal power of their own, being mere instruments of a first member.

(5) Though there is, of course, much about causality that demands extended deliberation, we need not get into such deliberation here and now; I will accept, provisionally at least, the distinction Feser has drawn and, moreover, agree with him that it is the essentially ordered kind of causal series that is the one at hand in Aquinas’s argument. Unfortunately, however, that the causal series with which the First Way is concerned is an essentially ordered causal series does not compel the conclusion that Feser thinks it does, that such a series must have a first member.

This was seen by, again, Edwards. Edwards was, first, aware of the distinction under a slightly different guise, though one recognizably similar in all pertinent respects:

[10] Many defenders of the causal argument would contend that at least some of these criticisms rest on a misunderstanding. They would probably go further and contend that the argument was not quite fairly stated in the first place — or at any rate that if it was fair to some of its adherents it was not fair to others. They would in this connection distinguish between two types of causes — what they call “causes in fieri” and what they call “causes in esse.” A cause in fieri is a factor which brought or helped to bring an effect into existence. A cause in esse is a factor which “sustains” or helps to sustain the effect “in being.” The parents of a human being would be an example of a cause in fieri. If somebody puts a book in my hand and I keep holding it up, his putting it there would be the cause in fieri, and my holding it would be the cause in esse of the book’s position.

Edwards goes on to bring out the point, on behalf of the defenders of the argument, of making the distinction:

[11] Using this distinction, the defender of the argument now reasons in the following way. To say that there is an infinite series of causes in fieri does not lead to any absurd conclusions. But Aquinas is concerned only with causes in esse and an infinite series of such causes is impossible.

He next quotes “the contemporary American Thomist, R. P. Phillips,” writing in support of the thesis that an infinite series of causes in fieri is impossible:

Each member of the series of causes possesses being solely by virtue of the actual present operation of a superior cause. . . . That a thing should cause itself is impossible: for in order that it may cause it is necessary for it to exist, which it cannot do, on the hypothesis, until it has been caused. So it must be in order to cause itself. Thus, not being uncaused nor yet its own cause, it must be caused by another, which produces and preserves it. It is plain, then, that as no member of this series possesses being except in virtue of the actual present operation of a superior cause, if there be no first cause actually operating none of the dependent causes could operate either. We are thus irresistibly led to posit a first efficient cause which, while itself uncaused, shall impart causality to a whole series …

The series of cause [sic] which we are considering is not one which stretches back into the past; so that we are not demanding a beginning of the world at some definite moment reckoning back from the present, but an actual cause now operating, to account for the present being of things.

Edwards does grant that the following can be said on behalf of the argument as thus understood:

[15] This formulation of the causal argument unquestionably circumvents one of the objections mentioned previously. If Y is the cause in esse of an effect, Z, then it must exist as long as Z exists. If the argument were valid in this form it would therefore prove the present and not merely the past existence of a first cause.

Yet the fundamental issue remains:

[16] But waiving this and all similar objections, the restatement of the argument in terms of causes in esse in no way avoids the main difficulty which was previously mentioned. A believer in the infinite series would insist that his position was just as much misrepresented now as before. He is no more removing the member of the series which is supposed to be the first cause in esse than he was removing the member which had been declared to be the first cause in fieri. He is again merely denying a privileged status to it. He is not denying the reality of the cause in esse labelled “A.” He is not even necessarily denying that it possesses supernatural attributes. He is again merely taking away its “first causiness.”

(6) It seems, then that Edwards has conclusively shown that neither Aquinas, at least in the Summa Theologiae, nor the twentieth-century followers of Aquinas, at least those quoted in his article, have demonstrated that an essentially ordered causal series must have a first member, an unmoved mover or an efficient cause itself having no causally prior efficient cause. What is to be said about the defenders of the argument writing some five decades after Edwards? If Feser, in his The Last Superstition, can serve as an example, today’s defenders have neither replied to Edwards’ criticism of the argument nor offered a compelling alternative demonstration of their own.

