Exploring possible human knowledge


Paul Vjecsner



Inasmuch as the title of the present pages is PRESUMED IMPOSSIBILITIES, it may be in order to turn attention to other questions that customarily belong in that category. The most significant one is doubtlessly to prove the existence of God. Although the attempt has been made by a number of thinkers through history, many suppose that at least since Immanuel Kant such a demonstration is impossible.

That I don't accept that judgment could be surmised from my indication on the home page of a book I published and so forth. Alongside fruitful explorations of other logical matters, there was a notion in me that reality just may contain certain evidence from which a simple demonstration of a supreme being can be inferred. It should be a matter of correctly assembling well-known phenomena as premises from which to derive a conclusion, the same as deduction in mathematics or other aspects of life.

And it is indeed our lives and by extension all life, as alluded to on my mentioned home page, that provides an opening in this regard. At this time, though, I want to concentrate on this subject of a supreme being and on others as they came up in a review of my book, so that I can point out flaws that beset respondents to me. (Since writing this about reviewing of my book, I decided to add a discussion regarding the issue of proof of the existence of God. It follows below.)

First, let me reproduce a letter from the editor of the journal that published the review. I should note that I am not a professor, as addressed there, and have no academic affiliation. But, as seen, the letter is quite positive, while the opposite applies to the review. Sadly, editor Castañeda died before that publication. Perhaps he would have been further helpful. Below this letter here, then, I discuss the review.

27 October 2003



PHOTOGRAPHY, continued1, 2, 3, 4

PORTRAITURE, continued1, 2, 3

COMMERCIAL ART, continued1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25


AUTOBIOGRAPHY, continued1, 2, 3, 4

It appeared in the December 1992 issue of NOUS. For convenience, I will add parenthesized numbers as hyperlinks to my numbered comments below the review.

Paul Vjecsner, On Proof for the Existence of God, and Other Reflective Inquiries (New York: Penden), 258 pp., $20.00.


University of Notre Dame

This book consists of an introduction, which outlines the author’s philosophical methodology, and four chapters. The first chapter is about language and concepts; it is divided into sections on the signification of language, concepts and their constituents, and definition. The second chapter is devoted to metaphysics; it contains a section on the self and mind and one on external reality that focuses on extension and causality. The topic of the third chapter is logic and mathematics. The fourth chapter offers an argument for the existence of God and concludes with some thoughts about goodness and the prospects for immortality.

It is a peculiar work. For one thing, it lacks the customary scholarly apparatus of footnotes and bibliography. For another, it contains numerous uninformed and cranky opinions about scientific matters. The author’s attempt to criticize relativistic physics is a typical example. The argument goes as follows: “As to energy, it is defined as the capacity for doing work, and it is hence a causal property. It can at once be noted that energy cannot therefore be an independent entity, let alone the constituent of material reality, as proposed in physics” (pp. 74-75). Physicists will not be impressed by this argument; nor should philosophers be. (1)

The chapter on logic and mathematics is particularly rich in astonishing claims. Here is one: “As infinities, however, cannot be unequal in size, possessing none, so can they not be equal” (p. 122). But what of Cantor’s proof that the set of real numbers has a larger cardinality than the set of natural numbers? The author’s objection to it goes as follows: “The reasoning flaw in set theory lay in supposing completion of these sets, so that by assuming completion of one of them the other can be continued since infinite. Neither can be complete, for their infinity allows continuance by definition” (p. 119). Modern geometry too comes in for criticism. After setting forth what he takes to be a proof of Euclid’s fifth postulate, the author dismisses non-Euclidean geometry with these remarks: “Meanings play instead a misleading part in non-Euclidean geometry, founded on the rejection of the just proven fifth postulate or its companion. These are replaced by postulates on which are built new geometries, which correspondingly, while thought to be consistent, engage in contradiction” (p. 133). Comments of this caliber about set theory and geometry seem to me a clear indication that they are subjects the author is not competent to discuss. (2)

If one reads this book from beginning to end, one has to get through more than two hundred pages studded with such claims (3) before arriving at its discussion of natural theology. Judging by the book’s title, it is of special importance to the author, and so I now turn to an examination of his treatment of arguments for the existence of God.

The final chapter begins with criticism of the work of others. The following argument is taken to be representative of the recent revival of interest in ontological arguments:


“2.i.  It is either necessary or impossible that God exist. But, it is argued,


2.ii.  It is not known to be impossible that God exist. Hence, it is inferred,


2.iii.  It is not impossible that God exist. In consequence and by 2.i it is concluded that


2.iv.  It is necessary that God exist” (p. 221).


