Posts Tagged ‘Logic’

Something of an Aside (cont.): More on Those Universal Propositions about Muslims.

Friday, July 23rd, 2010

In response to my critique of his post, “A Mosque Grows Near Brooklyn,” in The Maverick Philosopher, Bill Vallicella sent me a note telling me that he had “added an addendum [to his post] that addresses your concerns.” I really don’t want to be obnoxious, but I think his addendum only partially addresses the concerns I raised in my post.

In that addendum he took note of my critique thusly:

Over at Gnosis and Noesis, Professor Richard Hennessey rather pedantically and uncharitably picks at my “Muslims aren’t very ‘liberal,’ are they?” Do I mean that no Muslim is liberal? Of course not. A universal proposition can be refuted by a single counterexample. (And it is worth noting en passant that a necessary universal proposition can be refuted by a single merely possible counterexample.) Since it is obviously false that no Muslim is liberal, it is uncharitable to take my sentence as expressing that proposition.

In response, let me first confess that I am all too often pedantic, often boring myself; anyone, moreover, who uses the adverb “thusly,” as I did just above, is clearly and insufferably pedantic. And I freely admit that charity is not my most prominent virtue.

At any rate, I consider his statement, “Do I mean that no Muslim is liberal? Of course not.” to partially address my concerns.

If the next two sentences, from “A universal proposition” through to “merely possible counterexample),” were intended to reassure us that Mr. Vallicella knows his logic, they were hardly necessary; as I said in my post, he “has to my mind one of the best philosophical blogs to be found” and “the man understands and appreciates rigorous thinking.” Since, however, the cat is out of the bag about my lack of charity, I might as well allow myself to note en passant that I consider anyone who uses en passant instead of “in passing” to be a fellow pedant.

I will grant him the truth of the paragraph’s last sentence, “Since it is obviously false that no Muslim is liberal, it is uncharitable to take my sentence as expressing that proposition.” I have to say, however, that while Mr. Vallicella may see it to be obviously false that no Muslim is liberal, it is neither obvious that all are able to so see it nor obvious, from his pre-addendum post, that Mr. Vallicella so sees it. This is why I think my concerns have been but partially expressed: when one leaves the quantifier unexpressed he leaves the careful, if uncharitable, reader with the question of whether all or some are being talked about. So, when I read his “Muslims aren’t very ‘liberal,’ are they?” I really did find myself asking, “Does he mean ‘all’ or ‘some’?” And, quite frankly, reading and rereading the blog in its entirety did not go far towards allaying my concerns.

Now, to move from being merely obnoxious to being absolutely obnoxious, the same reasons that led me to my pedantic and uncharitable post leads me now to observe that I would have found myself with similar concerns were I to have read without benefit of his clarification the post he published immediately prior to the one about the mosque. In the opening to Will Liberals Ever Retire the Race Card?, that is, we read:

Why should they? As good leftists, they believe the end justifies the means, and their shameless race-baiting is a means conducive to their ends.

You know enough about me by now to have predicted that I will have already formulated the following categorical syllogism:

All leftists are believe the end justifies the means.
All liberals are leftists.
Therefore, all liberals believe the end justifies the means.

Well, actually, I may still have those concerns. Certainly the paragraph with which he closes the post does not reassure me all that much.

And you should do your bit to push back. The next time some scumbag of a liberal calls you a racist for standing up for fiscal responsibility or the rule of law, say this: You lie about us, we’ll tell the truth about you.

Now, about that question about whether Islam is a religion… nah, not today.

The Maverick Philosopher can be read at: http://maverickphilosopher.typepad.com/.

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Something of an Aside: On Some Universal Propositions about Muslims

Thursday, July 22nd, 2010

The Maverick Philosopher, Bill Vallicella, has to my mind one of the best philosophical blogs to be found; in the past week, for just a couple of instances, he has posted a couple of very interesting pieces on set theory, “Sets, Pluralities, and the Axiom of Pair” and “The Existence of Infinite Sets.” The man understands and appreciates rigorous thinking. It is for this reason that I was taken a bit aback when I read his July 20th post, “A Mosque Grows Near Brooklyn.”