Let us then return to Feser. First, his The Last Superstition does not provide us with any discussion at all of Edwards’ critique. I have to assume, however, that he is fully aware of it, so perhaps this is due to his thinking the argument he offers, for the necessity that that an essentially ordered causal series have a first member, is conclusive and thus that a reply to Edwards is unnecessary. Let us look then at the argument his The Last Superstition offers. It is found in the continuation of the illustration, already read, of the “essentially ordered” causal series; here it is again:

But it [the hand’s curving] would not exist in the absence of the firing of the motor neurons [in the arm]. Here we have an “essentially ordered” causal series, and we have one precisely because the cause in this case is (unlike the girlfriend’s request) simultaneous with the effect. The hand is held in the position it is in only because the motor neurons are firing in such-and-such a way; take away the neural activity, and the hand goes limp. Or, once again to make use of a stock example, if we think of a hand which is pushing a stone by means of a stick, the motion of the stone occurs only insofar as the stick is moving it, and the stick is moving only insofar as it is being used by the hand to do so. At every moment in which the last part of the series (viz. the motion of the stone) exists, the earlier parts (the motion of the hand and of the stick) exist as well.

The continuation reads (Ibid., pp, 92-93):

The stone, and the stick itself, for that matter, only move because, and insofar as, the hand moves them; indeed, strictly speaking, it is the hand alone which is doing the moving of the stone, and the stick is a mere instrument by means of which it accomplishes this. The series is “essentially ordered” because the later members of the series, having no independent power of motion on their own, derive the fact of their motion and their ability to move other things from the first member, in this case the hand. Without the earlier members, and particularly the first one, the series could not continue.

Let’s recall the characterization of an essentially ordered causal series we previously identified as Feser’s first characterization, that such a series is such a series “precisely because the cause in this case is (unlike the girlfriend’s request) simultaneous with the effect.” Now, in the immediately above paragraph, we have been presented with Feser’s second characterization of an essentially ordered causal series, that “the later members of the series, having no independent power of motion on their own, derive the fact of their motion and their ability to move other things from the first member, in this case the hand.”

The two formulations are not equivalent. To focus on but the central difference here: unlike his first, Feser’s second characterization appeals to an entirely new thesis, that an essentially ordered causal series has a first member. Now it does not seem to me that he has introduced this thesis simply “out of the blue.” Rather, it seems to me that the second sentence of the paragraph just quoted presents both the thesis as the conclusion embedded in a truncated argument and the truncated argument itself. I reconstruct the argument as:

All members of an essentially ordered causal series having no power of motion on their own are members having their power of motion derived from the first member of the series.

All later members of an essentially ordered causal series are members of an essentially ordered causal series having no power of motion on their own.

Therefore, all later members of an essentially ordered causal series are members having their power of motion derived from the first member of the series.

Thus construed, it is evident that it is a valid argument. It is not evident that it is a sound argument, however, because it is not evident that the first premise is true. There is an alternative available, that:

All members of an essentially ordered causal series having no power of motion on their own are members having their power of motion derived from the earlier members of the series.

Feser himself gave expression, two pages later (Ibid., p. 95), to an equivalent statement of it:

No [later] member of the series has any independent causal power of its own, but derives what it has from something earlier in the series.

But being dependent upon earlier members of a series is not the same as being dependent upon a first member of the series. The alternative to which Feser himself has just given expression is fully compatible with there being no first member, with every member of the series being dependent upon a prior member of the series.

(7) Notice that we can see a similar argument, also truncated, in the text of Phillips quoted earlier in this post, wherein we read:

It is plain, then, that as no member of this series possesses being except in virtue of the actual present operation of a superior cause, if there be no first cause actually operating none of the dependent causes could operate either.

Spelling it out, we have:

All members of an in esse causal series having their causal power only by virtue of the actual present operation of a superior cause are members having their causal power only by virtue of the actual present operation of the first superior cause.