This is indeed a bad argument; the inference from 2.ii to 2.iii is fallacious, as the author notes. But is it an argument any philosopher takes seriously? Though he mentions no one by name, the author presumably has in mind such philosophers as Hartshorne, Malcolm and Plantinga when he speaks of the ontological argument being recently revived. He makes absolutely no effort, however, to show that any of these philosophers or, for that matter, any philosopher has ever endorsed or even recommended serious consideration of this particular bad argument. It is so obviously fallacious that it would be silly to try to foist it on any good philosopher. (4)

The author offers three teleological arguments for the existence of God, all of which are variations on [a] theme. The simplest of them goes as follows:


III.1.  God equals the cause of purposive events of concerned scope.


III.2.  Purposive events of concerned scope exist in nature.


III.3.  Events that exist in nature imply the existence of a cause of them. Hence, by III.2 and III.3,


III.4.  A cause of purposive events of concerned scope exists. Therefore, by III.1 and III.4,


III.5.  God exists” (p. 231).


The first premise is said to be a “starting definition” (p. 231), and purposive events are said to be “events that are, proximate or eventual, objects of purpose” (p. 223). About the restriction to purposive events of concerned scope, the author says only this: “It should be prefixed that when referring in the proof to the scope of the powers and of events caused by them, meant is a correspondence between these magnitudes, in concord with earlier observations on force as measured by results” (pp. 223-224). Though I find this statement somewhat opaque, it suggests that purposive events of concerned scope are being defined as those purposive events from whose occurrence we may infer the presence of a particular kind of cause, namely, divine power, just as forces are inferred from their results. After all, it would seem that not all purposive events warrant such an inference since some at least are caused by humans or other organisms, and so some such restriction appears needed if the first premise is to be plausibly regarded as true by definition.

If this is right, then I think the argument is not a successful piece of natural theology. The trouble comes from the second premise. It would be hard to deny that there are purposive events in nature, but this is not what it asserts. Once the first premise is granted definitional status, what has to be established in order to show that there are purposive events of concerned scope in nature is that there are in nature certain events whose cause is God. This is not obvious and would not be hard to deny. And I can think of no way to establish it antecedent to or independent of showing that God exists and exercises certain causal powers. So I conclude that the argument is question-begging because, given its first premise, one would have to assume the truth of its conclusion in order to justify its second premise. In this respect it resembles the argument to the conclusion that God exists from the premises that 2 + 2 = 4 and that God exists if 2 + 2 = 4. This argument is sound, provided God exists, but it is not a proof of God’s existence or a successful piece of natural theology.

I can find nothing to praise in this book. I think its efforts to criticize the views of others are uniformly unconvincing and its attempts to set forth constructive arguments are failures too. I do not believe any professional philosopher would profit from reading it. (5)

My comments follow.

1. I responded to several points after the above letter, and more to the reviewer after the published review, but other than for a weakness of his he may have feared would be exposed, he did nothing about it. That my work be peculiar to him should be no surprise. It was not written in the form he is accustomed to, particularly in the style in which academic philosophers communicate among themselves. Instead it is an entirely independent work which avoids interruption by footnotes and too specific references to other work through bibliographies. That it contain numerous uninformed and cranky opinions about scientific matters can be itself understood as an opinion of one who adheres unquestioningly to science's views of the day, admittedly often tentative. I am not at all uninformed about the subjects I discuss, and challenging anything widely accepted is automatically viewed as coming from a crank. The reviewer says that my "argument [criticizing relativistic physics] goes as follows...". However, I present quite many arguments, going into the subject, as in other cases, very thoroughly. The argument of mine he quotes, furthermore, stands on its own, as anyone unbiased can tell by a careful reading. Professor Quinn says that physicists will not be impressed. This slavish approach to science commits the fallacy of "argumentum ad verecundiam", of appealing to a supposed authority, rather than using reasoned argument. (I do not hesitate pointing out particular fallacies, as in a recent response to a book, this likewise serving in reaching the truth, as do more noticeably constructive findings.) Back to the discussed

2. Of the three quotations in this paragraph two are "out of context", meaning they are isolated from their surrounding which explains them. The reviewer again mocks them without offering an opposing argument, merely voicing his opinion that it seems to him clear I am not competent to discuss the subjects. Why? Because I clash with received pronouncements, not because the reviewer knows much about it. The first quotation does not include my given explanation of why infinities have no size, and the third one, which by him "dismisses" alone non-Euclidean geometry, does not give my explanation of how the meanings are contradictory. And the second quotation, once again, is self-explanatory. If the reviewer had the decency to read it carefully, supposing an adequate intellect, he might recognize its validity. To the discussed

