Back in January 2014, soon after I completed and published my book A Fortiori Logic, I went to Israel for a well-earned vacation. I met Prof. Ely Merzbach in Jerusalem over a cup of tea. We had met before, years ago in his office at Bar Ilan University, and had kept contact since then through occasional e-mail correspondence. I was indebted to him for having, back in 1997, after publication of my book Judaic Logic in 1996, consented to publish a short article on that subject in the journal that he edited at the time, called Higayon. The article was an extract from the book, and was entitled Forms of A-Fortiori Argument.
In 2014, over tea, Prof. Merzbach kindly offered to publish an article related to my latest work in the journal he now edited, called BDD, which was dedicated to interfacing Jewish studies and Science. He specified the number of pages and mentioned that the article would have to go through a review process. I was delighted by his offer, having in truth hoped for it. I set about preparing the text in May of that year, after submitting its proposed content to him, and submitted a 20-page paper before month’s end. Three months later, to my great surprise, I received a report written by an anonymous reviewer rejecting the submission.
I did not greatly mind the rejection per se, but was truly shocked by the stark ignorance and intellectual dishonesty, and indeed outright hostility, of the anonymous ‘reviewer’ who recommended it. In my simplicity, I could not understand the possible motive of such unfair treatment, and went about replying to his technical criticisms point by point. In my innocence, I initially took these criticisms at face value, and responded bona fide. But it was, of course, useless: he was determined from the start to block publication of the article, irrespective of its logic and truth. The arguments he constructed were only rationalizations of this foregone conclusion.
You will find my two retorts below; these are interesting both from the standpoint of logic and from that of academia. Judge for yourself. The article I had submitted is now a chapter of the present book.
It is only a couple of months later (yes, I am slow at times) that, reflecting on the whole episode, I finally saw the elephant in the room! I realized that the reviewer was so intent on preventing my essay’s publication because it mentioned some of my findings critical of the Gemara (the later phase of the Talmud), even though my findings were generally favorable to the Mishna (the earlier phase). In his report and in his reply to my first retort, he tried to find fault with my method and logic, but was very careful not to mention or challenge my criticism of Talmudic reasoning. He did try to deny, in a brief, vague and unsubstantiated manner that my analysis of a fortiori argumentation was at all applicable to the Talmud, saying:
“the four moods of a fortiori arguments described by the author do not have any sense for qal vachomer arguments used in the Talmud. The matter is that the Sages appeal to the a fortiori argument limited by the so-called dayo principle.”
He could hardly have formulated a statement more ignorant, idiotic and dishonest than this one. This was a statement delivered ex cathedra by someone who was, as appointed “referee,” apparently not obligated to demonstrate through empirical evidence the correctness of his opinion. He mentions no scientific study on which he based it. And of course, there is no such study; if there were, I would surely have found it and cheerfully debunked it in my book, A Fortiori Logic, which was the most thorough study of the subject ever made in history. This man, manifestly without any knowledge of the subject at hand, not even considering the evidence presented in the paper he was supposed to read, had the gall to make this statement with a tone of authority and finality.
It is now clear to me that what really frightened the reviewer, and the editor behind him and the university powers-that-be behind the editor, were statements like the following:
Now, one would have expected all that has been said above concerning Mishna Baba Qama 2:5, our analysis of the qal vachomer arguments involved and of the dayo principle, to have been said in a Gemara commentary on this passage. But, no; surprisingly, nothing of the sort appears in it. Instead, we find the Babylonian Talmud embarking on a set of relatively irrelevant investigations and making some very doubtful claims.
I stress that this statement and others like it in my works are never gratuitous, but always based on truly very detailed and careful analysis. I have never been motivated by the desire to debunk Judaism, but always tried my best to study it with respect and fairness. When I make negative comments about Judaism, it is always with a sad heart, albeit with the conviction that I am being fully objective and truthful. Notice the mildness of my tone; there is no triumphant hostility in it. Moreover, earlier in the same essay I praise the Rabbis as follows:
Nevertheless, they mastered this form of reasoning [a fortiori argument] very well in practice (with a few notable exceptions); and they resorted to it very often.
But to dogmatic minds, statements like the above are heretic. ‘What! You dare suggest that some Rabbis of the Talmud may not be perfectly knowledgeable and wise?’ In their conventional minds, the Rabbis are effectively omniscient and infallible. All yeshiva and kollel studies, and all orthodox exegeses and commentaries, are based on this precise, scholastic assumption. This is, of course, absurd – no human being has or has ever had or will ever have such powers. Some people are very knowledgeable and competent, and some are much less so; but no one is free of occasional ignorance or error. To claim otherwise is mendacious.
One can, surely, say that the Rabbis were occasionally ignorant or in error, without thereby denying that their work was largely intelligent and accurate. But according to Jewish tradition, the Rabbis were divinely inspired, mere vessels for the transmission of Divine revelation; so, they could never say anything untrue or make any mistakes. This claim, of course, has to be taken on faith; it cannot be proved in any rational manner. Faith cannot be considered as proof of anything.
Once I realized this – that the real reason for the rejection was simply the unwillingness to publish any work (even a bit) critical of the Talmud – I was considerably appeased (though with many a shake of my head at the stupidity and bad faith of the people involved).
Obviously, the reviewer saw himself as heroically serving G-d by protecting the Jewish faith from inimical intellectual assaults. People involved in such apologetics do not worry about being guilty of misrepresentations and lies; they consider themselves to be engaged in holy work, with the end justifying the means. They do not ask themselves if G-d might perhaps by far prefer honesty and truth to such fake virtue. To my mind, having the courage to say the truth, even when much social pressure is brought to bear against doing so, is genuine service of G-d and virtue.
I don’t want to get heavy, but allow me to quote the Torah here: “Ye shall do no unrighteousness in judgment, in meteyard, in weight, or in measure” (Lev. 19:35); this I take to mean, in the realm of logic and philosophy, that one must strive for empirical exactitude, analytical accuracy and overall good judgment. Again, “Ye shall not steal; neither shall ye deal falsely, nor lie to one another” (Lev. 19:11); this I take to mean that one may not steal people’s belief and trust through consciously false doctrines, and by means of lies of commission or omission. In the realm of the intellect, as in that of commerce, honesty is surely the supreme virtue. To deliberately hide the truth is surely vicious.
Of course, the BDD people did not say out loud what motivated their rejection. To do so would have opened them up to universal ridicule in the academic world. Rather, the reviewer made a show of attacking other parts of my essay, pretending to find fault with my method and logic, while steering well clear of any comment regarding my analysis of relevant passages of the Mishna and Gemara, so as not to reveal his real motive.
Even though 30% of the text concerned the Talmud, he surprisingly found almost nothing to say on that subject, which one would have thought would have been his main area of interest. I assumed at the time that this was because he was too lazy to read what I wrote, or couldn’t understand it; but later I realized that he was just being very careful to avoid drawing attention to the deep fears this part of the text produced in him.