All inferior members of an in esse causal series are members of an in esse causal series having their causal power only by virtue of the actual present operation of a superior cause.

Therefore, all inferior members of an in esse causal series are members having their causal power only by virtue of the actual present operation of the first superior cause.

Thus construed, it is evident that this too is a valid argument, while it is not evident that it is a sound argument. It is not evident that the first premise is true. There is an alternative available, that:

All members of an in esse causal series having their causal power only by virtue of the actual present operation of a superior cause are members having their causal power only by virtue of the actual present operation of a superior cause.

This is clearly true, but it is equally clear that to be dependent for causal power upon a superior member of the series is not the same as being dependent upon a first superior cause. The alternative which has just been given expression is fully compatible with their being no first superior cause, every member of the series being preceded by another, superior one.

(8) To conclude: I said earlier that it seems that Edwards has conclusively shown that neither Aquinas, at least in the Summa Theologiae, nor the twentieth-century followers of Aquinas, at least those quoted in his article, have demonstrated that an essentially ordered causal series must have a first member, an unmoved mover or an efficient cause itself having no causally prior efficient cause. I asked what was to be said about the defenders of the argument writing some five decades after Edwards, in particular. I then claimed that, if Feser, in his The Last Superstition, can serve as an example, today’s defenders have neither replied to Edwards’ criticism of the argument nor offered an compelling alternative demonstration of their own.

Now it may well be that I have missed some crucial point in Feser’s The Last Superstition; if so, I would most appreciate having it pointed out. Or it may be that he has addressed the concerns raised in the foregoing elsewhere in his rather extensive and burgeoning corpus; again, if so, I would most appreciate being pointed in the right direction. Or it may be that Aquinas or some other defender of the argument, in whatever century, has addressed them, in which case I would also be grateful to have that pointed out.

Postscript: I’d like to add that, while I hesitate over some of the conservative moral and political asides scattered throughout Feser’s The Last Superstition, I have to say that it is as an important expression of contemporary Aristotelian, Thomistic, and Catholic thought. And, though again with the same hesitations, I recommend his blog, “Edward Feser,” as a very useful resource for those interested in contemporary traditional thinking. It can be found at:

http://edwardfeser.blogspot.com/.

If you wish, you can easily purchase The Last Superstition through Amazon.com by clicking on:

The Last Superstition: A Refutation of the New Atheism

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Gnosis and Noesis Returns: the First Way of Aquinas

Wednesday, June 16th, 2010

(1) It may well have been to the relief of some and not noticed by far more that some months ago postings to this blog ceased to appear. One primary reason for this was I had come to the realization that the theory of gnosis of Seyyed Hossein Nasr that had de facto been the blog’s primary focus has an absolutely unacceptable thesis as its basis. That thesis, which I dubbed theomonism, is the conjoint thesis that (a) there is ultimately but one reality and (b) that one reality is God.

True it is that that thesis has the virtue of making the oneness with God, that Nasr’s version of mysticism understands us, if we are well-advised, to be seeking, be an immediate and evident truth: if both there exists but God and we exist, then we are but God.

But it also has the vice of being false, for it is absolutely evident that there are many real and really distinct things, beings, or existents; you are real and I am real, but I am not you. And, equally obvious, neither are you one with or identical to God nor am I. Being then quite simply false, the theomonist thesis can in no way serve as the foundation for any rationally acceptable gnosticism.

(2) Still I am, with this post and the immediately previous one, resuming my quest for an answer to the question that gave rise to this blog, that of determining whether or not it is possible for a human being to attain, in this life, the immediate knowledge of the divine that “gnosis,” as I with Nasr use the term, refers to. Now, however, I am going to begin much closer to the beginning, with, that is, a question which is logically prior to that of whether gnosis is humanly possible, the question of whether or not God exists.

