Chapter 2. ADDUCTIVE LOGIC IN THE TORAH.
This chapter is intended mainly for historians of logic, or historians of philosophy, though it includes a brief overview of epistemology of value to all, and some interesting comments on prophecy.
Induction, as an epistemological concept, refers to the logical processes through which all propositions, and their various constituents, are gradually developed. Some philosophers have tended to define induction as the pursuit of general principles from particular ones, but such a formula is too limited and only reflects the greater difficulty of and interest in that specific issue. In the largest sense, induction includes all the following factors of cognition:
· perception (direct consciousness of concrete phenomena, whether material/sensory or mental/intimate) and conception (direct consciousness of abstract phenomena or indirect consciousness of anything), as well as recognition (memory of percepts and concepts) and imagination (perceptual or conceptual projection);
· identification (awareness of similarities between phenomena) and differentiation (awareness of differences between phenomena), which make possible classification (grouping), often accompanied by verbalization (naming);
· formulating propositions, with varying degrees of awareness, sometimes but not always verbally, which relate together various percepts and concepts in various ways (first as possible potential particulars);
· generalization and particularization (including the techniques of factorization, factor selection, and formula revision – see my work Future Logic for details), which are the processes through which one discovers how far one may extend or one must narrow the applicability of propositions;
· deduction, the inference of some new proposition(s) from one or more given proposition(s) of any kind, through a host of processes like opposition, eduction, syllogism, a-fortiori, apodosis, paradox, and others;
· adduction, the formation and tailoring of postulates, as well as their testing and confirmation or elimination, with reference to rational-empirical considerations (more on this topic below).
All the above depend on reference to the main Laws of Logic, which ensure the ultimate fullness and harmony of knowledge, namely:
1. Identity – acknowledging all phenomena cognized, as being at least appearances, and so problemacies with varying credibilities, whether ultimately found to be realities or illusions; never ignoring data or issues. (This is what we mean by “facts are facts”.)
2. Non-Contradiction – not acknowledging as real, but insisting as partly or wholly illusory, any set of propositions cognized as incompatible, whatever their levels of abstraction and cognitive roots; always pursuing consistency in one’s knowledge. (Contradictions are impossible in reality.)
3. Exclusion of the Middle – not rejecting all possible alternatives, but seeking resolution of conflicts, through some new alternative or some commonalty; seeking solutions to all problems. (There is no nebulous middle ground between being and not-being.)
Now, these various factors of cognition play a joint role in the acquisition of knowledge, and although here listed in a ‘logical’ manner, with some subdivisions and in a semblance of chronological order, they in actual practise function very interdependently, feeding off each other’s results in every which way and in no set order. Furthermore, they are here described very succinctly, so much so that their individual, relative and collective significances may be missed if one does not take time to reflect.
This brief overview of the theory of knowledge should be understood as both descriptive and prescriptive. That is to say, there is no essential difference between the palette of cognitive processes used by different human beings, be they common folk or expert scientists, trained in logic or purely instinctive, male or female, young or old, of whatever class or people, healthy or sick. This must be stressed: everyone has more or less the same cognitive tools; some people are, there is no denying it, better endowed, others somewhat handicapped, but their overall arsenal is roughly the same, as above listed.
What distinguishes individuals is perhaps rather the effort and skill they exercise with these same instruments, in each given context. Knowing is an art, and artists may vary in style and quality. Some people lay more stress on experience, others on reasoning, others on their emotions. Some people are more visual, some more auditory, some more touch-sensitive. Some people are excessively categorical or class-conscious, too verbal in their thinking, to the detriment of intuition; some people are slaves to their passions, exercising insufficient control on the objective quality of their thought processes. And so forth – but in any case, the range of faculties available to human beings is roughly the same. The art, as with music, as with painting, is to find a balance – the right measure, the right time and place, for each instrument.
It must be added that two people equally skilled in the art of knowing (or one person at different times) may arrive at different specific conclusions, due to different contexts of knowledge. The content and volume of one’s experience – in the largest sense of the term experience, including material and mental perceptions and conceptual insights – has a direct influence on one’s logic, affecting one’s every rational process.
Logic, since Antiquity and throughout the Middle Ages, in Europe at least, has been associated more specifically with deduction, because that was the field in which the most impressive theoretical work had been done, mainly by Aristotle. Only in recent centuries was a greater stress laid, thanks in large part to practitioners like Newton, on the experiential aspects of knowing (by philosophers like Locke and Hume) and on its adductive aspects (by philosophers like Bacon and Mill); and in more recent times on the crucial role of imagination in theory formation (by Einstein, for instance).