3. Thank you for the appreciative "studded". It happens that in these "more than two hundred pages" I explore very thoroughly and positively major issues in philosophy and beyond, offering new understandings in how we acquire knowledge, how language and formation of concepts get involved, how fundamental worldly realities can be ascertained, and how a complete system of logic can be constructed that should be an extensive improvement and simplification of what is extant in the field. In the process I include many carefully thought-out and designed diagrams, that either serve to demonstrate assertions in logic or to edify others. The reviewer doesn't bother to scrutinize any of this, contemptuously dismissing at the end all of my work offhand. Back

4. Just where, dear professor, do you think I picked up this argument? I certainly think myself capable of creative arguments, but I would hardly bother to invent this one in order to refute it. The subject is much too important to me. I did find it useful to cite some former arguments (not only this one) to point out the way they can be erroneous. And in the present case, in keeping with my quest for simplicity and clarity I had to distill it from arguments much worse. They are presented in The Encyclopedia of Philosophy by Macmillan, 1972 edition, volume 5, page 540, and they originate with the philosophers Hartshorne and Malcolm mentioned by the reviewer. Let me quote two passages.

Thus God’s existence is either logically necessary or logically impossible. However, it has not been shown to be impossible—that is, the concept of such a being has not been shown to be self-contradictory—and therefore we must conclude that God necessarily exists.


                  (6) Nq v N~q             Inference from (4,5)

                  (7) ~N~q                   Intuitive postulate (or conclusion

             from other theistic arguments):

             perfection is not impossible

                  (8) Nq                       Inference from (6,7)

The first passage sounds very much like my quoted form, does it not? So there goes the contention that no "philosopher has ever endorsed or even recommended serious consideration of this particular bad argument. It is so obviously fallacious that it would be silly to try to foist it on any good philosopher". Perhaps any "good" philosopher. That I make "absolutely no effort" to show that any philosopher has done those bad things is another unseemly accusation. It is enough that I give for the purposes a generalized example of these arguments advanced. I described above the amount of effort I put into the entire work, and there is no justification in expecting me to describe more specific attempts by particular philosophers. If there is an issue of insufficient effort, it applies to the reviewer in his perusing my writing.

Returning to the familiar sounding first passage above, it is yet worse in wording than is my citing of that bad argument. "Has not been shown" could be equated with my "is not known", but the qualification between the dashes confuses the passage still more. First I may note that the inference from either "has not been shown" or "is not known" commits the fallacy of "argument from ignorance". Not knowing something to be true does not imply its falsehood and so the truth of its alternative. But the injection between the dashes needlessly and falsely adds to the for whatever reason unknown. It is also false, because non-contradiction does likewise not make an inference valid. This may not be the place though to explain this.

The second above passage is worse even than the first. In the symbolism on the left side (I will simplify my definitions), "N" stands for "necessarily", "q" for "God exists", the tilde "~" for "not", and the "v" in line (6) for "or". That line then says "It is either necessary that God exist or necessary that he does not, namely impossible that he exist"; line (7) says "It is not necessary that God does not exist"; and line (8) "It is necessary that God exist". On the right side are the reasons for the inferences, and of interest is line (7), previously based on the like of "It is not known to be necessary that God does not exist". And this reason, at least clearly stated, is now substituted by a mysterious "intuitive postulate (or conclusion from other theistic arguments)". Back to the review

5. Here now came the most extended criticism of my work. The reviewer again groundlessly limits what I say to what he seems to see on first sight. He writes (after citing p.223 of my book) that about a certain subject I say "only this",  and then quotes a sentence of mine, as see. And that sentence does not concern that subject as referred to by him in the deduction there from III.1 to III.5 (p.231 in my book). It concerns and precedes a deduction on a previous page (224), and there should be no wonder he finds it "opaque" applying it to the wrong place. The sentence has to do, as it says, with the correspondence of the scope, the magnitude, of a force with its result. The scope referred to by him has to do instead only with events not as forces. And what the reviewer did mean to attack is my speaking of "concerned" scope.

Put simply, he charges me in that paragraph with defining "purposive events of concerned scope" as "those purposive events from whose occurrence we may infer...a particular...cause, namely, divine power", which would circularly assume conclusion III.5 in premise III.2. He says a statement of mine "suggests" this. Now what he sees as suggested does not therein constitute a definition. I do not so define those events anywhere. On the contrary, I describe them as ones observed in live organisms, without reference to any cause, let alone a special one.