Most immediately, I am going to begin with a presentation and an analysis of the proof, or attempted proof, of the existence of God offered by Thomas Aquinas and known as the “First Way;” this is, as I’m sure you know, the first of the five ways in which, Thomas tells us in his Summa Theologiae, God can be shown to exist. There is a handy English translation of Thomas’s exposition of his First Way available to you online at (you may have to paste the following URL into your browser):

http://dhspriory.org/thomas/summa/FP/FP002.html#FPQ2A3THEP1.

In today’s post I want to make fully explicit the logic of the Summa’s version of the argument. In the next post I will make fully explicit a major problem in the argument, not only as it is presented by Thomas but also as it is presented by Edward Feser, one of today’s foremost and most publically visible followers of Aquinas, in his The Last Superstition. A Refutation of the New Atheism (South Bend, Indiana: St. Augustine’s Press, 2008).

Thomas begins his exposition of the argument by telling us that “[t]he first and more manifest way [in which the existence of God can be proven] is the argument from motion. It is certain, and evident to our senses, that in the world some things are in motion.”

Noting, with Feser (p. 91), that “‘motion’ is the traditional Aristotelian term for what nowadays we’d just call ‘change’,” let us, then, set down the following as a premise of Thomas’s argument:

Some things are in motion.

That absolutely unassailable premise in place, Thomas continues, telling us that “whatever is in motion is put in motion by another.” Let’s set that down as another premise of the argument:

Whatever is in motion is put in motion by another.

This premise is not quite so immune to being assailed as the previous one and Thomas spends the next ten or so sentences attempting to justify it. For our present purposes, however, we can leave consideration of that piece of argumentation to a later post and pick up the main argument where Thomas himself picks it up, when he says, “Therefore, whatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again.”

We can observe that, in raising the possibility that “that by which it [the thing in motion] is put in motion [is] itself put in motion” as but the antecedent in a conditional statement, Thomas may well have had in mind the opposite possibility, that “that by which it [the thing in motion] is put in motion [is] not itself put in motion.” In so doing he may well also have had in mind the following disjunction:

Either that by which the thing in motion is put in motion is itself put in motion by another
or that by which the thing in motion is put in motion is not itself put in motion by another.

Either the former or the latter has to be the case, though not both. Now if the latter is the case, then it is also the case that there is an unmoved mover which, Thomas will eventually and no doubt too optimistically go on to say, “everyone understands to be God.” It seems plausible, that is, that Thomas had the inference from the latter possibility to the existence of an unmoved mover very much in mind and thought it to have been sufficiently obvious to not require an explicit exposition.

At any rate, Thomas went on to deal with the former, and remaining, possibility, that, again, “that by which it [the thing in motion] is put in motion [is] itself put in motion.” He states:

If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again.

This statement presents us with a mover/moved series that goes back, or regresses, from one mover that is moved by a previous one to that previous one and then to that previous one’s mover, etc. This obviously raises the question of whether or not this series goes back or regresses infinitely. Thomas tells us that it cannot, offering the following rather condensed sequence of arguments:

But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand. Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God.

Let’s start by noting that the argumentation falls into two, let us call them, movements. The first movement, concluding that the mover/moved series does not go back to infinity, is given expression in the first sentence, from “But this…” to “…by the first mover” and illustrated by the moving staff and hand. The second movement, concluding that there is an unmoved mover, is given expression in the second sentence, from “Therefore …” to “…to be God.”

Rendered more fully explicit, the first movement begins with the hypothetical syllogism:

If the mover/moved series goes back to infinity, then there is no first mover.

If there is no first mover, then there are no other, subsequent, movers.

Therefore, if the mover/moved series goes back to infinity, then there are no other, subsequent, movers.

He does not make explicit the next few arguments that are needed to reach the conclusion he has to reach. But what they have to be, or have at least to be equivalent to, to reach the conclusion he is after seems to me to be incontrovertible.

One of the needed arguments takes the form of another hypothetical syllogism:

If the mover/moved series goes back to infinity, then there are no other, subsequent, movers.

If there are no other, subsequent, movers, then no things are in motion.