This does not mean to say that induction, nor more specifically adduction, are novel concepts as such. People certainly always used all the factors of induction in their everyday efforts at knowing – they used their senses and their heads, to try and make sense of the world around them, sometimes more wildly than we do, sometimes more rigidly, sometimes more sensibly perhaps. Also, we have to admit that Aristotle, after some four or five centuries of development in Greek philosophy including his predecessors Socrates and Plato, was well aware of the primary issue of induction, the so-called ‘problem of universals’ (namely, how concepts are known).
Indeed, his formal work in logic, including on opposition, on immediate inference and on the syllogism, was a lucid attempt, however incomplete, to solve just that problem. Deduction, in Aristotle’s view, was not apart from induction, or against it, but rather a major aspect of induction. For him, it seems, certain generalities were known directly and indubitably (like the axioms of logic), others had to be developed empirically (seemingly, by complete enumeration); thereafter, one could arrive by inference to all other general principles. The grey areas in that view were, no doubt, the source and validity, and the number, of the initially given top principles, as well as the scope of empiricism in the light of the practical difficulties in complete enumeration.
Today, we would certainly agree that deduction is one of the instruments of induction – needed to infer predictions from postulates for testing purposes, and more broadly, to pursue consistency. The grounds of knowledge, in our view, are primarily experiential data, whether concrete or abstract, and to a lesser extent self-evident propositions whose contradictories are self-contradictory. We are more aware of the hypothetical and tentative nature of much of knowledge; and instead of complete enumeration, we refer to processes like generalization and particularization.
But if we regard the perceptual and conceptual phenomena which are the starting-points of knowledge as being effectively ‘axioms’ (in an enlarged sense of the term), then our view is seen as not much different from Aristotle’s in essence, though varying in detail and emphasis. The historical point I am trying to make is certainly not, that Aristotle was omniscient and as fully aware of epistemological questions and answers as we are today. Rather, that in his time and earlier still, a search for such questions and answers was already in motion, and a spirit of intelligence, honesty and objectivity was already at work, so that to make a fair assessment we must focus on his contributions instead of his blanks.
I think it is important for historians to keep in mind that philosophers are human. They do not have time to put everything they know or think into words, down on paper. Often, too, they intuit a larger horizon than they have the time to actually tread in detailed thought. No one philosopher can therefore be expected point out and clarify every aspect of induction, or to develop a truly full spectrum of logical techniques. Not saying something is not necessarily not knowing it, or at least being on the way to know it. Some unimaginative disciples, as well as historians, tend to ossify philosophies, and make them seem more rigid and limited than they were to their living wellsprings.
Thus, the suggestion that general propositions are arrived at by ‘complete enumeration’, attributed by some historians to Aristotle, contains within it the seeds of empiricism. We today certainly acknowledge the major role played by partial enumeration – this is how particular propositions are known: one experiences one or more cases of a kind to have a certain attribute or behavior, and one expresses that observation verbally, without thereby presuming to comment on the unobserved cases or to claim that they have the same attribute or behavior.
This is the common ground, between us and Aristotle; the issue is only, how one moves up from there to generalities. Complete enumeration may have been, for Western philosophy, a first and tentative suggestion; but upon reflection it was soon enough seen to be an impractical ideal, because most classes we deal with are open-ended. Today, we realize that the answer is to be found in the trial and error processes of generalization and particularization, or more broadly speaking in adduction.
Nevertheless, in spite of their manifest deep roots in the past, it is evident that until the Enlightenment the concept and laws of adduction were relatively little discussed and little understood, in Western philosophy at least. Historians tend to attribute to Francis Bacon (1561-1626, London) the clear formulation of these laws. As Anthony Quinton points out, the crucial innovation in Bacon’s ‘new method’ was that it was eliminative (“major est vis instantiae negativae“). Bacon also gave due credit to the positive aspects of induction (i.e. observation and confirmation), and he made explicit many of the pitfalls possible in the course of such processes (which he referred to as “idols”).
Needless to say, Bacon’s words were not the last on the subject; many further contributions have happily been made since then. Whatever their precise history, the Laws of Adduction may be expressed as done below. By ‘postulate’ is meant a set of imagined propositions of yet unsettled truth. By ‘experience’ is meant any appearance, preferably concrete rather than abstract, taken as is, as it appears, as a mere configuration of phenomena, without classificatory work of comparison and contrast to other, remembered phenomena. By ‘confirmation’ or ‘weakening’ of a thesis is meant adding or subtracting some credibility from it; whereas by ‘proof’ or ‘disproof’ is meant extreme credibility or incredibility.
1. If some postulate has certain necessary logical implications, and these implications are found to be in accord with experience, the postulate is thus far confirmed, though not necessarily proved (Positive Law).