Needless to say, if the BDD editor and the people above him were confident of their beliefs, they would have allowed the article to be published, and simultaneously or later allowed other contributors to publicly debunk its claims. This is, after all, in theory, one aim of truly scientific journals: to stimulate thought and debate; in logic and philosophy, errors can be as interesting as correct findings. The fact that they chose to block the article from being publicized at all was a demonstration, if anything, that they feared it and could think of no credible way to refute its findings. They thus selected a sufficiently dull ‘reviewer’ to make a parody of reviewing, and make it seem as if they gave the matter due consideration.
This episode made me discover that still, in this day and age, there is a university out there, Bar Ilan, which is not entirely loyal to the modern academic ideal of truth and science, and is willing to suppress observations and analyses that are antithetical to its religious assumptions. Surely, to deliberately prevent knowledge from being transmitted is evil. I must say that, before I started writing the article I wondered whether the publisher would react negatively to critical thought; but I said to myself, “nah, it can’t be the case.” I assumed no self-respecting university would do such a thing! How naïve of me.
Sir, acting in your capacity as ‘referee’ for the journal BDD, you have (on Aug. 12) written a very negative assessment of my paper, “About A Fortiori Argument, in General and in Judaism” (submitted May 28), ref. #261. The following lines constitute my reply to your two-page essay. I hope you will have the courage and attention span required to read it all.
I do not know who you are, since you did not sign your work, and therefore I do not know what your paper qualifications are. Even so, I can easily see and demonstrate that you are in fact unqualified for the task handed to you.
1. Let us to start with go to the crux of the matter, and find out the level of your personal logical knowhow and skill. You evidently fancy yourself quite knowledgeable and capable, but I will quickly show you that you are quite incompetent.
You claim, in the superior tone of one who is ‘teaching a lesson’, that I “implicitly” appeal to the following semantics: viz. that “P is more R than Q is R; Q is R enough to be S; then P is R enough to be S” means:
“P is R” ≥ “Q is R”;
“Q is R” ≥ “S is R”;
then “P is R” ≥ “S is R”.
Now, I can assure you that I do not anywhere and would never assume or suggest this inane symbolic interpretation of a fortiori argument (or more specifically, of the positive subjectal mood of such argument)! This is your own moronic concoction, and I strongly resent your attributing it to me since it is utterly erroneous.
For a start, if the given major premise is “P is more R than Q is R” then its symbolization would be “P is R” > “Q is R” (and not as you have it ≥). This is not very important in the context, but it demonstrates your inattention to detail.
Secondly, the minor premise and conclusion certainly do not and cannot mean “(Q is R) ≥ (S is R)” and “(P is R) ≥ (S is R)”, respectively. This is obvious immediately, since S is a predicate (of Q, then of P) in the said propositions, whereas you represent it as a subject (of R)!
The correct symbolic interpretation of these propositions would rather be (in part): “(Q is Rs) → (Q is S)” and “(P is Rs) → (P is S)”, respectively, where Rs is a certain threshold value of R required to be S, as made clear in my own paper. (Here, of course, the symbol → means ‘implies’.)
You claim to have read my essay; but I very much doubt that you have more than very quickly skimmed through it. For if you have read it, how is it possible that you have not even grasped, let alone digested, this central concept of my whole teaching regarding (positive) a fortiori argument, namely that it inevitably depends on sufficiency of possession of the middle term (“is R enough to be”)? This is repeated again and again in my paper, not to mention the book it is derived from. For instance:
It is important to grasp the intent of the word “enough” (or “sufficiently”) in the minor premises and conclusions above detailed. These tell us that the subject has whatever amount of R it takes to merit the predicate; i.e. that the subject has at least the amount of R required for the predicate. The word “enough” informs us that there is a threshold value of R as of and above which the subject indeed has the predicate, but anywhere before which the subject does not have the predicate; the R-value of the subject is then specified as falling on the required side of the known threshold.
The above shows that your understanding of the text at hand is nil. You cannot even correctly formulate a logical sentence; yet you pretentiously posture as able to judge the matter at hand from a higher plane! A man cannot learn anything if he does not open his mind and patiently study a matter.
Your claim that a fortiori argument may be symbolized as “P is R” ≥ “Q is R”; “Q is R” ≥ “S is R”; then “P is R” ≥ “S is R” is simply a claim that it is inference from quantitative comparisons, i.e. argument of the form: if A ≥ B, and B ≥ C, then A ≥ C. Not only do I not advocate this in my writings, but I repeatedly warn against it.
What is evident from your effective advocacy of it (or your attribution to me of such advocacy) is that your knowledge of the possibilities of logical argument is limited to a very narrow range. You try to reduce things too complex for your mind to grasp to simple formulas within your intellectual range, refusing to broaden your perspective.
Note also that I said above that “(Q is Rs) → (Q is S)” and “(P is Rs) → (P is S)” is only part of the symbolic interpretation of a fortiori argument, because there is also a negative aspect to consider, as I do in my paper (see quotation below). Your account totally ignores this.
As regards your underlying claim that my theory of a fortiori argument is limited to Aristotelian relations (essentially, just the copula ‘is’) – this too is utterly false. In my book (AFL 4.1), I explicitly say that such limitation is not intended:
I have called the first four moods ‘copulative’ because they involve categorical relations indicated by the copula ‘is’ (or ‘to be’). But it should be clear that they could equally well involve other categorical relations; also, negative polarity may be involved and non-actual modalities (can, must, and different probabilities in between) of various modes (de dicto or various types of de re).
And in fact, I give umpteen examples where such variation occurs. Moreover, I do not limit my theory to categorical propositions, but I mention and extensively deal with implicational a fortiori arguments. All this seems to have escaped your notice, no doubt because you have been so intent in finding fault with my work.
2. Moreover, wishing to appear like a cognoscenti, you write:
“The paper contains many theoretical errors. For instance, he offers the four valid moods for a fortiori reasoning. Nevertheless, he formulates only syntactic expressions of those moods without their semantics. In the whole text, the author does not define semantics for a fortiori reasoning as such.”
This is of course, nonsense on your part, further proof that you do not know what you are talking about. The syntax of the valid moods of a fortiori argument is their outer form, the language they are expressed in everyday speech. Thus, “P is more R than Q is R; Q is R enough to be S; then P is R enough to be S” is the form or syntax of the positive subjectal mood of a fortiori argument. The semantics or inner meaning of the forms is their full interpretation in more accessible terms for the purpose of validation. Thus, the semantics of the positive subjectal form is given in my paper as follows:
· Positive subjectal a fortiori argument validation:
The major premise, “P is more R than (or as much R as) Q is,” means:
P is R, i.e. P is to a certain measure or degree R (say, Rp);
Q is R, i.e. Q is to a certain measure or degree R (say, Rq);
and Rp is greater than (or equal to) Rq (whence: Rp implies Rq).