Therefore, if the mover/moved series goes back to infinity, then no things are in motion.

The consequent of that conclusion, that “no things are in motion,” contradicts the first premise, introduced above, that “some things are in motion.” We have therein the sole premise of the second argument needed, an instance of the argument form known as “double negation”:

Some things are in motion.
Therefore, it is not the case that no things are in motion.

The third argument needed, a modus ponendo ponens argument, has the two conclusions most immediately arrived at as its premises:

If the mover/moved series goes back to infinity, then no things are in motion.
It is not the case that no things are in motion.
Therefore, it is not the case that the mover/moved series goes back to infinity.

Now, to the second movement: we introduced above and made use of the following premise:

If the mover/moved series goes back to infinity, then there is no first mover.

The converse is also true:

If there is no first mover, then the mover/moved series goes back to infinity.

The fourth argument needed, also a modus ponendo ponens argument, has as it first premise the latter statement and as its second the last of the conclusions arrived at.

If there is no first mover, then the mover/moved series goes back to infinity.
It is not the case that the mover/moved series goes back to infinity.
Therefore, it is not the case that there is no first mover.

The fifth argument is, quite obviously, another case of double negation:

It is not the case that there is no first mover.
Therefore, there is a first mover.

Note that the series of arguments thus far set forth have concluded only that there is a first mover, i.e., there is at least one. They have not ruled out there being many. In what follows, I will use the expression “the first mover under consideration” to refer to the one alone the existence of which the arguments have, if sound, demonstrated, with no assumption, at least not yet, that there is also at most one first mover.

That said, we’re not quite done yet, though the remaining steps are obvious. One is:

If the first mover under consideration is a moved mover, then it is posterior to a prior mover.
If the first mover under consideration is posterior to a prior mover, it is not a first mover.
Therefore, if the first mover under consideration is a moved mover, then it is not a first mover.

There is no need to prove that:

The first mover under consideration is a first mover.

The pertinent double negation argument is obvious:

The first mover under consideration is a first mover.
Therefore, it is not the case that the first mover under consideration is not a first mover.

Next, another modus ponendo ponens:

If the first mover under consideration is a moved mover, then it is not a first mover.
It is not the case that the first mover under consideration is not a first mover.
Therefore, the first mover under consideration is not a moved mover.

Finally:

If the first mover under consideration is not a moved mover, then it is an unmoved mover.
The first mover under consideration is not a moved mover.
Therefore, the first mover under consideration is an unmoved mover.

It is quite evident that all of the foregoing arguments are perfectly valid. That is, if their premises are true, then their conclusions must also be true. It is not, however, quite as evident that all of the foregoing arguments are perfectly sound. That is, it is not fully evident that all of the premises invoked are true and it is therefore not fully evident that all of the conclusions arrived at are true.

The next post will be devoted to the way in which the following critical premise is not evidently true.

If there is no first mover, then there are no other, subsequent, movers.

Please note, that in having said that the premise “is not evidently true,” I have not said that it “is evidently not true.”

In an earlier post, the Logic and the Argument from Evil: Logic of September 12th, 2009, I spelled out for those not familiar with the terminology of logic the basics needed to understand the foregoing. In the succeeding post, Logic and the Argument from Evil: The Argument, I used an obviously valid, but not so obviously sound, argument against the existence of God to illustrate the way I think logic should be put to work.

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A Few Steps Ahead of Myself: A Note on Infinite Causal Regress

Thursday, May 27th, 2010

I intend, in a forthcoming post or two, to say a few words about the lack of postings over lo! these past many risings and settings of the sun. For now, however, eager to get restarted, I want to post in this blog a criticism of an argument against infinite causal regress posted, without comment, in “Turretin on Infinite Regress,” in an interesting blog, Siris, at:

http://branemrys.blogspot.com/2010/05/turretin-on-infinite-regress.html.

Some preliminaries:

First, I am commenting on the Turretin post within my own blog because Siris has a 500 character limit on comments.