2. If some postulate has certain necessary logical implications, and these implications are found to be in discord with experience, the postulate is disproved, and not merely weakened (Negative Law).
These laws may be explained, and unified, with reference to the concept of probability, and on the same basis many corollaries can be derived from them. The corollaries emerge from the consideration of competing postulates – a couple of examples: every time a postulate is confirmed, while a competitor is not confirmed, then the latter is weakened; when a postulate is disproved, then all its remaining competitors (whether known or unknown alternatives) are strengthened (though all equally so, unless some of them predicted the disproving experience, rather than merely accepted it). However, these issues and details are too voluminous for the present study (see my work Future Logic).
Adduction is generally regarded as a historically relatively recent philosophical concept, and those who do so, whether out of traditionalist or modern tendencies, may therefore consider that its application to Biblical or Talmudic contexts is an anachronism. The truth of the matter, in my view and I will now demonstrate it, is exactly the opposite. The laws of adduction are found almost explicitly formulated already in the Torah of Moses, evidence of a very early logical maturity, and it is not surprising therefore that they should have been used with such frequency and skill in Talmudic times.
The essentials of adductive method are given in two passages of Deuteronomy. I will now quote them and explain the aspects of adduction that each clarifies (referring to the positive and negative laws written in the previous section). Note that the term ‘prediction’, used below, should be understood to comprise all descriptive details of the event(s) concerned, including eventual time limits and location.
FIRST LAW: Deuteronomy 13: 2-4.
If there arise in the midst of thee a prophet, or a dreamer of dreams – and he give thee a sign or wonder, and the sign or wonder come to pass, whereof he spoke unto thee – saying: ‘Let us go after other gods, which thou hast not known, and let us serve them’; thou shalt not hearken unto the words of that prophet, or unto that dreamer of dreams; for the Lrd your Gd putteth you to proof, to know whether ye do love the Lrd your Gd with all your heart and with all your soul.
SECOND LAW: Deuteronomy 18:21-22.
And if thou say in thy heart: ‘How shall we know the word which the Lrd hath not spoken?’ When a prophet speaketh in the name of the Lrd, if the thing follow not, nor come to pass, that is the thing which the Lrd hath not spoken; the prophet hath spoken it presumptuously, thou shalt not be afraid of him.
Evidently, the first law deals with the positive aspect of adduction: it acknowledges the natural tendency of humankind to be moved to belief by correct prediction (the prophecied event empirically ‘comes to pass’, i.e. occurs), but it comes to teach us that such confirmation does not constitute proof, and therefore that good reason may yet be found to reject the thesis in question (such as its calling for a turn to other gods). The second law elucidates the negative aspect of adduction: it suggests that false theses ultimately stumble, teaching that incorrect prediction (the prophecied event empirically ‘follows not, nor comes to pass’, i.e. does not occur as and when predicted) is not merely a weakness but constitutes disproof, so that the thesis in question must be eliminated.
The logical value of these biblical statements, the legitimacy of their interpretation as here done as general epistemological principles, is (I think all will agree) manifest. Note well the empiricist criteria explicitly given here: the prediction ‘comes to pass’ or ‘comes not to pass’; the thesis in question (the prophecy) is tested empirically with reference to public events and not solely by the (rationalistic) comparison to the religious document or tradition.
The following comments are incidental to this overriding issue, but while we are on the subject of prophecy they are worth making.
We have to note for the record that traditional commentators have, with reference to passages relating to prophecy found throughout the Tanakh, further refined the above rules, and thereby incidentally showed their full understanding of their implications. They pointed out that the two Deuteronomic rules were formulated with reference to false prophets. They are logical techniques for the identification and evaluation of candidates for the dignity of prophet, teaching us not to automatically believe those who claim to be mouthpieces for Gd and how to find out that they are not.
I was told by R. Abraham Y. Schlesinger of Geneva (but have not verified it) that the refinements under discussion are elucidated notably by Maimonides, in Hilkhot Yesodei haTorah 10:4; as for the Talmudic source, it is not the Babylonian but the Jerusalem Talmud, namely Sanhedrin 15:5, “Ani mitnabei…“. However, I found the main Biblical source thanks to the Encyclopaedia Judaica article on prophets and prophecy: it is Jeremiah 28:8-9, which I now quote (Yirmeyahu is talking to Chananyah ben Azur, a rival prophet, who has promised good things for the Judeans):
The prophets that have been before me and before thee of old prophesied both against many countries, and against great kingdoms, of war, and of evil, and of pestilence. As for the prophet who prophesies for peace, when the word of that prophet shall come to pass, then shall it be known that the Lrd has truly sent the prophet.