The reviewer starts the next paragraph with "If this is right", referring to that suggested definition. This is typical hypothesizing by contemporary thinkers. I would expect a substantiated claim instead, namely pointing at the alleged definition. He continues, "then I think the argument is not a successful piece of natural theology". Again, "I think" is not successful reasoning itself. And if my "piece" is not successful, whose is? Natural theology has been notorious for getting nowhere.

He goes on saying, "The trouble comes from the second premise". Now how would you know? You only hypothesize and "think" something is true. How then do you also know there is trouble? I am glad you say that it would be hard to deny that there are purposive events in nature. This has been really the bone of contention in the most publicized theistic arguments, exemplified by the dispute between Darwinians and Creationists.

The critic proceeds saying that "what has to be established in order to show that there are purposive events of concerned scope in nature is that there are in nature certain events whose cause is God" and that he "can think of no way to establish it antecedent to or independent of showing that God exists...". Again, that he can think of no way does not imply someone else can't, but how again does he substantiate his first statement quoted in this paragraph? No, "what has to be established in order to show that there are purposive events of concerned scope in nature is that there are in nature" purposive events of, to be redundant, concerned scope—meaning a wide-ranging scope that goes beyond the purposive events "caused by humans or other organisms" he refers to, to extend to life in general. That's all.

The striven for refutation is fallacious simply because the presumed definition of the events of concerned scope in premise III.2 as ones caused by God is not part of the deduction. Rather, the cause of those events is established separately, first as requirement via III.3 and III.4, and only then as identified with God via his definition III.1, to lead to conclusion III.5. This demonstration, incidentally, is not the simplest I offer, unlike the reviewer states, and the simplest excludes reference to that scope.

That this reasoning resemble the reviewer's argument with 2 + 2 = 4 is quite a clumsy analogy. The professor would have to point out again where in my deduction this kind of reasoning takes place. As a matter of fact, he fails to show in any way how my claimed question-begging is performed.

The last paragraph is shamefully unkind, refusing a single good word if for no more than the work put into the project. This although he knows nothing else about me, or maybe because of it, since he displayed a disgusting air of superiority when I once met him. It may be, as he puts it in his last sentence, that no "professional philosopher would profit" from my work, and I wonder if that would be my desire. Professionals, or more precisely academics, belong to a "club", which as in the preceding will look down on an outsider like me, but will lavish unbounded praise on in my eyes immeasurably less insightful writing of an insider. The person I would like to profit is anyone who is professionally or otherwise disinterested, but has an interest in genuine and beneficial learning.

31 October 2003

It seems to make sense for me to include here another review of my book, and my reaction to it. It appeared in the December 1989 issue of THOUGHT, published by Fordham University. As before, I am adding parenthesized numbers as hyperlinks to my numbered comments afterward.


ADVERTISED AS A “CARTESIAN REEXAMINATION OF BASIC PRESUPPOSITIONS, old and new, in philosophy and sciences,” this is a painstaking effort. Its stated purpose is to disclose how various truths such as free will, and including some now considered undemonstrable, “can be reflectively demonstrated and thereby an actual rather than speculative edifice of existence revealed” (3). The author sedulously presents his “[process] of inquiry” (4-8) and then four chapters: on language and concepts; on self, mind, and external reality; on logic and mathematics[;] and finally on the existence of God (216-33), with further inquiries into “the goodness of God and man["] and “heaven and immortality” (233-51). The chapters are independent but are cross-referenced, and “premises on which conclusions there are based may be substantiated elsewhere” (8).

A prospective reader, then, should not be misled by the title into expecting the early chapters to simply underpin the “proof for the existence of God.” The caution that “sections can be read individually by individual readers” (8) could alert those interested expressly in that proof and not in the exercises of erudition, acumen, and reasoning skill that precede it. “The existence of God is uppermost in consideration, because of its momentousness” (4), yet it covers 18 of 251 pages of text, in contrast to 112 on logic and mathematics.

Three theorems with their two dozen parts, and proof and explanation of each part, run through pages 41-171. The first theorem defines definition; the second deals with self, the world, and causality; the third relates to existence, attributes, and laws of thought. Among parts of Theorem III e.g. are: “A thing does not both have and not have a given attribute at the same time” (144); “A quantity is either a given one, a smaller one, or a larger one” (146); “when some A is B then some B is A” (171). Stages of the proofs are illustrated by 85 diagrams, and postulates and propositions of Euclid are discussed (e.g. 123-34). (1a)

Thereafter Vjecsner examines and rejects “former arguments” for the existence of God (219-21). In the “recently revived["]:[?] ontological argument (“It is either necessary or impossible that God exist”) the “error lies in equivocating the two uses of ‘possible’, or of ‘not necessary’…”(221). Among cosmological arguments are three of Aquinas’s “five ways,” but against them “the general concept of God can be held to require some power additional to that of first causation.” And the “proposal that a primal cause would be of greatest perfection, as advanced by Aquinas in his fourth way…is derived neither through natural nor logical law” (219).