Second, the Turretin in question is, according to Wikipedia, one François Turretini (1623–1687), a Swiss-Italian Calvinist theologian.

Third, the argument against the thesis of infinite causal regress is perforce one in favor of the thesis that there is a first cause, i.e., a being which is the cause of everything else while not itself being caused by anything else, i.e., God. You are most likely familiar with the most famous version of the argument, that of Thomas Aquinas.

Preliminaries thus dispensed with:

“Turretin on Infinite Regress” takes the form of a single paragraph. I quote, reformulate, and critique here that only which is found in the first half of the paragraph.

The first half of the paragraph reads:

Neither can an infinite series of producing causes be allowed because in causes there must necessarily be some order as to prior and posterior. But an infinite series of producing causes rejects all order, for then no cause would be first; rather all would be middle, having some preceding cause.

My reformulation, the purpose of which is to more clearly exhibit the formal structure of its argumentation, reads:

1. Only series having a first member are series ordered as to prior and posterior.
Therefore, all series ordered as to prior and posterior are series having a first member.

2. So, all series ordered as to prior and posterior are series having a first member.
But all series of producing causes are series ordered as to prior and posterior.
Therefore, all series of producing causes are series having a first member.

3. But no series having a first member are infinite series.
And all series of producing causes are series having a first member.
Therefore, no series of producing causes are infinite series.

My critique: that the three arguments are perfectly valid is perfectly evident, for there is no way in which their several premises can be true and their conclusions false. That they are not just valid but also sound, however, is not, for the premise of the first argument is, it seems to me, false and all premises of a sound argument must be true. For a series to be ordered as to prior and posterior it is not necessary that it have a first member; it is necessary only that all the members be, well, ordered as to prior and posterior.

We are not, I conclude, forced by Turretin’s argument to accept as true the conclusion that “no series of producing causes are infinite series” or the further conclusion that all series of producing causes are finite, i.e., terminate in a first uncaused cause.

A postliminary: the text of Thomas Aquinas’s best known arguments for the existence of God, the so-called “five ways,” are to be found in the third article of the second question of the first part (prima pars) of his Summa Theologiae. A link to an excellent online translation is:

http://dhspriory.org/thomas/summa/FP/FP002.html#FPQ2A3THEP1.

I will be using Aquinas’s and related arguments, both pro the existence of God and con, as the springboard for an exploration of the question of whether or not there is a God. There being a God, after all, is a necessary condition of there being a positive answer to the question of whether or not it is humanly possible to have a direct knowledge of the divine in this life, the question which motivated the bringing of this blog into existence.

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The Definition of God: A Reply

Saturday, September 5th, 2009

My friend and colleague Craig Looney has posted a comment (on my August 26th, 2009th post, “On My Motivation in Seeking a Demonstration That There Is or There Is Not a God”) that warrants a response in the form of a post, more visible than a comment on a comment would be. He begins by speaking of “a couple of it issues that fuzzy up the project of finding a proof of the existence or non-existence of ‘God.’” This post is devoted to the first of these issues, which he spells out as:

[1] The term “God” can mean a wide range of things. In order to even ask the question, it is necessary to define the properties (or ranges of properties) of the God that is to be proved or refuted. This may seem obvious, but many people advance a God that is “beyond definition,” or “the thing that is no thing,” etc. These God concepts are likely beyond logical proof/refutation, and are often beyond empirical testing (but see below).

If we define God as someone who can fly, kill people by pointing at them, etc (that is, as something a primitive culture might view as a deity) then God already exists, because we can outfit a person with a jetpack and a machine gun.

On the other hand, if we define God as all powerful and indestructible, then such a God is a logical impossibility, “for if it can destroy itself it is not indestructible, and if it can’t destroy itself then it isn’t all-powerful.