This passage implies that if a prophet made a prediction which did not come to pass, it did not follow that he was not a true prophet. It depended on the polarity of the prophecy in question. If it constituted a blessing from Gd, then once announced it had to come to pass, because Gd’s blessings are irrevocable. If what was predicted was a curse, it might well not come to pass and yet still be true, because such negative prophecies are always (i.e. up until they are realized) conditional and contingent on the eventual failure of the audience to repent and change their ways (as in the story of Jonah and Nineveh, for instance).
The proposal is consistent. We may just add that the same loophole, in fairness, equally well applies to prophetic candidates as to established prophets. In other words, negative predictions of theirs which do not come to pass, do not disqualify them, either; only positive predictions which do not come to pass, do. For an example in the Bible (other than the above mentioned by Chananyah) of false positive prediction, look at 1 Kings 22 (and 2 Chronicles 18), where some 400 ‘prophets’ in the court of Achav (Ahab) promised him victory over the Arameans, while only Micah foresaw the death of the king of Samaria.
It should be noted that good and bad are often relative – what is good for one person or group may be bad for another, and vice versa, or even with regard to one and the same person something may be good in some respects or at some time and bad in/at others. Blessings are often ‘mixed’. Assumably, the evaluation of a prediction as ‘positive’ or ‘negative’ is made with reference to the terms of the prophecy itself: whom it intends to favor or disfavor, how, and when.
With regard to prophecies of neutral events, like some astronomical events or perhaps some unnatural apparition in public, without good or bad impact on human lives, other than serving to reveal the predictive power of the prophet, (I assume that) they fall under the Deuteronomic rules quoted earlier. Which means, neutral events predicted by a reputable prophet are bound to come to pass; and, a prophetic candidate predicting neutral events which fail to occur is disqualified.
Note that the Enc. Jud. article mentioned above points out that, even with the refined rules proposed by Jeremiah, difficulties arise when prophecies accepted as true by tradition are tested with reference to later events as described in the Bible itself. However, such difficulties are generally surmountable, because one may always ex post facto interpret even ‘failed’ positive prophecies as having, as in the negative cases, been tacitly conditional. One can say that the good things were promised to happen, provided we stayed on our positive path or improved our ways in certain obvious ways, just as one can say that the bad things were promised to happen, unless we got off our negative path and improved our ways.
One more comment which may be profitably made in this context, with regard to prophecies, whether in the Bible or in the analogous documents of other religions or sects, is that they are very often sufficiently vague, with regard to time and place, if not with regard to descriptive details, that they can be evaluated rather generously by those who already believe in them and additionally be twisted by interpretation to fit any scenario they wish. Prophecies are not always conveniently vague, of course; for instance, in Jer. 28, Chananyah sets a two year time limit for his prophecy and Yirmeyahu, a clear one year for his.
Some of these comments no doubt sound very skeptical, but one must be honest and see: just what is being prophecied, in relation to whom exactly, and precisely when and where. Without these specifications it is very hard to apply the adductive laws in a strict and conclusive manner. The real difficulty is to know where to draw the line, between justification and pretext; for this we must refer to context: the past reputation of the prophet, the turn of subsequent events, and the overall theme of the Bible. (I do not here even consider the issue of historicity, whether the events reported actually occurred; this too calls for context, but still wider a context than that provided by the text itself.)
It is necessary to distinguish between the adductive evaluation of prophecies and that of prophets. A prophet, one might say, is a bundle of prophecies. First, each prediction must be evaluated, using the given principles; second, the person making the predictions is evaluated, with reference to his/her overall record of predictions. This distinction is made clear through the story of Bilaam, a false prophet who was nonetheless used, even against his own will, by Gd as the vehicle of true prophecies which predicted the blessings of Israel (Num. 22-24).
Another issue is to distinguish between claims to prophecy, and ordinary predictions. Even if we regard (as I do, with gratitude) every item of knowledge, however ordinary its methodology, however natural its source, as a wondrous gift from Gd – a distinction must be drawn. The medieval commentator Nachmanides interprets terms in the above quoted passages as follows: ‘a prophet’ – one who claims that Gd communicated a message to him while he was awake; ‘sign’ denotes the prediction of a natural incident, while ‘wonder’ implies the forecast of a supernatural event. A meteorologist, say, makes no claims to prophecy, yet forecasts the weather; we would judge him as an effective scientist is his predictions were consistently (or even usually) right, but never assign him prophetic powers.