The fifth way, “the teleological[", "]may be of widest appeal….It reasons by analogy, comparing the purposiveness of organisms to the similar purposiveness of a watch or of an arrow in flight….Analogy is inadmissible, however, as a form of inference. It constitutes what is known as the fallacy of undistributed middle” (221). Incidentally, Vjecsner appears to treat the “five ways” as arguments to convince atheists, instead of ways for believers to see how reasonable is their faith. (2a)

The proof [by the author] for the existence of God, presented in various forms (224-31)[,] comes to this: “Purposive events of concerned scope exist in nature” and “imply the existence of a cause of them”; and since “God equals the cause of purposive events of concerned scope,” therefore “God exists” (231). The question is better and more fully treated in Hans Küng’s Does God Exist? (1980) and much better still in John Macquarrie’s In Search of Deity (l985). (3a)

This serious work should not have been published in its present form; it reads at times like a labored translation. The author deserves an able and informed copy editor, or a colleague versed in standard English. He says that “the ideas discussed…require no specialized knowledge” and he strives to “make acquaintance with much of what follows feasible for every contemplative reader” (8). After an “informally abbreviated” proof he adds: “All this can be held comprehended by a hearer of the demonstration, as were observed comprehended beside truisms complex meanings behind ordinary words” (226). But diction, syntax and usage sometimes are so foreign that the full meaning may elude a careful reader. Hence a thorough revision is needed. (4a)

Loyola College in Maryland                                             William Davish, S.J.

1a. This is the first paragraph that runs into trouble. My theorems in the book are twenty-three, not three. The reviewer may have thought that my numbering of theorems as, for instance, II.1 and II.2 meant they are parts of a theorem II, whereas my prefixed numbers I, II, and III signify the first three chapters, containing these theorems.

My impression, however, is that he tried to belittle my work, as expressed by his ho-hum attitude. I should note that the reviewer, unlike the previous one, is not a philosophy professor but a theologian. Correspondingly I hope not to be too harsh in saying that he largely doesn't know what he is talking about in the review, and may have tried to impress the editor. Thus he says in that paragraph that the "third" theorem "relates to existence, attributes, and laws of thought", quoting some of its "parts". But these concern known laws of logic (which belongs to philosophy), referring only incidentally to existence and so on. Also, only a smaller portion of the diagrams deals with logic. But lacking most is a discussion of any of the content as to its merits, as expected of a review. To continuation

2a. There is again in these two paragraphs no discussion of the merits of the quoted. As to the last sentence, Aquinas presented his "five ways" as proofs, not as articles of faith, and they have been treated accordingly since. In my case, I direct my arguments as much toward believers, of whatever creed, as toward non-believers. I make a point of the dangers of conflicting dogmas, witnessed these days tragically, and hence of the value of approaching these issues in the same reasoned manner as in other matters of knowledge; at the same time I mean to show to those of only secular viewpoints that this manner is applicable in other areas as well. Back

3a. Interestingly, regarding the existence of God the reviewer gives more than twice the space to my discussions of former arguments than to those of my own, dispensing with them in this shortest of paragraphs. He picked the same deduction of mine as did the previous reviewer, but in a disorderly fashion, so that the reasoning cannot really be followed. It is obvious to me that he does not understand the process of deduction, and he accordingly again does not discuss the cited one of mine, merely ranking it beneath some work by others, without explanation. That my "proof...comes to this..." and "The question is more fully treated" in that work fails to recognize that my deductions are extensively explained in what precedes and follows them, including the other chapters, and they should be judged on their own merits. Back to the review

4a. Although the reviewer compliments me somewhat in the first two and this last paragraph, he offends at the same time. His remark that I deserve  "a colleague versed in standard English" is an insult which may be resented by anyone even if it applies. But because of my history as a past immigrant, I did never learn any but standard English. I studied its grammar as a youth before coming to the U.S., and am frequently reminded of mastering it better than many who are native-born. They often grow up speaking a colloquial version and don't pay much attention to, or even have not acquainted themselves with, formal grammar.

And I should note that these comments by the reviewer came after I furnished a brief biography of myself at his request. I mentioned in it that I was foreign-born, and he quickly seized on this to make those unpleasant remarks. He didn't know that I had then been in America for over 40 years, about twice the years of my previous life, giving me plenty time to add to my linguistic skills. It may be notable that the previous and longer review above, whose author knew mentioned little about me, had no complaint about my language.