Many things are said in the post, but for now I’ll focus on just one paragraph. The paragraph reads:

Muslims aren’t very ‘liberal,’ are they? They are intolerant in their attitudes and their behavior. Now the touchstone of classical liberalism is toleration. Toleration is good, but it has limits. (See the posts in the category Toleration.) So why should we tolerate them when they work to undermine our way of life? The U. S. Constitution is not a suicide pact. We are under no obligation to tolerate the intolerant.

With a full understanding that to point to the utterly obvious is to risk being seen as simply obnoxious, Let me observe that he has made three universal statements about Muslims in the course of that paragraph. First, then, surely the rhetorical question, “Muslims aren’t very ‘liberal,’ are they?” is actually an expression of the proposition:

No Muslims are very liberal.

or even, perhaps, in view of the sentence which immediately follows:

No Muslims are liberal.

There is second, then, that immediately following sentence, “They are intolerant in their attitudes and their behavior.” I am hard-pressed to take it as meaning anything other than:

All Muslims are intolerant in their attitudes and their behavior.

Third, there is the complex question, “So why should we tolerate them when they work to undermine our way of life?” It is a complex question in that it assumes that they, i.e., Muslims, are working to “undermine our way of life,” i.e., that:

All Muslims are working to undermine our way of life.

Now I personally know a number of Muslims. I can assure you that at least one of them is very liberal, at least one of them is tolerant in attitudes and behavior, and at least one of them is not working to “undermine our way of life.” The three universal statements that I see staring out at us from the quoted paragraph are all then false, as even the most rudimentary acquaintance with old Aristotle’s logic and its “square of opposition” would have you see.

On the other hand, of course, I willingly admit, again on the basis of personal experience, that at least one Muslim is not very liberal, at least one is intolerant in attitudes and behavior, and at least is working to “undermine our way of life,” albeit in, yes, legal ways.

Of course, we can’t leave things like that, simply saying that, while at least one Muslim is liberal, tolerant, or supportive of “our way of life,” at least one Muslim is not, for these are serious matters. But serious matters require serious treatment. The matters of the liberality, the toleration, and the support for “our way of life” of Muslims therefore require serious treatment, and first and foremost some serious social science, inquiring into how many Muslims are or are not liberal, tolerant, and supportive of “our way of life,” in what ways, and to what degree.

I agree with what I take to be the sentiment expressed by the last sentence of the paragraph, “We are under no obligation to tolerate the intolerant,” albeit with the proviso that more specification is sorely needed. I’ll put it more strongly: we are under an obligation not to tolerate the intolerant. Now surely one of the first things that someone who likes to think of himself as a philosopher should do in accordance with that obligation is challenge any intolerant position that he encounters, especially if it one held by a philosopher. Thinking, then, that our maverick philosopher has, on the points at hand, at least if I have understood him correctly, become one among the intolerant, I am challenging him to present the evidence that would back up his assertions, implicit or otherwise.

The Maverick Philosopher can be read at: http://maverickphilosopher.typepad.com/.

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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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The Mutual “Inness” of the Human and the Divine

Wednesday, September 30th, 2009

In my previous planned and on-topic post, the “Where We Are Coming from and Where We Are Going to: 6” of August 23, I distinguished between two distinct, as I was then thinking, understandings, of the nature of God, the human, and the relation of the human to God, as two distinct potential metaphysical foundations for gnosticism.

One of the two understandings, I said, is contained in the thesis that I have identified (in the June 28th, 2009, post, “Nasr’s Gnosis and ‘Theomonism’”) as theomonism, the thesis that the divine being is the one and only real being. In “Where We Are Coming from and Where We Are Going to: 6” I offered the following argument against that thesis, an argument the validity of which is quite evident and the soundness of which is, if not quite as quite evident, immediately adjacent to being so.

1. If there is anything that is in any way other than the one and only divine being (if such latter there indeed is), then the one and only divine being is not the only being.

2. There is something that is in some way other than the one and only divine being (I offer my own being as evidence; you can offer yours).