What counts in the judgement concerning prophecy is the source of the knowledge, or the methodology which led to it. If natural means are used, like satellites, even daily and invariably correct predictions do not imply ‘prophecy’. This is equally true in the case of predictions so vague that there is a natural probability that such and such a kind of event happen at some time in the future somewhere in the world! Of course, the wild guesses of charlatans, however convinced they themselves might be of the unnatural origins of their predictions, are bound to turn out wrong sooner or later, and reveal the fakeness of their authors. Prophecy, then, has to predict natural events unpredictable by ordinary means or to predict supernatural events (which are, in any case, unpredictable by ordinary means).
The concept of an ‘unnatural’ event presents logical difficulties, by the way. The perfectly scientific mind has no preconceptions, no foreknowledge, regarding Nature or what is natural; whatever happens, whatever happens to happen, is natural, and Nature is the sum total of all things ever happening. Just because an event is unique, different from routine events, it does not follow that it is unnatural, just less frequent. The definition of magic or miracle would have to refer to some special genesis of event, like telekinesis or supernatural intervention. However, once such event is established as capable of occurring in this world, then we would have to include it in our concept of the World, and it would thereby qualify as normal and natural in our expanded world-view. Thus, the term ‘natural’ is logically very relative; but we can still give it its understood connotation conventionally.
Also note: prediction is not, as commonly thought, the essential or even main attribute of prophecy. Prophecy seems to be primarily a high-level relationship to Gd – which, rather incidentally, implies special cognitive and other powers. The principal prophets, like Moses, Samuel, Elijah, Elisha, and so forth, are especially spiritual leaders of the Israelite and human community; their cognitive and other powers are mere means to this end, the outer garb of their profound dignity.
In conclusion, to return to the central topic of the present chapter, I think that the documentary evidence adduced above shows without shadow of a doubt that the Jewish religious tradition had a very clear understanding of the two logical laws of adduction well before Greek philosophy, let alone post-Renaissance Western philosophy. For those who believe in the Divine source and traditional dating of Deuteronomy, these laws of logic were Gd-given at Sinai some 3,300 years ago, almost 1,000 years before Aristotle’s time. For those who doubt this, and regard the Book as of human and more recent origin, say around the First Exile period – these laws of logic are still a couple of hundred years older than Aristotle’s discoveries!
However, it should be emphasized that (so far as I know) the Torah laws of adduction were never highlighted and discussed by the Rabbis of the Talmud and after as logical principles applicable to all thought. They evidently unconsciously practised adduction in their debates on the law, but they never enshrined such reasoning in a hermeneutic principle or analyzed why it is effective. We could accuse them of having doctrinal reasons for this silence, namely to prevent the development in people of scientific modes of thought, which could weaken religion; but the truth is more probably simply that they did not notice the hint in the Torah. Very probably, I would not have noticed it, either, had I not studied philosophy, long after the advent of modern science; credit must be given where it is due.
One of the difficulties in religious thinking is its categorical expressions of knowledge.
There exists a tendency, in the human mind, to confuse conceptual insight with perception, and view them as having the same degree of probability. However, whereas perception (and its derivatives, which we term ’empirical fact’) has a rather high level of credibility (rarely is what we perceive, as such, in an as near as possible unprocessed form, found incorrect), conceptual consciousness has broader possibilities, as it includes the imaginary, which allows us to propose alternative scenarios, and therefore relatively less credibility, ab initio.
For the simple mind, which has not reflected on epistemological issues, the mere event of thinking of a conceptual scenario in answer to some query, is sufficient in itself to justify that scenario. No further evidence is needed, no checking procedure. Of course, this is an extreme case. A person practising this approach to knowledge full time, would be most likely in a nuthouse, I presume. Rather, we all practise such shortcuts to knowledge, though to varying degrees, and in some cases in different domains.
The danger here, is to confuse speculation with knowledge in its finished state.
Every insight or belief is strictly-speaking a speculation, which may be right or may be wrong. After proper evaluation, which is itself to some extent speculative, we may be closer to the truth, and may with more confidence declare it to be right or wrong. Such evaluation consists in examining the perceptual and conceptual context, all known fact and insight, and judging its consistency with the proposed newcomer, the thesis under scrutiny, and considering the mutual impact of these blocks of information. Furthermore, the context is in non-stop flux, so that the evaluation must constantly proceed and recur, to remain accurate. Only thus can we be reasonably sure.
In the early stages of human development, whether historical or individual, we tend to be less careful in our evaluations of knowledge. More maturely, we must regard our alleged knowledge more critically and fairly, without prejudice one way or the other, more objectively and freely. If we fail to, we in the long run must needs succumb to doubt, the structure is bound to seem shaky eventually. If it is strong, it will withstand all tests; if it is weak, it might be strengthened, or else does not deserve respect. This is a challenge religion, too, must face, to survive.