The minor premise, “Q is R enough to be S,” means:
Q is to a certain measure or degree R (Rq);
whatever is at least to a certain measure or degree R (say, Rs) is S and
whatever is not at least to that measure or degree R (i.e. is not Rs) is not S;
and Rq is greater than or equal to Rs.
The conclusion “P is R enough to be S,” is composed of four clauses:
P is to a certain measure or degree R (say, Rp);
whatever is at least to a certain measure or degree R (say, Rs), is S;
whatever is not at least to that measure or degree R (i.e. is not Rs), is not S;
and Rp is greater than (or equal to) Rs.
These four components are obtained as follows: the first from the major premise, the second and third from the minor premise, and the fourth from the tabulated quantitative argument (see below) which is drawn from both premises. Here, note well, the “enough R” condition of the conclusion (implied in its second and third components) comes from the minor premise, because it concerns the subsidiary term (S). Here, then, the crucial threshold value of R is Rs, i.e. the minimum value of R needed to be S; knowing that Rq equals or exceeds Rs, we can predict that Rp does so too.
Note that I say “the major premise means” etc. Thus, when you claim that “he formulates only syntactic expressions… without their semantics” and that “in the whole text, the author does not define semantics for a fortiori reasoning as such,” you just show that you are unable to recognize a semantic intent even as it stands right before you!
You further write: “In some cases, he assumes that this semantics is Aristotelian, in some cases it is not. In the Aristotelian syllogistic, relations among terms are interpreted as set-theoretic operations of inclusion, exclusion and intersection among them. The author uses this idea as well…” (here you place your wrong formula already examined above, and continue:) “Probably, he supposes that the relation ≥ is the Aristotelian inclusion (reflexive, antisymmetric, and transitive relations among terms). But evidently it cannot be for different reasons.”
Here, too, you are just strutting around trying to look intelligent, dishing out conventional words you hardly comprehend, attributing to me (let alone to Aristotle) opinions that I have never expressed. Have I ever, would I ever, suppose that “the relation ≥ is the Aristotelian inclusion”? That you even suggest this implies that there is some confusion in your own mind regarding the symbol >.
You also claim that my theory of a fortiori argument depends on elucidation of the relation of quantitative comparison (i.e. ≥). In your words: “Then the author concerns the validation of a fortiori argument on 5 pages. However, it has no sense without semantics at all. The relation ≥ is unclear absolutely.”
But as I showed above, this relation (quantitative comparison) is not, contrary to your imagination, the central pillar of a fortiori argument. It is one item among others – see my own analysis above. Furthermore, it is not my role as a logician to elucidate it – I can take it as dealt with and passed on to me by mathematicians, since it is a purely quantitative issue. I would need to address the issue if it was peculiar to a fortiori argument; but it is not (just as predication or implication are not).
And anyway, what do you find so “unclear absolutely” about “the relation ≥”? It is simple and obvious enough. You seem to imply that there is some profound secret about it that I do not know – but you do not say what your objection to it is, precisely. You are here again, obviously, just trying to project a flattering self-image and engaging in malicious innuendo.
All this shows again that you do not have first-hand understanding of logic, but you have only a smattering of second-hand formulas and expressions that you throw around without knowing what they really mean. You think you can fool people with such mimics, but you only succeed in publicizing your own ignorance and moral deficiency.
3. Another thing that needs pointing out is that you seem to imagine that because I avoid modern symbolic logic like you but resort to ordinary-language logic, my understanding of logic must be inferior to yours (the very little you have displayed). Quite the contrary is true, I submit. If you take the trouble to actually read the book, or at least Appendix 7 of it, you will see that one of my themes throughout this work is that modern symbolic logic is con game – a means that people who do not understand logic use to give themselves and others the false impression that they do.
Your essay once again proves my point. You thought to look skillful with your misinterpretation of a fortiori argument – but all you did was to make manifest your own logical incapacity. If you had reviewed your proposal in ordinary-language terms, i.e. in plain English, you might have been able to see its stupidity for yourself. A Fortiori Logic was written with the intent to help people like you. If you want to develop your skills and evolve intellectually, you should make the effort to read it, and to do so with a duly receptive attitude. But, to tell you the truth, I do not think you will ever have the intelligence needed. I sincerely mean that. You write:
“From the fact that there is no true semantics it follows that the author formulates the subjectal moods and predict[a]tal moods which are the same in fact, as well as the following Aristotelian propositions: “S is P” and “P is a property of S”. Syntactically, they differ, but semantically, they do not.”
Seeing you write this, I regard you as a lost cause. This sentence of yours by itself convinces that you did not study the paper submitted to you, but merely skimmed through it. If you have truly read it and have not been able to see and grasp the radical differences between subjectal and predicatal argument, there is no hope for you. It is not a matter of conversion of “S is P” to “P is a property of S” as you claim – if it were, then subjectal arguments could be reduced to predicatal ones, and vice versa – whereas I have looked into this question rigorously and shown clearly that this is impossible. You make statements based on no research, just on the big prejudices in your little head.
Again, just as you see no great difference between subjectal and predicatal argument, you fail to see any significant difference between purely a fortiori argument and a crescendo argument (proportional a fortiori argument). Thus, you write:
“The next section ‘Arguments involving proportionality’ on 6 pages contains several syntactic variations of a fortiori moods formulated in the first section. In my opinion, this section has to be reduced, because it contains much unimportant information for the main topic.”
Clearly, you are unaware of the history of a fortiori argument and the controversy surrounding this issue in the course of that history. You consider something unimportant simply because you find it tedious – i.e. your mind tires easily. But that is not a valid standard of judgment in this context. It is amazing to me that someone like you, who has obviously contributed nothing whatsoever of value to the field of A Fortiori Logic, but on the contrary misunderstands most of what he reads, offers an “opinion” as to what is “the main topic” and what is “unimportant information”!
4. Let us now take a look at your reading of a concrete example of a fortiori argument. You write:
“In order to illustrate the meaning of moods, the author provides some examples. Let us consider one. “Jack (P) can run faster (R) than Jill (Q); if Jill can run fast enough to cover one mile in under 15 minutes (S), then surely so can Jack; and if he can’t, then neither can she”. First, the relation “faster” is not transitive for any distance, because there are stayers and sprinters. And somebody can run faster as stayer but slower as sprinter. Second, the semantics of “S is R” in the form of proposition “fast enough to cover one mile in under 15 minutes” readily differs from the semantics of “P is R” and “Q is R”. In the first case, S from “S is R” is a distance. In the second case, P from “P is R” and Q from “Q is R” are human beings. It is a kind of the logical fallacy called ignoratio elenchi.”
I analyze this argument in my book A Fortiori Logic (AFL 1.1) as follows:
For example: granted Jack (P) can run faster (R) than Jill (Q), it follows that: if Jill can run (at a speed of) one mile in under 15 minutes (S), then surely so can Jack; and if he can’t, then neither can she. Needless to say, the conditions are presumed identical in both cases; we are talking of the same course, in the same weather, and so on. If different conditions are intended, the argument may not function correctly. The a fortiori argument is stated categorically only if there are no underlying conditions. Obviously, if there are conditions they ought to be specified, or at least we must ensure they are the same throughout the argument.