3. Therefore, the one and only divine being is not the only being.

It follows that, since it is false, the thesis of theomonism cannot serve as a basis for the doctrine of gnosticism.

I closed “Where We Are Coming from and Where We Are Going to: 6” by saying that in the post that ended up being the present one I would “take a look at the other of the two distinct understandings … as a second potential metaphysical foundation for gnosticism, different [from theomonism] but also figuring prominently in The Garden of Truth.” This understanding, encapsulated in the title of today’s post, “The Mutual ‘Inness’ of the Human and the Divine,” can be put a bit more explicitly as: God is in us and we are in God.

Nasr’s statement of the thesis of the mutual “inness” of the human and the divine is contained in a sequence of three densely packed paragraphs (The Garden of Truth, pp. 5-6). In the first of these three paragraphs, we read:

[Sufism] provides, within the spiritual universe of the Islamic tradition, the light necessary to illuminate the dark corners of our soul and the keys to open the doors to the hidden recesses of our being so that we can journey within and know ourselves, this knowledge leading ultimately to the knowledge of God, who resides in our heart/center.

By journeying within ourselves, we journey to God, who resides in, and therefore is in, our “heart/center.”

The next paragraph distinguishes between the being in God which we both have eternally had and even now have and the created being which we also have now. It reads:

Not only were we created by God, but we have the root of our existence here and now in Him. When we bore witness to His Lordship as mentioned in the Quranic verse, “Am I not your Lord?” the world and all that is in it were not as yet created. Even now we have our pre-eternal existence in the Divine Presence, and we have made an eternal covenant with God, which remains valid beyond the contingencies of our earthly life and beyond the realm of space and time in which we now find ourselves.

That is, we have been and are in God.

Besides introducing two other key themes, that of a “fall” and that of our having “become forgetful beings,” the next paragraph confirms both of the beings in, ours in God (“our reality in God”) and God’s in us (“God, who resides at the depths of our being”).

The answer to the question “who are we?”is related in a principial manner to our ultimate reality in God, a reality that we have now forgotten as a result of the fall from our original and primordial state and the subsequent decay in the human condition caused by the downward flow of time. We have become forgetful beings, no longer knowing who we are and therefore what our purpose is in this life. But our reality in God, who resides at the depths of our being, is still there. We need to awaken to this reality and to realize our true identity, that is, to know who we really are.

Now to the point of the present post and the reason why I have had second thoughts about holding that the thesis of the mutual “inness” is distinct from that of theomonism: if by “in” is meant “entirely in” and if the sense in which the one is in the other is the same as the sense in which the other is in the one, then if there is an existent a and an existent b such that a is in b and b is in a, then a and b must be at least co-extensive. And the thesis that the human, in its true identity, is at least co-extensive with the divine is consistent with, indeed implied by, the theomonist thesis.

It seems to me that both the theomonist thesis that only the divine is real and thus that, if we are real, we are identical with the divine and the thesis of mutual “inness,” such that we and God are at least co-extensive, provide all too simple answers to the question of how humans can enjoy an immediate and direct knowledge of the divine, the “beatific vision,” in this life. If identity or co-extensiveness were sufficient conditions of knowledge, then the coffee cup to which I have turned so frequently this morning would know itself.

In the next planned and on-topic post, I will have something to say about the “fall” and our having “become forgetful beings” that Nasr speaks about.

***

If you wish, you can easily purchase The Garden of Truth through Amazon.com by clicking on:

The Garden of Truth: The Vision and Promise of Sufism, Islam’s Mystical Tradition

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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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Where We Are Coming from and Where We Are going to: 4

Sunday, July 26th, 2009

In my July 11th post, “Where We Are Coming from and Where We Are Going to 3: More Logic,” I made two claims. One is that, in the passage from his The Garden of Truth currently under examination Nasr does not provide us with proofs, or even arguments, that we humans have both a life prior to our incarnate life and a life posterior to our incarnate life. (It will be helpful at this point to recall, from my July 6th, 2009, post, “Where We Are Coming from and Where We Are Going to 2,” that “ours is an ‘incarnate life’ if and only if there is an immaterial or non-physical something, be it a soul, a psyche, a self, or whatever, that is other than but somehow incarnate or in our physical bodies as we live out this life, ‘here and now on earth as human beings.’”)