To add more to this dissertation of mine, the now responded to reviewer, though quoting me abundantly (and I think he made me sound pretty good), points at no instance again where my language is to fail. What does happen in his review of barely one page are several compositional errors of his own, marked above between brackets, beside a superfluous "since...therefore" in the next to last paragraph—either of the two words will do without the other.

My justification for spending this much space on that review's last paragraph is that I feel I should fully, if rightfully, defend myself for the sake of my work, though in this case only language is involved. The reviewer might indeed concern himself more with the rightness of the content than of the language.

While discussing here in regard to the above two reviews, and elsewhere on this website, my reasoning concerning the existence of God, I do not try to explicate the idea more in this place. The reason is chiefly that the thought of demonstrating that existence is met with such powerful skepticism and sometimes ridicule that any effort in that direction is ignored no matter how sound. And past thinkers have in my view indeed not been able to penetrate the surface of the matter. They are hampered by through the times built up conceptions, beyond which they find it difficult to see. These conceptions, for example of what the semblance of God must be, may have to be set aside for a better understanding, and therefore I reserve further discussions for more conducive opportunities if arising.

28 April 2005. It appeared right to me to now further discuss the just mentioned subject. (The material on this page that begins with this paragraph was alone here earlier. For space reasons I moved the now preceding material on this page to here, and it seems an appropriate preliminary to the following.)

As elsewhere noted, I decided to add here an exposition of the demonstration of the existence of God I offer, my being fully aware of how preposterous this move is considered to be. I find that the demonstration can be so simple that I would be remiss in not presenting it to present readers, regardless of the kind of reception it does or fails to receive.

The title on my webpages is “Exploring possible human knowledge”, and I chose it for important reasons. I find that the possibility at issue has not even been close to being exhausted. Today it seems tacitly accepted that the only area of discovery, of any addition to human knowledge, lies in physics, despite the extensive advances in mathematics, a field with a conceptual base, relying mainly on deduction.

This last method is almost forgotten as itself a discovery in its conscious application. The ancient Greeks are particularly known for having made geometry a deductive enterprise, exemplified by Euclid’s enormously influential Elements. In the last two or so centuries thinkers in contrast came to regard many questions as unanswerable, prompting, beside more, the title of my present section, “Presumed impossibilities”.

As remarked earlier, among attempted proofs held impossible—most of which are themselves mathematicalthe most ridiculed are perhaps those concerning the existence of God, although like others they have been approached by many prominent thinkers. My assertions in this regard are accordingly of course likewise not paid attention to, especially since not coming out of academic circles, which assume to have exclusive competence in these matters. 

But the subject itself, the existence of a higher power over all of us, suggests that it should not be comprehended only by a limited few, ones thought to be accorded insights by virtue of their official positions rather than personal ability. For that matter, it is my intention to show that despite thoroughly embedded convictions to the contrary the issue is not only as accessible to reason as are other problems of inference, but that it can easily be understood by anyone. It concerns some simple ideas which have been overlooked, and which correctly understood can be as commonplace as are many ordinary facts.

Above I referred to the examples of ancient geometry as known forms of deduction. But one can fall back on much simpler examples—if less familiar, because they are not concerned with the more widely taught mathematics but have to do with deduction in general, which, though it has its rules, is mostly done inadvertently.

In this light let me introduce a famed syllogism, used in connection with Aristotle’s logic:

1.  All men are mortal;

2.  Socrates is a man;


3.  Socrates is mortal.

From two premises is deduced a conclusion by what is known as transitivity. This is a process so common in our lives, even in that of animals, that one is unaware of using it. If one knows that A (Socrates) leads to B (man) and B to C (mortality), one instantly infers that A leads to C.

The Socrates example can be examined more closely. Premise 1 asserts an object of experience; we find that all men are mortal. Premise 2 asserts an object of definition; Socrates is a man by the meaning of “man”. The point is that one can draw a conclusion from premises known true by whatever criteria, even by what is meant by an expression.

Now it is time to turn to the existence of God. It may be noted that the present exposition relies on factors that should be easily accepted as correct without express substantiation. Many of them may want to be looked into in greater detail, as professional philosophers insist on to the extent of hopeless entanglement, often brought on by ingrained prejudices. Nevertheless I do in the book deal more with many particulars in this and other subjects, particulars that are of interest there, but would make the ideas only more obscure at this point.

In the preceding I mentioned definition as possible part in an inference, and in wanting a proof about God, his definition is especially critical. What sort of being do we want to know about? What are one’s hopes and expectations regarding a supreme being? 