In your first comment, about the relation “faster” being potentially variable, you are only repeating in other words what I already say in my book, viz. that “the conditions are presumed identical” etc. However, what you are not aware of is that this is just a small forewarning to the reader regarding an issue treated in more detail later, namely the possibility of using a middle term in more than one sense. For instance, a bit further down in the same chapter and section (AFL 1.1) I write:
On a formal level, what this means is that if we do not specify or keep in mind the middle term R intended in the major premise, we might easily intend another middle term, say R’, in the minor premise and conclusion; in which case, our reasoning (whether unconsciously or deliberately done) would of course be faulty. This often happens in practice, and is one reason some people doubt the validity of a fortiori argument in general. But the problem here is not with the argument as such, but with the use of two middle terms. If we use, explicitly or implicitly, two middle terms, the argument is of course invalid, for it cannot be validated any longer. We could label such practice ‘the fallacy of two middle terms’ so as to remember to avoid it and not be taken in by it.
Thus, what you present as your own critique of my presentation is a possible fallacy that I have already pointed out and explained. Your suggestion is that the middle term “faster” can vary in meaning, i.e. that the “faster” intended for a stayer is different from the “faster” intended for a sprinter. You effectively accuse me of this fallacy – but I am the one who has discovered it before you! This is dishonesty on your part. You pretend to be the teacher while you are in fact the pupil.
As regards your second comment, all it succeeds in doing is to advertise again your own total mental confusion. The proposition “S is R” is nowhere to be found in my treatment of positive subjectal a fortiori argument, but is your own invention as we saw above (in the symbolic formula you proposed)! So, your criticism that the subject S (a distance) is not comparable to the subjects P and Q (human beings) is nothing but a criticism of your own misperception of the formalization of a fortiori argument! In my analysis of subjectal argument, S is a predicate not a subject. You only here once again demonstrate your own absurdity, and in no way provide a valid critique of my work!
And you have the gall to accuse me of committing the fallacy of ignoratio elenchi. Really, whatever your name is, what a fool you are – I feel sorry for you.
5. I will now address the following passage in your review, in which you try to put in doubt my scientific credentials! That got a bitter laugh out of me, considering your ridiculous lack of learning.
“The paper is written in the way that it is evident that the author is not a scientist. For example, he claims that 80 cases of a fortiori argument are found in Aristotle’s works (p. 4). But is it a subject of discussion which works are Aristotelian in fact and which ones are pseudo-Aristotelian, etc. Are all the cases of a fortiori contained in Aristotle’s Rhetoric or Organon? I know that reasoning by analogy was often used in biological works by Aristotle. How many are a fortiori arguments contained there? Another example of reference that cannot be in any scientific work is the reference to Ramchal’s Sepher haHigayon (p. 15). The author claims that the four moods of a fortiori arguments formulated in the paper were first formulated by Ramchal. In this case, it is unclear what scientific result of the author is. Is it only the syntactic formulation of these four moods?”
First, you attack my account of Aristotle’s use of a fortiori argument. If you were really a scholar, you would have simply looked into my book A Fortiori Logic before making these comments. In chapter 6 and Appendix 4 thereof, there is a full description and analysis of this topic. The following table summarizes my findings there:
Book in which a fortiori found
On the Heavens
On the Soul
On Sense and the Sensible
On Memory and Reminiscence
History of Animals
This original research is based mainly on mechanical search for a fortiori argument expressions in The Works of Aristotle (Ed. William David Ross. Chicago: Encyclopædia Britannica, 1952).
Now, these works by Aristotle were all included in a reputed collection, published by Enc. Brit. You will find in W. Windelband’s History of Ancient Philosophy (on pp. 236-247) a discussion of which extant works of Aristotle are genuine, doubtful or spurious. All the above are counted by him among the genuine. Anyway, while this issue could play some role in determining Aristotle’s use in practice of a fortiori argument, it makes no significant difference to the point being made in the paper that a fortiori argument in all its forms was frequently used in Greece as well as in Israel. Whether Aristotle wrote 60 or 80 or 100 a fortiori arguments makes no difference to this point.
Therefore, your raising this question at all could only be in bad faith. You have raised it only to fake scholarship, i.e. to seem historically savvy. I am willing to bet you have never read any of these works; at most a few lines out of one or two of them. This is easy to tell from your manifest ignorance of logic. It is also obvious from the following phrase, “reference that cannot be in any scientific work,” that you have never done any original scientific research yourself. You are constantly in search of external authorities. Well, let me tell you, you need look no further – I am the authority in this field.
As regards your comments regarding my findings on the Ramchal, if you bothered to look at chapter 9 section10 of my book A Fortiori Logic, which you would have done if you were genuinely scholarly, I do not merely claim that he listed four moods of a fortiori argument, I show it in detail. What is the scientific purpose of doing that, you ask? Well, A Fortiori Logic is a book dedicated to tracing the true history of the use and understanding of a fortiori argument, so the discovery that the Ramchal was apparently the first to clearly list all four moods of copulative a fortiori argument is very significant.
However, as regards the syntax, and for that matter the semantics, I show that his understanding was incomplete, because he lacked the crucial factor of a threshold value of the middle term in the minor premise. This and other deficiencies go to show that my own work is in fact significantly more advanced. Nevertheless, this does not diminish the importance of Moshe Chaim Luzzatto’s contribution.
To repeat, had you been a scholar, you would have simply looked into my book before speaking. But of course, you are not interested in the facts of the case, are you? You are merely intent on projecting doubt in the value of my work. All you achieve thereby is to show up your own intellectual and moral deficiencies.
6. Now let us examine your brief pronouncements concerning Judaic logic. You write, in your usual know-it-all tone of voice:
“the four moods of a fortiori arguments described by the author do not have any sense for qal vachomer arguments used in the Talmud. The matter is that the Sages appeal to the a fortiori argument limited by the so-called dayo principle. As a result, any reasoning of the form
P is more R than Q is R; Q is R enough to be S; then P is R enough to be S
“P is R” ≥ “Q is R”; “Q is R” ≥ “S is R”; then “P is R” ≥ “S is R”
is not valid for the Sages. There is no analogy with the ordering relation ≥.”
Here again, ironically, you judge the matter at hand in relation to your own erroneous interpretation of my formula “P is more R than Q is R; Q is R enough to be S; then P is R enough to be S” as meaning “’P is R’ ≥ ‘Q is R’; ‘Q is R’ ≥ ‘S is R’; then ‘P is R’ ≥ ‘S is R’,” saying that “There is no analogy with the ordering relation ≥.” This has nothing to do with my account, but constitutes a criticism of your account!