Logic has no in principle objection to mysticism. It has no prejudice with regard to the eventual content of the world. What concerns logic is the morphology and aetiology of our knowledge, the forms and processes which gave rise to it. With regard to mysticism (the “Qabalah”), it would seem to constitute an attempt to conceive scenarios – which are speculations, at first sight, as far as logic is concerned – to explain certain phenomena or texts. Since the questions posed concern domains inaccessible to scientific investigation, the answers are, ultimately, inherently unverifiable, although some degree of confirmation, doubt, improvement or rejection may be possible.
In other words, there are propositions which are not likely to ever be proved right, or wrong, which may even be impossible to evaluate convincingly. They concern Gd, the Beginning of things, the End of days, and so on. They are beyond Man’s mind, because they are out of his mental reach or outside of his universe. Anything said about them, positive or negative, is purely speculative, from a normal human point of view. Even what is claimed Divinely inspired, though it may well indeed be so in reality, is viewed by logic as speculative; since we, ordinary people, when we hear such claims, are forced to consider the possibility that the speaker may not have been inspired, for instance. It is a stand-off.
We must neither reject offhand, nor be naive, but must do as much evaluation as possible, and still remain open at the end. This is to some extent implied by the Biblical laws of adduction. The fact that these laws are found in the Torah, testifies to the need for a certain degree of empiricism and exercise of the critical faculty. It is an admission that men (or women), by their nature, may confuse their imaginations and speculations with reality, and often come forth with unfounded claims of Divine inspiration. We are called upon to judge carefully.
Even within religion, if not especially in that realm, people can very easily err, and tend to accept the offerings of their conceptual faculty at face value. Which does not mean, let us make clear, that such error is inevitably or even usually implied within religion.
The speculation concerning heavenly spheres provides us with a telling example. This doctrine, made popular by the Safed mystics (16th Cent. CE), is reputed to be rooted in the Talmudic literature and regarded as Jewish tradition of Mosaic origin, and is for this reason considered as certain. Yet if we look at the historical record, a different picture emerges.
Seven celestial bodies close to Earth were known since antiquity, namely the Sun, the Moon, and the five planets Mercury, Venus, Mars, Jupiter and Saturn. These bodies were visibly mobile, in distinction from the Stars which seemed relatively fixed. To explain the suspension of these celestial objects and the daily rotation of those closer to us in the sky, Plato and Aristotle (5th-4th Cent. BCE) proposed the theory that there are concentric spheres around the Earth, seven of them on which the heavenly bodies travel, and additionally an eighth sphere in which the stars, or heavenly lights, are imbedded. This theory was found to present certain difficulties, and was consequently much refined by Ptolemaeus of Alexandria (2nd Cent. CE). The Ptolemaic model of the universe, as it became known, remained accepted truth for centuries thereafter, until the development of the Copernican model.
By Talmudic times the idea of heavenly spheres was culturally well-installed and considered obvious. It is of course not totally inconceivable that it antedated the Greeks, but there is no written evidence to this effect and it seems much more probable that it arrived in the Middle East in the wake of Alexander the Great (who was a pupil of Aristotle). The Seven Heavens became a fixture of Jewish mystical speculation, serving as much to transmit spiritual and ethical teachings as to explain various aspects of our physical world. However, as it turned out, it was a bad investment: new discoveries in relatively modern times in the field of Astronomy have completely overturned this model.
Since Copernicus, we learned that the Earth, the Moon and the five planets rotate around the Sun (the Earth does so in 365.25 days), and that the appearance of rotation of the Sun around the Earth is rather due to the latter’s daily rotation around its own axis. Furthermore, the Sun was found to be a burning ball, a fundamentally different entity from the six other neighbours of Earth; the Stars were understood to be burning heavenly bodies like the Sun, and found to be moving in various ways; the Moon was distinguished by its rotation around the Earth from the five other planets, whose trajectories were rather parallel to that of the Earth. Furthermore, previously unknown planets, not to mention the Asteroids, were discovered: in 1781, the planet Uranus; in 1846, Neptune; in 1930, Pluto; and many of the eight planets were found to have moons of their own; our Solar system was found to be but an average member of a galaxy of some 100,000 stars, and the universe was found to consist of a multitude of scattered such galaxies each with a myriad of stars and planets and moons and comets, all moving in various ways. And so forth.