The other claim that I made arose from the observation that:

The statement, “We have one incarnate life,” is not as explicit as logic demands that it should be. For one thing, it actually represents the conjunction of two statements, viz. “We have at least one incarnate life” and “We have at most one incarnate life.” The first statement rules out our having no incarnate life and the second rules out our having two or more incarnate lives.

The claim, then, was that Nasr does not provide us with a proof of or even an argument on behalf of the second of the two conjuncts, “We have at most one incarnate life.”

He does, however, it seems to me, provide us with an argument on behalf of the first of the two conjuncts, “We have at least one incarnate life.” This, I believe, can be extracted from the continuation of the passage at hand and will provide us with the focus of today’s post.

Picking the passage up from the point at which we left it, we read (p. 7):

The answer of the materialists and nihilists is that we came from nowhere and we go nowhere; we had no reality before coming into this world, and nothing of our consciousness survives our death. They reduce our existence to simply the physical and terrestrial level and believe that we are merely animals (themselves considered as complicated machines) who have ascended from below, not spiritual beings who have descended from above. But if we are honest with ourselves, we realize that even the concept of matter or corporeality is contained within our consciousness and that therefore when we ask ourselves who we are, we are acting as conscious beings and have to begin with our consciousness. If we are intellectually awake, we realize that we cannot reduce consciousness to that which is contained in our consciousness.

The argument, however, that I think we can see to be contained within or lying behind the passage can be stated in the following way:

1. We are conscious beings.
2. Conscious beings are beings not reducible to being exclusively material beings.
3. Therefore, we are beings not reducible to being exclusively material beings.

Let’s call this argument the “main argument.”

The first premise of the main argument, that we are conscious beings, can be arrived at as the conclusion of the following chain of argumentation:

1.a. There is a concept of matter or corporeality that we have in our consciousness.
1.b. Therefore, we have consciousness.
1.c. Only conscious beings have consciousness.
1.d. Therefore, we are conscious beings.

The key premise here, that there is a concept of matter or corporeality that we have in our consciousness, is either equivalent to or at least implied by his “even the concept of matter or corporeality is contained within our consciousness.” The remaining steps in the argument follow with nearly complete explicitness. So, if we grant him that key premise, any reasonable person would say that he must be granted the conclusion that we are conscious beings. The argumentation is, in other words, valid.

But is the argumentation sound? That is, is the premise, that there is a concept of matter or corporeality that we have in our consciousness,” actually true? Certainly no materialist worth his or her salt would accept it. For a rigorous materialism, to speak of a “concept,” as in “the concept of matter or corporeality,” is but to employ an in the end misleading manner of speaking. While we can with various instruments observe various activities of the brain, no observation of the activities of the brain will bring anything like a concept to light. The same is true of “consciousness.” While materialists will be willing to admit that we are conscious, and certainly when we are asking who we are, no observation of the activities of the brain will bring anything like consciousness to light.

Then there is the second premise of the main argument, that “conscious beings are beings not reducible to being exclusively material beings.” It takes a bit more work to extract this premise from our passage, but I think that, with the help of some charitable reworking, it can be so extracted from the passage’s last line, which says that “we cannot reduce consciousness to that which is contained in our consciousness.”

Now this statement is a bit odd, for according to what Nasr says earlier in the passage it is “the concept of matter or corporeality” [my emphasis] that “is contained within our consciousness,” not matter or corporeality itself. But, while he actually says that we cannot reduce consciousness to the concept of matter or corporeality, he must mean to say that we cannot reduce consciousness to matter or corporeality, as the materialists wish to do. Otherwise the passage would not actually constitute a reply to materialism. So, I propose to understand him as having intended to say just that, that we cannot reduce consciousness to matter or corporeality. Accepting this as a premise and conjoining an equally reasonable additional premise or two, it will follow that conscious beings are beings not reducible to being exclusively material beings, the premise sought.