But anyway, it is untrue to say that the Talmud does not indulge in quantitative analogies (i.e. making inferences based on quantitative sameness or difference), or that a fortiori argument is “not valid” for the Sages. As I show in my books, Judaic Logic and A Fortiori Logic, and everyone who has studied Mishna and Gemara well knows, the Talmud is replete with quantitative analogy and with a fortiori argument, and the Sages effectively consider such arguments in principle quite valid since they resort to them, even if they raise occasional objections to particular arguments.
You make authoritative statements as if you know something, but you give zero evidence in support of your claims. Where is the scientific research on which you base those senseless denials? Do you think your mere say-so has any worth whatsoever? All my statements are based on detailed rigorous research which anyone can verify by reading the books or papers I have written and published on this subject. And I have done a great deal of research—original research that no one else has done. But of course, you are too lazy to look at the evidence before speaking. This is more dishonesty on your part.
7. Having shown your technical and theoretical incompetence in logic, logic history and Torah logic, let me now turn to your pretensions of being a scientist or speaking in the name of science. You write:
“we find not a scientific research in the strict sense, but the excerpts from those books. So, there is no introduction, where the author would formulate his goals, research methodology, etc. There are no conclusions, where the author would say a couple of words about results of his research. There are no connections among sections at all. Scientific paper is a genre that strongly differs from the books distributed for free in the Internet. There must be a good composition with introduction, conclusion, etc.”
Here, you are implying that BDD is a scientific journal with specific standards regarding formal presentation of material, say like Nature. First, let me reply that looking at the articles in English in the couple of issues that I have of BDD, I do not see these lofty standards adhered to. To me, this journal is intended to house thought-provoking articles addressed to a rather Jewish audience which is intellectually attached both to secular science and to Judaism.
Second, contrary to what you suggest, the paper is not merely composed of “excerpts” from the book A Fortiori Logic. As I wrote to Prof. Ely Merzbach when I submitted the paper to him, it “took me about 12 hours to write” and it was “not a mere cut and paste from my book,” but “an original paper. Some of the material was copied verbatim, but some I rewrote especially.” So, here again you are wrong.
Third, you perhaps do not know that I was invited to contribute an article to this publication (BDD). I did not send in an article on my own initiative, in the hope of getting it published and thus being ‘vindicated by my peers’. I never do this – precisely because I do not consider people like you, the writer of this scandalous hatchet job you call a review, to be my peers. I know the value of my work independently – I certainly do not need your worthless confirmation of it. I am a teacher, not a pupil, for the likes of you. This is not conceit on my part; it is knowledge of fact (as I have proved above).
In any case, the following is what I wrote to Prof. Merzbach before I started writing the article in question:
As I recall, you proposed an article of about 20-page (BDD sized pages). Are there any other technical specifications I should know about? As regards the content, what I have in mind at this stage (granting space) is simply to:
– give some basic facts about the formal aspects of a fortiori argument, and its history and geography;
– describe the most important a fortiori debate in the Mishna (Baba Qama 2:5), which introduces the ‘dayo’ principle in Talmudic hermeneutics;
– describe and criticize the Gemara take on this debate, and some later commentaries on it;
– present a brief exposé of research on a fortiori argument in the Tanakh, the Mishna and the Gemara.
On the whole, then, my idea is to summarize the main aspects of my new book, selecting the topics of most likely interest to your readers, i.e. to a religious Jewish audience with a scientific bent of mind.
Please confirm your interest in such an article as here described, so I can start work on it. If you have any requests or conditions, please tell me about them now.
He replied that he approved of this project. As you can see, I did not manage to get all this information into the paper, but had to content myself with much less. Note well my description of the assumed readership. If you are looking for a formal scientific document, the book called A Fortiori Logic is it. There you will find ample description of scientific and historical goals, of methodology, of final conclusions. The paper submitted to BDD is not intended to play that role. As I say quite frankly in that paper, it is not possible to summarize the contents of a 700-page book in 20 pages:
The present paper is a very brief guide to that book, highlighting a few of its salient findings. It is of course impossible in the 20 or so pages of the present paper to summarize the 700 pages of the book. I strongly urge readers to study AFL, part 1, regarding formal issues, and AFL, part 2, regarding Jewish matters.
If you want to know what guided my choice of material for the paper, I can tell you. As regards general logic, it seemed most important to me to clearly show the difference between purely a fortiori argument, a crescendo argument, pro rata argument, and mere quantitative analogy, because, having studied the literature from antiquity to the present more thoroughly than anyone else, I found that this was a crucial problem in people’s conception and comprehension of a fortiori argument. As regards Judaic logic, I decided that what needed clarification for readers of BDD above all was the discussion between R. Tarfon and the Sages in Baba Qama 2:5.
All this is of course clearly stated in my paper, notably in the Abstract, which you apparently did not notice:
This paper first details the formal relationships and distinctions between purely a fortiori argument, a crescendo argument (which refers to proportional a fortiori argument), pro rata argument and quantitative analogy. These various forms of argument are often confused, so it is well to clearly describe and explain them. The author then uses these general findings to formally analyze the debate between R. Tarfon and the Sages in Mishna Baba Qama 2:5, in the course of which the important dayo principle is introduced. Thereafter, the author takes a look at the Gemara’s take on this Mishnaic passage (in the Babylonian Talmud, Baba Qama 25a-b).
There was and is no reason for me to present this information in the rigid form of a ‘scientific paper’. My object was to draw the attention of interested readers to these crucial issues and to stimulate them to further study. I was not and am not interested in narcissistic posturing, contrary to your baseless accusation, where you write:
“this paper is already published as a part of the book A Fortiori Logic (2013) written by the author which is a modification of his old Judaic Logic (1995). Both books are available for free in the Internet. Moreover, the author considers this recent paper in BDD just as an advertisement of his A Fortiori Logic. So, the only idea of the Introduction is that A Fortiori Logic is “a novel, wide-ranging and in-depth study”. It has “a great many new theoretical insights”. And the paper is “a very brief guide to that book”. Such self-estimations that my book is a very good study and please read my guide to that great book cannot be allowed in any scientific paper. This concerns not only usual modesty that is ever expected, but also the fundamental principles of science that any work is reviewed and evaluated rather by others.”
A Fortiori Logic is not a mere “modification of” my book Judaic Logic, as you claim, obviously trying to downplay it. A Fortiori Logic makes very many important corrections, clarifications and expansions to Judaic Logic (see AFL 33.1). That both books are available for free in the Internet is proof that my wish is to promote knowledge using today’s technology without thought of financial profit – it is ridiculous for you to present this as something with negative implications.
You also accuse me of submitting the paper to BDD as just “an advertisement” for my book A Fortiori Logic. This too is base insinuation on your part – if I mention the book to the readers of the paper, and indeed urge them to read it, it is because the book contains a great deal of valuable information not included in the highlights given in the paper. It would have been wrong for me to give the impression that what is found in the paper covers the subject.