My discussion is accordingly guided by what the most universally held attributes of God may be. An indication is how he is most commonly referred to, and it appears to be as the “Almighty”, or more formally the “Omnipotent” and “Omniscient”, or the above “Higher Power”. The issue is that of general interest in a supreme being is not perhaps a certain physical appearance but a supreme power of a kind over our lives. 

This recognition should fundamentally influence the approach to the question discussed. We are interested in the presence or absence of a certain power. We are not seeking a physical identity, as is often supposed. And a power is determined by outcome, which means that in order to determine the existence of the supreme being, one should not seek the presence of an image of a sort—whose powers would come into question regardless—but see if those powers are manifested in known reality, the place of interest.

What kind of power are we then speaking about? Evidently it is a power that can purposely affect our lives or destiny, preferably to good ends. Ends toward which a power is directed is indeed what I mean by it acting “purposely”. The question then is, are our lives directed toward ends? 

The question of direction toward ends—of purpose—in nature is in fact with regard to the present subject hotly today debated. The dispute is known to take place between Darwinism and Creationism or Intelligent Design, and it concentrates on whether organisms, their bodily structures, have come about by purpose or not. The argument for purpose has been represented by that of the 18th-century cleric William Paley, who compared organisms to objects like a watch, which is constructed for the purpose of timekeeping, as appears, for instance, an eye constructed for the purpose of seeing. Darwin on the other hand is well known for his argument for evolution, in the course of which organisms are said to gradually change in accordance with a random process of natural selection.

There occurs, however, a gross oversight on both sides of the dispute about purpose. What appears entirely overlooked is that, aside from the organism's bodily form, its live activities are themselves purposeful, directed toward ends. Paley only had lifeless objects as models, and Darwin accordingly likewise remained oblivious of life’s activities, in a neglect advantageous to his contention. But on considering the functioning of life, we know that each organism develops into its complex form individually during its lifetime—from fertilization to full formation—rather than acquiring that form through prolonged periods of time, as if the organism were a single object existing and changing through the ages. And each organism functions, to so develop and otherwise preserve itself and its species, purposely. Evolution’s concept of formation of the organism by accidental changes is consequently not a finding, but only a false denial of the purpose, seen in the organism's individually occurring formation and propagation.

And this occurrence is the evidence needed. All of life is characterized by purpose, by being what is sometimes called “goal-directed”, and the general goal is known to be preservation of self and the species, in what can be viewed as in the organism’s interest. 

Returning now to the consideration of a power, it is easily seen that these occurrences in the living presuppose a corresponding power, specifically a power directed toward their ends. The logic is again that once the supreme being sought is understood as a pertinent power, the power can be verified by its manifestation in nature, and the preceding establishes that manifestation. 

The simplicity of the reasoning can be put in a form similar to the above syllogism. Making the first premise the definition of God as the appropriate power, and the second premise the manifestation of that power as found in nature, the corresponding connection between the two is stated in the conclusion. 

1.  God is the power of purpose in the interest of living things.

2.  Power of purpose in their interest is revealed in living things.


3.  God is the power of purpose in their interest revealed in living things. 

To put this plainly in the above sequence of A, B, and C, God (A) is identified by the purposeful power (B), revealed in life (C). 

It may be observed that scientists as well as laymen are inclined to explain away any contention of action resulting from other than aimless laws of nature. These laws are, in fact, utilized as a means in any activity, including the carrying out by humans of their own purposes, which purposes, incidentally, are themselves manifestations of disputed purpose in nature. Of account is that, with the aid of otherwise aimless forces, live organisms function in the larger picture with their preservation as aim, and to call that function aimless is in consequence a contradiction.

With an open mind to the preceding it should then be easy to grasp the simplicity of demonstrating in nature the higher power in question. This may make it evident why peoples so naturally gravitate toward faith in supreme guidance of their lives.

It seems worthwhile here to clarify more some ideas about deduction, which unless appearing in entertaining ways like a detective story strikes one usually as quite intimidating. As a matter of fact, to explain how exactly one thing is deduced from another has baffled the best of minds in history. In Euclid and other works to this day rules of deduction are somehow presented as unproven axioms, those by him, for instance, known as common notions. The first of them states: "Things which are equal to the same thing are also equal to one another", and it is the basis for the strings of equations in mathematics that are today accepted without much thought at all.