Once again, however, while we find ourselves having an apparently valid piece of argumentation, we are faced with the question of the argumentation’s soundness. That is, is it true that we cannot reduce consciousness to matter or corporeality? Is it then true that conscious beings are beings not reducible to being exclusively material beings?

Now I am by no means claiming that the materialist thesis is true or that the argumentation extracted from Nasr’s passage is not sound. I have my opinion, but I do not know whether the materialist thesis is true or false. It is my intention, at some point later in the history of this blog, to subject the question to a thorough investigation.

***

If you wish, you an easily purchase The Garden of Truth through Amazon.com by clicking on:

The Garden of Truth: The Vision and Promise of Sufism, Islam’s Mystical Tradition

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Where We Are Coming from and Where We Are Going to: 3: More Logic

Saturday, July 11th, 2009

In my July 6th post, I began to assess the answers that Nasr’s Sufism gives to the questions of where we come from and where we are going, that, in brief, we come from and we are going to God. In today’s post I continue that review of those answers.

Nasr has stated, then, as explicitly as we might want, that we humans have a life prior to an incarnate life, an incarnate life, and a life posterior to an incarnate life. In the passage at hand, from his The Garden of Truth, however, he has not provided us with a proof, or even an argument, that this is so. In today’s post I want to point out further that his view that we have one incarnate life is equally unproven and lacking of an argument on its behalf; it stands as an assumption to which there are alternatives which have not been ruled out.

We need to first observe that the statement, “We have one incarnate life,” is not as explicit as logic demands that it should be. For one thing, it actually represents the conjunction of two statements, viz. “We have at least one incarnate life” and “We have at most one incarnate life.” The first statement rules out our having no incarnate life and the second rules out our having two or more incarnate lives.

The pertinent truth-table spells out the possibilities. That is, letting “L” abbreviate the statement, ““We have at least one incarnate life” and “M” abbreviate the statement, “We have at most one incarnate life,” that truth-table is:

L M
T T
T F
F T
F F

Nasr is assuming the truth of the view represented by the first row, that we have at least one incarnate life and we have at most one incarnate life. But the second row, representing the view that we have at least one incarnate life and we (in fact) have more than one incarnate life. This view represents a particularly live option for those who, like Nasr, understands us to have at least one incarnation; if at least one incarnation is possible, why would not two or more incarnations, all but the first of which would be reincarnations, also be possible? In fact, why should we not admit the possibility of, not just a finite number of reincarnations, but an infinite number? And similarly for, let me call them for brevity’s sake, pre-incarnations.

If we bring in additional considerations, possibilities abound; e.g., if there are multiple incarnations, need they be continuous, such that no time elapses between one incarnation and the next, or can they be discontinuous? But I propose leaving such additional considerations aside, unless and until they impose themselves upon us.

In closing today’s post proper let me underline the fact that I am not yet in a position to claim that Nasr is wrong in assuming the truth of the view represented by the truth-table’s first row. I am simply pointing out that there is at least one other logical possibility the falsehood of which he has not proven or even argued. But I plan to take up the reason why Nasr thinks he can accept the perspective he does in the next scheduled on-topic post.

P.S. The distinction between “at least one” and “at most one” shows up, of course, in other contexts. Shifting the meaning of “incarnation” to the one operative in the standard Christian doctrine of Christ, or Christology, and letting “L” here abbreviate “There is to have been at least one incarnation” and “M” abbreviate “There is to have been at most one incarnation,” we find ourselves looking at the same truth-table as above. The first row obviously represents a Christian Christology and the second a non-Christian Christology.

Again, turning to geometry and letting “L” now abbreviate “Through a point not on a given line there is at least one line parallel to the given line” and “M” abbreviate “Through a point not on a given line there is at most one line parallel to the given line,” we once more find ourselves looking at the same truth-table as above. The first row obviously represents Euclidean geometry and the second a non- Euclidean geometry.

***

If you wish, you an easily purchase The Garden of Truth through Amazon.com by clicking on:

The Garden of Truth: The Vision and Promise of Sufism, Islam’s Mystical Tradition

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