You continue your gratuitous insults, suggesting that I am boastful and lack “modesty” when I say that A Fortiori Logic is “a novel, wide-ranging and in-depth study” with “a great many new theoretical insights”. How else could I describe it, if that is the true description of it? It becomes evident that you are actually jealous of this achievement and wish to suppress it by all means possible to you. One may well wonder why. Many people would benefit from this article, even if you don’t want to.
Some people rejoice when they see another person achieve something good or great; while others are made to feel small and wasted and they react with malice. What creative work have you done in your life? Are you perhaps a second-rate sophomore student trying to impress someone? Or are you a failed lecturer or professor driven by dreary antipathies he does not understand? I do not know, so I can only guess at your motives. Do I know you? Do you bear a grudge against me? It is interesting that you have kept your identity concealed from me even though I have requested its disclosure.
You start your grotesque ‘review’ by saying “I strongly recommend to reject this paper for many reasons,” and you end it similarly by saying “To sum up, the paper cannot be published in any scientific journal for many reasons: composition, readability, theoretical weakness, etc.” What is interesting is that nowhere in the whole of your essay do you give one word of praise, or concede one admission that anything of value is to be found in the submitted paper, or for that matter in the book it is based on!
Now, isn’t that suspicious? One would think that the three long years of research and writing produced something good for logic science and history, and for Torah study. But no – you were focused only on looking for faults. And as I have shown above, the “faults” you have found were only your own – none of the reasons you give for rejection of the article stand up to scrutiny.
What is clear is that you are not driven by reason, by love of truth, by love of scientific knowledge, or even by love of Torah, but by unstated petty personal considerations. Moreover, your knowledge and skill in logic, in science and history, and in Torah, are far below your personal estimation of them. Indeed, I would rate your brief essay as the most vacuous piece of writing I have ever come across; and I have analyzed very many in my career, so that is quite a distinction for you to have earned.
Sir, I have just received your (untitled, unsigned) reply to my Retort of Sept. 9, 2014 to your earlier “review” of my paper called “About A Fortiori Argument, in General and in Judaism” submitted for publication in BDD.
In this new essay, you propose three lame excuses for your preceding tract. Truly, one can apply to you the statement of Proverbs: “But a scorner heareth not rebuke” (13:1).
1. To my complaint that your interpretation, of my formula (for positive subjectal a fortiori argument) “P is more R than Q is R; Q is R enough to be S; then P is R enough to be S” as “P is R ≥ Q is R; Q is R ≥ S is R; then P is R ≥ S is R” – all you manage to reply is the lame excuse that “On p. 7 there is the table… where Avi uses the symbol ≥ in the way I said.” Does this constitute a credible “counterargument,” as you claim?
The fact that I use the relationship “≥” in my work certainly does not mean that I adhere to your moronic interpretation of the said a fortiori argument as “P is R ≥ Q is R; Q is R ≥ S is R; then P is R ≥ S is R.” This interpretation, as I said in my first Retort, has nothing to with me and is indeed repeatedly disapproved by me. First, because “S is a predicate (of Q, then of P) in the said propositions, whereas you represent it as a subject (of R);” and second, because a fortiori argument cannot be reduced as you attempt to a mere “inference from quantitative comparisons, i.e. argument of the form: if A ≥ B, and B ≥ C, then A ≥ C.” What you have still today evidently not yet understood is the significance of the clause “is enough R to be,” which is the crucial point of my formula.
Moreover, as I state in my first Retort, the fact that I use the relationship “≥” in my work does not make it “the central pillar of a fortiori argument. It is one item among others.” If you actually look at the use of this relationship in the validation process (stated in the original paper and quoted in full in section 2 of my Retort), you will see that it is simply found in: Rp ≥ Rq and Rq ≥ Rs, whence, Rp ≥ Rs, where Rp, Rq and Rs refer to the quantitative values of predicate R for P, Q and S, respectively. To say this is very different from saying as you do that “P is R ≥ Q is R; Q is R ≥ S is R; then P is R ≥ S is R.” The fact that we both use the relationship “≥” does not make these two statements equal.
Furthermore, to repeat, my statement that “Rp ≥ Rq and Rq ≥ Rs, whence, Rp ≥ Rs” is only part of the validation process cited. What you keep failing to notice – which is the reason for my accusing you of lazily skimming over a text you are supposed to carefully read before pretending to comment on it – is that the full validation process involves crucially important if–then statements. It is these that clarify the said “enough” clause. It is because you have not closely scrutinized these if–then statements that you are able in your initial review to asininely propose that subjectal and predicatal arguments are the same, i.e. that one can convert one to the other. If you compared these statements in the two forms of the argument (both given in the submitted paper) you would be able to see for yourself that such conversion is logically impossible.
This is one of the reasons I have called you utterly incompetent.
Moreover, you are again here trying to suggest that my use of the relationship “≥” constitutes a fault in my work. As I explained in my first Retort, the statement in your initial review where you claim that “the relation ≥ is unclear absolutely” is a ridiculous attempt to discredit a perfectly legitimate use of mathematical concepts in a logical context. There is no shame in my use of “≥” contrary to your insinuations. It is your insinuations which are shameful.
To see the absurdity of your whole approach, consider a reviewer of a paper on physics submitted to the journal Nature who, upon reading, say, the formula x2 = y2 + z2, freely “interprets” it as 2x = 2y + 2z (because he does not understand what the square of a number is, and thinks it means multiplied by two), and on top of that he suggests (in a condescending tone, without giving any explanation or even any reference) that the mathematical relations ‘=’ and ‘+’ are “unclear absolutely.” Do you think such a reviewer would be allowed to retain one moment more his post as “referee”? Your ignorance and stupidity are all too manifest.
2. I now turn to your second pseudo-intellectual “counterargument,” where you state:
“Semantics assumes some abstract entities, e.g. trees, sets, etc. with some operations over them. Entities and operations over them are presented as models and semantics is a way of interpretation of propositions (theories) on models. Informal meaning of propositions is not a kind of logical semantics. For example, ‘All S are P’ is not a logical semantics for ‘SaP’, because there are not defined abstract entities S, P, and operations over them to interpret ‘SaP’ on models. Logicians must know what semantics is and which role models play there.”
Needless to say, I well know that in symbolic logic, a symbolic formula like ‘SaP’ (syntax) may have a number of interpretations, such as ‘All S are P’ (semantics). But I do not deal in the silly artificial abstractions of symbolic logic, which I consider (as I said to you before, and demonstrate repeatedly in my book A Fortiori Logic, e.g. in Appendix 7) as a con game. Obviously, in your limited perspective on the field of logic, you think that making an inane statement like that makes you seem knowledgeable; but in fact it only shows up your ignorance once more.