Now, the fact is that the Talmudic luminaries had no advance inkling of these major developments in Astronomical science, and by all evidence later Jewish mystics like those of Safed were ignorant of them even as they were occurring all around them. That these people all constructed doctrines around theories which turned out to be unsound, or even out of date in their own times, just goes to show that they cannot be considered, by any stretch of the imagination, to have been omniscient and infallible. The Torah laws of adduction have to be applied, and speculations which go against empirical evidence have to be rejected, however attached we may be to their spiritual and ethical message. The only face-saving thing we can do is allegorize, and say that the Spheres are spiritual domains, in a non-physical dimension of existence; or that they refer to different levels of consciousness or states of mind.
We may go further still, given the clear formulation of the laws of adduction in the Torah. The fact that the Torah teaches this logical (inductive) process makes it kosher, and indeed a mitzvah; it cannot be claimed by traditionalists to be a newfangled, foreign technique, an invention of atheist or non-Jewish scientists. But moreover, if we look at the context in which these laws are formulated, it becomes clear that they are to be applied very widely (to the extent possible) – not only to the far-out speculations of mystics, but also to the down-to-earth legal discussions of Halakhists.
For, if it is permissible, indeed imperative, to evaluate the truth of alleged prophecies, then a-fortiori, all the more so, is it ethically, according to the Torah, possible and necessary to evaluate the pronouncements of Rabbis, who are of lesser rank in the spiritual hierarchy. And again, if we may and must evaluate these and those religious leaders using adductive techniques, then a-fortiori, all the more so, we may and must do so with all other inductive and deductive techniques, which are more certain logically. It seems to me that these inferences are incontrovertible.
The Torah, in the above described laws, makes a clear statement in favour of empiricism and use of the critical faculty. It does not recommend an unconditional credulity towards apparent ‘authorities’: it demands integrity, a healthy reference to objective fact and an intellectual judgement. The Torah does not condone the obsessive ‘believer’, who denies his or her senses and his or her mind in pursuit of his or her fantasies; or, sheeplike, of other people’s fantasies, be they ‘sincere’ or manipulative. It recommends a respect for truth, and due process in ensuring that truth. This viewpoint is upheld in other passages of the Torah, notably Exod. 23:1-3 and Lev. 19:15…
Thou shalt not utter a false report; put not thy hand with the wicked to be an unrighteous witness. Thou shalt not follow a multitude to do evil, neither shalt thou bear witness in a cause to turn aside after a multitude to pervert justice; neither shalt thou favour a poor man in his cause.
…nor favour the person of the mighty; but in righteousness thou shalt judge thy neighbour.
These statements (and others like them, e.g. Exod. 23:6-9; see also the relative commentaries) are traditionally understood as relating especially to jurisprudence, to the witnesses and judges in a tribunal. A witness is bound to say the truth precisely, neither adding nor omitting information, not confusing fiction or evaluation with fact; a witness must not, either, be moved by love, hate or indifference, nor let others sway his or her testimony, for good or bad, by means of bribery, threats, or even ‘ideological’ considerations. A judge is bound to obtain and consider all the facts of the case; he must not be diverted by any personal passions, or allow anyone to interfere with his judgement, to influence it unduly; and at the moment of judgement, he must exercise his judgement to the best of his ability, and not surrender his considered opinion, whether to higher authority (in the case of less prestigious judges, who are required to vote first) or to majority opinion (in the case of the more senior judges, who vote last).
The intent of such passages of the Torah is obviously primarily juridical, to found a just society. But to achieve such a social and political result, a strong culture of honesty and respect for truth above all is required. This implies ethical work, at a deeper, more personal level; a habit of using one’s faculties of cognition to their fullest potential, and independently of inner or outer pressures logically irrelevant to the issues at hand. If people habitually fail to put a supreme value on truth, then when the moment of witnessing or judging arrives, they may easily stumble. Thus, the Torah’s teaching, in passages like the ones on prophecy and on justice is, if only indirectly, essentially cognitive. With regard to religious and lay authorities, while the Torah elsewhere upholds them firmly (as pillars of a good society), it here (I suggest) reminds us that they are human, capable of errors or lies, and therefore to be evaluated honestly (that, too, being good for society).
 The process of abstraction consists in ignoring (excluding from consciousness) all but certain aspects of something perceived in whatever way; this process precedes the comparisons, contrasts and mental manipulations through which we conceptualize.
 Notwithstanding, the Talmud, in its effort at creating dogmas, at least as we view it nowadays, preferred to keep these adductive processes relatively hidden and tacit, so as to give the impression, false but convenient, of being a purely deductive discipline – but that is another issue.
 That this is an accepted and used manner of reasoning by traditional commentators may be demonstrated with reference to a difficulty in Gen. 28, pointed out by R. Adin Steinsalz in a talk in Geneva recently. During Jacob’s dream of the ladder, Gd promises him many good things (v. 13-15), yet immediately thereafter Jacob seems to doubt these promises, when he says “If Gd will be with me…” (v. 20-22). The explanation Rashi gives (according to R. Steinsalz, but I did not find the place) is that Jacob understood Gd’s promises as depending on his continued good conduct, i.e. on his remaining the same person. Thus, here a positive promise is taken as tacitly conditional.