One of my endeavors in my book is to show how axioms like those in geometry can be established deductively, and my preceding treatment of the parallel postulate is part of this. This attitude angers many, because they insist that one cannot make the first deduction from other than something assumed true without proof. Correspondingly I dealt thoroughly with the problem of how basic logical truths are determined. We determine worldly truths by observation, why then can conceptual truths not be determined similarly? Logical truths, regarded as holding in "all possible worlds", have in fact been described as not conceivable otherwise, meaning they are somehow "conceived" as true, not having to be assumed.

A lengthy mathematical formula, of course, can hardly be merely conceived as true. But the formula follows from simpler ones, following from yet simpler ones, and so on, as knowledge in general grows from simple beginnings. And basic logical truths, by the means of which others are found, can indeed be found by conceptualization. It is part of the above referred to inadvertent comprehension of connections, and, since holding in all possible worlds, these can be depicted diagrammatically, in likeness to figures in geometry. I should note that using the last cited figures as proof has been vehemently attacked, with certain justification. Like the mentioned mathematical formulas, the figures can be intricate and subtle. But they, also, are built on simpler concepts, and so forth, and I want to emphasize that the simplest logical connections carry far more certainty conceptualized than assumed.

To use corresponding diagrams is in accordance with the preceding likewise resisted, which may be ascribed to pride in the contenders' purely mental prowess, notwithstanding that insistence on unproved axioms amounts to guesswork. Diagrams instead accurately represent understood connections that cannot be demonstrated with words alone (although thinkers have in failures of proof, and the tendency to dismiss any learning not physical, tried to convince themselves that logical truths are so by definition, are tautologies). Diagrams have been used in the past, notably by the 18th-century mathematician Leonhard Euler, but they have had limited application and were somehow used mainly for confirmation, not demonstration. I went into the subject extensively in my book again, and here want to focus only on the simple connections discussed above.

As said there, we, and even animals, know instantly that if A leads to B and B to C then A leads to C. The first diagram below depicts why this is so regarding the first given syllogism; since Socrates (A) is a man (B), all of whom are mortal (C), Socrates is seen as among the mortals. The second diagram depicts the other implication; since God (A) is identical with the purposeful power (B), shown in the living (C), God is shown in the living.


It may be appropriate to caution against responses relegating these observations to a particular camp in the disputes discussed. Darwinists would accordingly without examination sweep aside the preceding as coming from the Creationist camp. This response in general is classified as committing the "ad hominem" fallacy, of speaking about the opponent instead of the subject. In my case, I don't belong to any camp, and am ignored equally by those arguing for God's existence and those arguing against it. As indicated, academic thinkers, who, beside perhaps some theologians, are virtually the only participants in these debates, regard outsiders as not worthy of listening to, and they furthermore take offense at any criticism of ideas accepted in their own midst.

This applies in any field, including of course science, and my main point here is that my thinking is not based on allegiance to any group. As made evident, I am not a Christian, unlike the predominance of those arguing on the theist side, nor do I endorse another doctrine. At the same time I don't feel constrained by scientific statements made on the other side. Much of the scientific community cannot get over the conflict between religion and science in Galileo's time, and it is reluctant to allow that it too is fallible. My own inquiries led for these and other reasons to questioning convictions in any area, with corresponding results.


24 April 2009. The below image was influenced by a puzzle shown in a recent book (page 108) titled How To Be An Intellectually Fulfilled Atheist (Or Not) by William A. Dembski and Jonathan Wells, both authors proponents of "Intelligent Design", the currently well known theist approach.

The authors illustrate the puzzle, not a recent one, with the first two depictions here of nine dots forming a square; the question is what is the possible least number of continuous line segments connecting the nine dots; the authors point out that many people assume that the lines must be confined to the square formed by the dots, when the line segments can't be less than five; but the problem doesn't require such confinement, and the second depiction gives the solution with four segments.

The authors use this puzzle in analogy with theist versus atheist arguments, observing that the latter unjustifiably confine themselves to "materialist" approaches, ones intending to explain all of life by undirected causes, while it is advisable to explore other possibilities.

On wondering whether the puzzle could not somehow be solved with even less line segments, it occurred to me it also doesn't require lines to pass through a specific part of the dots, e.g. their center, a dot not lacking dimension; accordingly two lines passing each through a different row of three dots can meet by Euclid's famous 5th postulate, as illustrated in the third depiction.

I cannot vouch that this three-line solution has not been thought of before; I would welcome information about it. But I feel it may encourage a reader to be open to the possibility of demonstration of the kind put forward above on this page. The last geometric solution below may suggest that one can not only, as advocated by Intelligent Design, go beyond supposing undirected causes to supposing directed ones regarding the formation of living things, but one can go beyond that formation to their actual disclosure of goal-directedness in their activities.



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