I am not interested in the meanings of symbolic formulas; I deal in ordinary-language logic. I deliberately eschew symbolism as far as possible, regarding it as superficial and misleading. That is why I patiently explained to you in my first Retort that, in my approach to logic, the syntax is the form (the ‘All S are P’ interpretation in your view) and the analysis of the form (which I give in the validation process) is the semantics. For me, the only items needing symbols are the terms (e.g. S and P in ‘All S are P’) or theses (e.g. P and Q in ‘if P, then Q); I avoid symbolizing relations (e.g. a is ‘SaP’ or ‘P→Q’). You call this “informal” – but this is in fact the traditional meaning of “formal logic.”
To me, any more abstract symbolic formula (such as ‘SaP’ or ‘P→Q’) can only be proposed as a final step, after all the logic of a topic has been sorted out. That is why I never in my book propose a reading like “P is more R than S, and (Q is Rs) → (Q is S), therefore (P is Rs) → (P is S)” (as part of the formula for a fortiori argument) – so as to set the example of restraint in symbolization (I propose it in my first retort to you as a reply to your moronic proposal). To do this at the outset, before one has understood the subject at hand and sorted out its logic, is utter foolishness, bound to lead to confusion and error.
But being exceptionally unintelligent you cannot understand all this, but are stuck in repeating platitudes you have barely heard and never fully digested. What is worse is that you have the chutzpah to lecture your betters as if you know something. You ask: “Why must I read this book?” Well, the answer to that is simple: because you are very ignorant and need to make a serious effort to educate yourself. I doubt, however, that you will ever follow this kindly advice.
3. For your third “counterargument,” you state, regarding the issue of the number of a fortiori arguments in Aristotle’s extant works:
“The matter is that Avi does not cite works to support his claims. In this case he assumes that anybody must have read his book and found out that Aristotle used a fortiori 80 times. However, he did not cite this place of the book. Even if he did so, it would not be enough. He should have said where a fortiori was found in the Aristotle’s works in the way: Categories 1b10. It is important. If somebody claims in his/her scientific paper that 80, it has to satisfy the reality and to be 80.”
In footnote 4 to the paper I submitted to BDD, I say clearly: “See AFL appendices 1, 2 and 4 for more details on these findings.” This footnote is at the end of the sentence: “If we look at usage statistics, we find this assertion clearly confirmed,” following which I list the statistics “Of the 80 cases found in Aristotle’s works, 50 are +s, 22 are –s, 5 are +p and 3 are –p.” If you go to Appendix 4 (section 2), you will there find not only a reference (as you demand) for each and every case, but a full quotation of the case and an analysis of it. Therefore, your claim that I did not cite the place in my book where this is researched is false – more proof of your totally unconscious and dishonest approach to reviewing texts and to “counterargument.”
Furthermore, remember that your argument in your initial review was that some of the 80 instances mentioned might have occurred in pseudo-Aristotelian works. My reply was that the exact number does not matter – even if some of the books cited were not really authored by Aristotle (although, as I showed, they all probably were, and your criticism was wholly gratuitous), since the reason that I stated this statistic was to show that a fortiori argument in all its forms (the positive and negative, subjectal and predicatal moods) was extensively used in literatures from other cultures (in fact, as I show in the book, though do not bother to mention in the paper, in all the main world cultures, including India and China). Therefore, so long as some cases were found in Aristotle’s real works that belonged to these four moods of a fortiori argument, the point would be proved.
Indeed, I describe precisely in the research on Aristotle (and similarly in other researches) how the research was carried out and what the limits of accuracy of its results are. In truth, although I doubt that a case could be made to reduce the number of a fortiori arguments for Aristotle (as you suggest, on pure speculation), I do not doubt that more instances might yet be found. Indeed, I later found a number more, and listed one of them as a sample (see end of Appendix 4). Therefore, here again, contrary to your insinuations, my approach is not all dogmatic but fully open-minded and scientific. But of course, you know that – all you want to do is posture as superior.
So much for your pretentious three “counterarguments.” I note that these replies of yours address only a small fraction of the criticisms leveled against you in my first Retort. I take it this means that you were unable to contrive an answer to any of those criticisms you do not mention. This is typical of your method of work, that you gloss over anything you do not understand or cannot answer. You try to look savvy, but you are an ignoramus – and not only that, a fake.
I think it is very significant that you have to date not dared to disclose your identity to me. What is your name? What are you professionally, a student or a teacher? Tell me, so I can have a good laugh. If you are any sort of teacher anywhere, G-d help your students for you are certainly not qualified to teach logic or any science. I have said this to the Editor, and I have advised him not to ever again use you as a reviewer for BDD. I hope he takes my advice. You simply do not have the qualifications for such tasks.
My assumption until the above episode occurred was that Bar Ilan University was created to give Jewish religious assumptions a fair hearing in any eventual conflict with secular studies. It is true that other Israeli universities, notably Hebrew U. and Tel Aviv U., tend to abandon most such religious assumptions, rejecting them offhand at every opportunity; they thus seem to be biased against religion. It was thus a good idea to found a new university that would, while offering a full secular curriculum, also show respect for Judaism. It is with that thought in mind that I have been, thus far, sympathetic to this particular university.
Possibly, in neutral fields like mathematics and physics, this program presents no difficulty (though in truth there are many difficulties, even in such fields). But evidently (judging by the episode here recounted) when it comes to subjects like logic and philosophy, which could directly impact on Jewish religious assumptions, Bar Ilan University (if only through its BDD organ, which ostensibly aims at Torah-Science reconciliation) has a hard time being open-minded and objective. It tends towards filtering of information and apologetics, even if in a masked and indirect manner.
In my view, anyone who consciously distorts or suppresses information given in good faith cannot be regarded as a scientist; and a university that houses, and worse still produces and maintains, such unscientific personnel (not to mention its ignorance and closed-mindedness) is not worthy of being called a university. We are, after all, in the 21st Century, and not in the Middle Ages. It is alright to defend religion so far as it can be objectively defended; but it is not acceptable to defend it at all costs, notably by effectively engaging in censorship of perfectly scientific discourse. That is shameful behavior.
A religious community that cannot sustain any amount of criticism, however justified, has very fragile faith. It should not try to impose “religiously correct” standards that contradict empirical and rational studies that are clearly devoid of anti-religious prejudice. The fact is that there are many serious ‘issues’ in the Jewish religion, as in all other religions. Jews should show intelligence and honesty, and take such problems in stride, even when no solutions are forthcoming. It is silly to insist on perfection.
Already in the first chapter of the Torah, the account given of the order of things in creation, if taken quite literally, does not correspond to the scientific account, which is based on detailed factual observation and tightly reasoned theory.
The material universe, the planet earth and mankind are not a mere 6,000 years old as the Sages of Judaism imagined and claimed. The world was not literally created in six days, 5777 years ago. The Big Bang (the earliest material event known to modern science so far) took place about 13.8 billion years ago; planet earth was formed from stardust some 4.5 billion years ago. Life arose within it after (roughly speaking) half a billion years, and was monocellular for the first two billion years or so. Thereafter, more complex, multicellular life forms gradually evolved, coming and going, until perhaps some 200,000 years ago the creature we refer to as Man emerged (from earlier life forms, not ex nihilo).