Incidentally, R. Steinsalz himself offered an alternative explanation of Jacob’s doubt: namely, that Jacob may not have been sure whether his dream was indeed a prophecy or merely the wishful thinking of a worried traveler. But, though this explanation is psychologically interesting, epistemologically it implies that a prophet can doubt his own prophecy. Such a premise would, in my view, put all prophecies in doubt; we must assume that the prophetic experience is intrinsically indubitable, or else it loses its special status.
 This story is full of interesting details about prophecy. According to Nachmanides (Cohen, p. 921), that Bilaam was not a prophet beyond the events recounted in it is suggested by the use of the expressions “Gd came unto Bilaam” (22:9) and Gd or the Lrd “met Bilaam” (23: 4, 16), which suggest a non-habitual encounter (yikar) initiated by Gd (yavo). Furthermore, the expression “the Lrd put a word in Bilaam’s mouth” (23: 5, 16) seems to imply a forcible takeover by the Lrd of Bilaam’s faculties of speech, at least in the first two prophecies; in the third prophecy “the spirit of Gd came upon him” (24:2). Other technical details include: having the eye opened (24: 3, 15), hearing the words of Gd, seeing the vision of the Alm-ghty, fallen down yet with opened eyes (24: 4, 16), and knowing the knowledge of the M-st H-gh (24:16).
 But see Num. 12:6-8, where a ‘prophet’ is defined as someone to whom the Lrd makes Himself known in a ‘vision’ or speaks to in a ‘dream’, with the exception of Moses who is spoken to ‘mouth to mouth, even manifestly, and not in dark speeches’ and who beholds ‘the similitude of the Lrd’ (Cohen, p. 855).
 Cohen, p. 1062.
 In the case of Deuteronomy, which concerns us here, some say that it dates from the reign of king Josiah, one of the last kings before the exile. Whatever the age of the Books of Moses, they were apparently well established by the time of Ezra. Judging by the Book of Ezra, this period may have been, rather, the starting point of Rabbinic Judaism, which reached its full momentum through the Mishnah and Gemara.
 Their positions were first mapped, apparently, by the Chaldeans. The maps depict the Constellations dear to Astrologers.
 More precisely, the stars were supposed to be holes in the fabric of the Eighth Heaven, through which light was visible.
 We can, in truth, still today, conceive of the celestial bodies as ‘rotating’ around the Earth. That is, we can construct a model in which the Earth is Cartesian origin (geometrical zero point) and all other bodies trace various paths relative to that origin. Such a model, which is the Ptolemaic, would simply reflect the way we observe the sky, standing here on Earth. However, the paths traced by the celestial bodies in such a model are very complicated and difficult to explain and predict. The value of the Copernican model, which shifted the center of the world (actually, of our solar system), was its ability to simplify the mathematical problem posed by the observed trajectories. Galileo and Newton were then able to provide an explanation, with the concept of gravity and the laws of mechanics, which neatly fitted in with this model.
 It is not my object, here, to go into the history of Astronomy; but I have to list some facts to put certain yeshivah students, steeped only in traditional learning, up to date! In any case, note well, the mystic number of Seven cannot be changed into a mystic number of Ten.
 Or again, that they symbolize the stages of Creation or the veils separating us from the ultimate reality of the One. The Spheres postulate is, of course, but one component of the mystical theory of the Sephirot. Another major component is the metaphysical idea of Emanation, according to which the existence of the world is continually produced by emanation from Gd, through the successive layers of the spheres. This idea is supposed to reinforce the concept of the separateness of Gd, His distance and insulation from the lowly material world, while at the same time stressing His sustenance of it. Our rejection of the Spheres idea, or at least of its physical version, does not imply a rejection of the Emanationism. However, here again, we should take note that the latter theory has, according to historians, Greek roots, coming to full expression in Neoplatonism, with Plotinus (3rd Cent. CE). All this goes to show that philosophy (here, its natural or metaphysical branches) has historically often enough affected Judaic thought, more so than certain traditionalist opponents of philosophy were aware of or would care to admit.
 We may also mention the Ninth Commandment, concerning false witness against one’s neighbor (Exod. 20:13, Deut. 5:17). Some commentators have referred to the commandments relating to just weights and measures (Lev. 19:35-36, “ye shall do no unrighteousness in judgement…,” and Deut. 25:13-16), which may be viewed more broadly as calls to intellectual honesty.