Craig is absolutely right that in saying that “The term ‘God’ can mean a wide range of things” and that “in order to even ask the question, it is necessary to define the properties (or ranges of properties) of the God that is to be proved or refuted.” In this post, therefore, I will begin to deal with the matter of what a god is, if there is one, or would be, if there were one. The raising of this question of the demonstrability of the existence or non-existence of a god has come, however, at an earlier point in the life of this blog than I had foreseen or laid the groundwork for; Nasr does not directly address it in The Garden of Truth. So I am approaching even as basic a matter as the definition of a god with some diffidence and reserving the right to revise later what I have to say now.

That being said, the god the existence of which can be demonstrated must of course be a “logical possibility.” Thus “the thing that is no thing,” taken thus baldly, is clearly not something that can be demonstrated to exist. In fact, contra Craig, its existence can be immediately refuted, for, applying the Principle of Non-Contradiction, no being or existent can be both a thing and not a thing, in any one respect and at any one time. Of course, if by “the thing that is no thing” we actually mean “the being that is no physical thing,” the immediate refutation just given is no longer relevant.

Going with Craig a bit deeper, a god that is “all powerful and indestructible” is indeed “a logical impossibility,” for, as he says, “if it can destroy itself it is not indestructible, and if it can’t destroy itself then it isn’t all-powerful.” But all is not lost here, for that observation does not rule out as logically impossible an indestructible god that is, not simply all-powerful, but, to use a formulation that is perhaps good enough for the time being, capable of doing all that is possible. (I say “perhaps good enough for the time being” because there is much in “capable of doing all that is possible” that begs for further elucidation, e.g., just what does the “doing” or activity of a god consist in.)

Now if it exists, the god of which I have said, in the post immediately previous to this one, that I hope it exists and fear it does not and the existence of which I hope to eventually prove or disprove is an absolutely perfect being, an ens perfectissimum. From this and some allied assumptions it follows that it is a being absolutely perfect in knowledge, in love and will, and in power, and perhaps in yet other things (e.g., aesthetic appreciation of the beautiful). (All this is said in full awareness that there is much that needs to be made explicit in just what a perfect being might be and even more so in just what a being perfect in knowledge, in love and will, and in power might be.)

That’s on the one hand. On another hand, in the immediately previous post I made reference to an argument for the existence of a god, the validity of which is evident, though its soundness is not. That argument is not one that makes use of “perfect being” or “being perfect in knowledge, in love and will, and in power” as the operative definition. A variation of the kind of argument evident in the first two of Thomas Aquinas’s quinque viae, it has as a point of departure a definition of a god looking something like this: “an efficient cause of all other beings and effect of no other,” i.e., an “uncaused cause.” All this needs spelling out and that such a being would in fact be perfect requires further demonstration. So too would the thesis that that god is unique, not just a god, but the god.

On a third hand, if I may, in the immediately previous post I also made reference to an argument for the non-existence of a god, the validity of which argument is evident, though its soundness is not. This argument, known as the argument “from evil,” does make use of a conception of a god as a “being perfect in knowledge, in love and will, and in power.”

Setting my review of The Garden of Truth aside a bit longer, in my next post I will spell out the argument from evil in the way that I think it has to be spelled out.

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On My Motivation in Seeking a Demonstration That There Is or There Is Not a God

Wednesday, August 26th, 2009

A good friend of mine, and a reader of this blog (the unkind might say that the second descriptor can only apply if the first one does), sent me the following comments and question (lightly edited) via email.

As usual it was good to see you and to have the discussions. I still remember the one in your back yard a couple of years ago. Anyway, I had a thought concerning your seeking a logical proof that god does or does not exist. Besides the fact that this question has been a devoted cause of a great many determined thinkers, there is the real problem of defining what is meant by the term logical. My question is – have you asked yourself why this is such an important issue to you. In short why are you asking the question?