There is no evidence of discontinuity. There was no Adam and Eve couple six millennia ago; or if there was, they were certainly not the biologically first man and woman. If they existed at all, they were, at best, the last survivors of preceding populations and the parents of all subsequent populations. But (so far, at least) there is no genetic evidence of such a single ‘first family’ for all humanity; human population worldwide was very scattered much earlier than 6,000 years ago, and though the total numbers were at some periods very low (e.g. about 30,000 humans, according to one account I read somewhere), they were never that low (i.e. limited to one or two specimen). Perhaps Adam and Eve were the forebears of Middle Eastern peoples, but not of all peoples. The facts here cited are scientifically very well established.
Similarly, science does not confirm the narrative of a worldwide Flood, or that of the Babel incident (put forward as explanation of national and linguistic differentiations), or many other ancient myths found in the Bible. The facts are physically evident, with no room for doubt. Anyone who sticks to the literal Biblical narrative on these questions, and many others for which there are similar doubts, cannot claim to be a scientist. There are likewise many pronouncements made in the Talmud and related literature that are simply unsustainable, if not utterly ridiculous, in the present context of knowledge; notably, statements on pseudo-medicine, on demonology and other superstitions. I have no axe to grind – this is all just fact that anyone who studies the matter sincerely can see for himself. It may be sad, but it is true.
Of course, the mental rigidity of the defenders of orthodoxy is understandable. Once one doubts a single claim made in the Torah or in the Talmud, all claims in these documents become reasonably open to doubt. Once the principle of omniscience and infallibility is breached, the whole edifice collapses; or so it seems to them. But it need not be so: they could retreat gradually, only when and as far as they are rightly pushed back by science to do so. What is sure is that facts are facts. Ignoring them or suppressing them or distorting them won’t make them go away. To think otherwise is self-delusion. Intellectual maturity, and plain honesty and decency, requires that we face reality, however unpleasant it may be some of our fondest religious assumptions.
It is true that science presents a danger to religion, and that once one goes down this road of preferring scientific accounts to religious ones, there is no end in sight, and religion can easily end up melting away. We can see the effects freethinking has had on Reform and Conservative Judaism. We can also see the Christian example, where many churches (especially Protestant ones) are simply denying their own religion, if not altogether dissolving. But the way to prevent such outcome is not through ignoring facts or lying about them. That just causes thorough loss in credibility and deep distrust. The way is to admit and study the errors, while rationally delimiting and explaining them as far as possible, thus showing due regard for reality and mental sanity. Factual errors can often be explained away by allegorical (derash) or mystical (sod) interpretation.
One could, for example, plausibly claim that the Biblical myths refer, not to the material domain that science studies, but to another, more transcendental domain unknown to it. Perhaps the 6,000 years refers to another time dimension, or maybe to a variable time dimension (so that 6,000 years, or even the Creation first week, corresponds to 13.8 billion years). It is philosophically acceptable, at least prima facie, to put forward such far-fetched ideas, provided they do not head-on contradict scientific truths (or each other). This is the work of allegory or mysticism, which however imaginary and difficult to prove is at least remotely conceivable. But it is certainly not acceptable to blithely ignore or deny outright, without any evidence or rational argument other than blind faith in the Biblical account, scientific truths. It is not saintly; it is folly.
This reflection is true not only for physical sciences like astronomy, geology, biology and medicine, to name only them, but equally well for logical science. If strict logical analysis, such as that I used in my books Judaic Logic and A Fortiori Logic, shows that some Talmudic modes of reasoning are non-sequiturs or contradiction-forming, no one can simply ignore the fact or arbitrarily deny it without losing all credibility and intellectual respectability. It is shamefully dishonest to deny manifest truth (and worse still, try to obscure it). Some people in Bar Ilan U. have manifestly not understood these obvious truths yet.
 Although I asked repeatedly for revelation of the critics’ name and qualifications (if any), it was denied to me. It is amazing to me that an academic journal keeps such information secret: this is akin to judgment by a kangaroo court. In this particular case, the ‘reviewer’ was manifestly ignorant and lacking in intelligence; so, I am sorry not to be able to publicize his identity. His remaining anonymous is proof of his lack of qualification; if he was qualified, he would have proudly given his name, taking full responsibility for his words and deeds.
 Ely Merzbach disappointed me by not, as editor, reading and judging the article for himself. He did propose to me to submit the article to a second reviewer, and I accepted, although I told him not to send me the reviewer’s report this time, as I was in no mood to waste more time on the subject (I was in fact, at that time, suffering from chronic intense physical pains due to a recent accident). A few months later, in January 2015, one year after my submission, he regretfully sent me a negative final verdict. Apparently, the editor of BDD has no say in these matters; he is a passive intermediary. Nevertheless, I resent his having refrained from telling me from the start (either before I wrote the paper or as soon as he received it) that a Bar Ilan publication could not countenance a critical discourse like mine; that would surely have saved me much time and vexation. Or at least, after I refuted all the fake objections that his evil stooge put forward, he should have had the good grace to admit that the verdict was unjustified and to apologize; but he chose to keep silence, effectively condoning the lies and insults. I am sorry, in retrospect, to have trusted him.
 See chapter 1.
 And of course, the Jewish tradition is not the only one to make such claims for its saints and teachers; other religions do the same for theirs.
 Note that I use the word ideal. I do not believe the ideal is fully adhered to in any university. But that’s another discussion.
 See my remarks on self-publishing in chapter 6 of the present volume (N.B. this footnote was not included in the original retort).
 Moreover, you speak about me throughout your reply as “Avi” – this is more chutzpah on your part; my name to you is Dr. Sion.
 Including, note well, on the Australian and American continents.
 See Everyman’s Talmud, by A. Cohen. In chapters 8 and 9, many examples of incredible pseudo-medical, demonological and other superstitious beliefs and practices are cited. That some Sages indulged in such ignorant and stupid beliefs and practices shows that they were not as knowledgeable and infallible as they are sometimes claimed to be. Judging from the said examples, these were unaware of the scientific method: they allowed their imaginations to run wild, they drew hasty conclusions from very little empirical data and engaged in some quite fallacious reasoning. Broadly speaking, they seem to have been admirable men in the ethical and religious domains, but were less adept in the physical and logical domains. Of course, nowadays, mainstream Judaism no longer adheres to such beliefs and practices; but still, these are not loudly decried. Read online at: https://books.google.ch/books?id=HWKjAQAAQBAJ&printsec=frontcover&source=gbs_atb#v=onepage&q&f=false.
 As for Islam, it has so far not managed to at all break away from fanaticism. From its inception, it was very adept at crushing dissent. There were vague attempts by some philosophers to break away from dogmas, but they were very soon silenced. For this reason, Muslims are today locked in intellectual backwaters with no end in sight. They are to be pitied for their utter lack of courage.