The first sentence refers to a couple of extensive and intensive discussions that he, another good friend and conversation partner, and I had with several others at a social gathering this past Saturday evening. The third sentence refers to my having stated and maintained, in the course of the discussions, the following. First, I want to know, and not just believe, either that there is or that there is not a god, or absolutely perfect being. That is, if there is a god, I want to know, and not just believe, that there is, via a proof that there is, a proof as absolutely and rigorously valid and sound as any to be found in, to look towards that which is generally accepted as the “gold standard” of proof, mathematics. And, if there isn’t a god, I want to know, and not just believe, that there isn’t, via a similarly absolutely and rigorously valid and sound proof. There, in “absolutely and rigorously valid and sound,” lies my understanding of what a “logical” proof is.

The fourth sentence, noting accurately that “[definitively answering] this question [of the existence of a god] has been a devoted cause of a great many determined thinkers,” has as its backdrop the skeptical or agnostic claim that neither the affirmative nor the negative answer to the question of the existence of a god can be proven to be true. This scepticism was shared by both the agnostics who took part in Saturday evening’s conversations and the fideists (fideism, as I use the term, is the thesis that belief, in matters of theology, on the basis of faith can be a justified belief). I for my part maintained that, while I could well accept as plausible, indeed likely, a claim that there has as a matter of fact been no proof in either the affirmative or the negative, I knew of no absolutely and rigorously valid and sound argument proving that there cannot, as a matter of principle, be one.

I could have added more specifically that I am aware of both at least one argument, concluding that there is a god, the validity of which is perfectly evident and at least one argument, concluding that there is no god, the validity of which is perfectly evident. I do not, however, know of any argument, the soundness of which is so evident, concluding that there is a god nor do I know of any argument, the soundness of which is so evident, concluding that there is no god.

I notice that in this post I have been making use of the logician’s technical distinction between “validity” and “soundness” as if it were obvious to all. In the relatively near future, then, I plan to post an explanation of the distinction, so that we are all “on the same page.” I will in addition, to illustrate the distinction, spell out a valid argument, the classical “argument from evil,” the conclusion of which is that there can be no god, or absolutely perfect being. And I will spell it out in such a way that its validity will be perfectly evident, even while its soundness is not.

But now, then, towards an answer to the question posed: I have indeed asked myself why this question of the existence of a god is such an important issue to me. I do not, however, actually have anything like a full answer. As a preface to the minimalist answer that I am now prepared to give, let me note that, from the point of view of science, mathematics, and philosophy, the question of the personal motives of the scientist, the mathematician, or the philosopher are of but secondary interest; the conclusion arrived at and the logical rigor of the steps taken to arrive at it are the matters of primary concern. If I may dare to compare the case of a much the lesser yours truly with the case of a much the greater Stephen Hawking, the question of his personal motives in thinking about, say, the “Big Bang” is of but secondary interest; the conclusion that the “Big Bang” took place and the logical rigor of the steps taken to arrive at that conclusion are the matters of primary concern.

And now, then, what will have to pass as an answer: modifying slightly what I said in my June 14th post in response to another good friend’s question, that of whether or not I believe in a divine being, I will say the following: I both honestly hope that such a divine being does exist, at least the divine being which is such as I would have a divine being be, and honestly fear that there isn’t such a being. I can concurrently both so experience hope and fear, as opposed to joy and sorrow, because, on the one hand, I neither know nor believe that such a divine being exists and yet, on the other, I neither know nor believe that such a divine being does not exist. While I have hopes and fears, I have no knowledge or belief either way. I desire to know, one way or the other.

Why do I so hope, fear, and desire to know? It is because (1) I further hope that life has an other than merely ad hoc purpose and fear that it does not and (2) I have a conception that life has an other than merely ad hoc purpose only if there is a god, that is, an absolutely perfect being. I call it a “conception” because I have not yet given it an articulation sufficient to warrant its being called a hypothesis. Far less have I subjected it to the dialectics of concerted consideration and discussion, weighing its pros and cons. Far, far less have I demonstrated it to be true. I hope, in the (admittedly relatively distant) future, to move in the direction of changing that set of circumstances.

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