A FORTIORI LOGIC
CHAPTER 14 – Adolf Schwarz
The equation or assimilation of a fortiori argument with syllogism may be much older, but it is often – or at least, usually in literature on Judaic logic – attributed to Adolf Schwarzwith reference to his workDer Hermeneutische Syllogismus in der Talmudischen Litteratur(published in Viennain1901, byIsraelitisch-Theologischen Lehranstalt). This was of course written in German. However, the work has been translated into Hebrew by Mikhal Berkovitsh under the title:Midat ḳal ṿa-ḥomer ba-sifrut ha-talmudit: pereḳ be-toldot ḥokhmat ha-higayon be-artsot ha-ḳedem(published inCracow in 1905, byY. Fisher). Unfortunately, the work has apparently to date not been translated into English, so I have not read it (and I suspect many people who mention him nowadays have not, either).
Based on other readings (see chapter 9.9), it seems safe to say that the identification of a fortiori argument with syllogism occurred much earlier than the early 20thcent., maybe in the middle ages or perhaps even in ancient times. This being the case, it may be that Schwarz’s originality lies in the degree of attention and conviction he gave to this thesis. However, not even having read Schwarz’s work, I cannot say anything on these historical matters for sure.
But I did happily find an article written (in French, in 1897) by Lajos Blau, a contemporary of Schwarz’s, about another work of his,Die hermeneutische Analogie in der talmudischen Litteratur, focused on the hermeneutic rule ofgezerah shavah. Judging by this article, this earlier work unfortunately says little or nothing about the rule ofqal vachomer; nevertheless, Schwarz appears in it as critical and innovative, a powerful researcher and sagacious commentator, so I would not hastily discount his opinions.
Many logicians and commentators, still today, identify a fortiori argument with syllogism. For instance, the Oxford Dictionary of Philosophy gives the following alleged example of a fortiori argument:if all donkeys bray then a fortiori all young donkeys bray. That not everyone has this opinion may be seen in the Internet site of the Philosophical Dictionary, which gives the following example:Frank can’t run to the store in less than five minutes, and the restaurant is several blocks further away than the store.Thus, a fortiori,Frank can’t run to the restaurant in less than five minutes.Needless to say, I consider the first example inappropriate, and the second correct.
As regards Schwarz, not having read his work or seen a detailed description of it, I cannot actually quote him or say for sure what motivated the opinion attributed to him, viz. the equation of a fortiori argument to syllogism. If that was truly his opinion, I don’t suppose he thoroughly understood a fortiori. Rather, supposedly, he reasoned by an analogy of sorts: vaguely aware of the quantitative undercurrents in both a fortiori argument and syllogism, he equated the two offhand. It may be that Schwarz was influenced by Jewish writers of the medieval era, who opted for this viewpoint due the dominant position of Aristotelian syllogism in the logic of their time. But without seeing Schwarz’s actual text it is of course impossible to say who (if anyone) influenced him. Maybe he frankly tells us who.
However, we can safely say that Schwarz didnotarrive at this opinion following Aristotle. We have already in an earlier section (6.4) looked into the question of the latter’s opinion on this issue, and found that we could not be sure whether or not Aristotle formally equated these two kinds of argument to any extent. Some might contend that he (Aristotle) regarded syllogism as the essence of all rational argument; but I think an overall consideration of his work would suggest he did not have such a sweeping prejudice. The fact of the matter is that, although he studied syllogism in great detail, he only (so far as we know) glossed over a fortiori argument (even if he did so with considerable accuracy), and so could not have developed an informed opinion either way.
Louis Jacobs, in his interesting workStudies in Talmudic Logic and Methodology(1961), reports the following concerning Schwarz (p. 3):
“Adolf Schwarz, in his well-known work,Der Hermeneutische Syllogismus in der Talmudischen Litteratur[(1901)], suggests in the title, and develops in the work itself, the idea that the Talmudic hermeneutic mode ofqal wa-homeris identical with the Aristotelean Syllogism. It will be shown here that not only is thereno connection between the twoforms of reasoning but that an analogy to the Syllogism is found in Talmudic literature [ha-kol] as something quite different from theqal wa-homer. The refutation of Schwarz’s view is important because all too many scholars uncritically follow Schwarz in his identification.”
Two items stand out, here. According to Jacobs, Schwarz considered a fortiori argument as “identical with” syllogism. If this is true, we have to repudiate Schwarz’s theory, for we have definitely established, on formal grounds, that these two types of reasoning cannot be equated. However, we cannot endorse Jacobs’ own contention that there is “no connection between the two,” since we have found that syllogism and a fortiori argument can to some extent be correlated in both directions. Jacobs’ rejection of Schwarz’s alleged thesis is correct; but the justification for such rejection and the alternative theory that he offers are incorrect. We shall further on show more precisely why when we examine Jacobs’ own theory of a fortiori argument; but the following can already be noted.
Although Jacobs begins his exposé by categorically stating that there is “no connection between the two forms of reasoning,” he further on says: “of the two types ofqal wa-homerit is the simple one which has affinities with the Syllogism” – so his rejection of Schwarz’s equation is not as thorough as it first appears. It is only, according to him (by implication), the complex version of a fortiori argument that is thoroughly distinct from syllogism.
Jacobs goes on to argue that the fact that “the Pentateuch and other parts of the Bible in which this argument [i.e. the simple form of a fortiori argument] appears can hardly have been influenced by Aristotelian logic,” in contrast to the complex form, which being a later development (according to him) might well have been so influenced, “is in itself a valid refutation of Schwarz’s view” [that a fortiori argument is “identical with” syllogism]. However, I would not agree with Jacobs that the Pentateuch contains no instance of what he calls “complex” a fortiori argument; a case in point would be Deuteronomy, 31:27. So that part of his critique is useless.
Furthermore, I doubt that Schwarz ever said or had in mind that Aristotle affected reasoning within the Bible! But this attempted refutation of Schwarz by Jacobs is anyway absurd in my opinion. If the question we are asking is purely logical (i.e. can a fortiori argument be formally identified with syllogism?), then the answer is not affected by temporal issues. Of course, if we only think in historical terms, it is obvious that since Aristotle came after the Bible in time he cannot have affected it; but since he came before the Talmud he might conceivably have affected that. It must have been Talmudic and rabbinic reasoning that Schwarz had in mind. It is conceivable that Greek logic in general (and not just Aristotle’s syllogism) may have hadsomeinfluence on the early rabbis’ thinking, since they lived in the Greco-Roman world; but the issue ishow muchinfluence?
Further on, Jacobs suggests that Schwarz was in this regard influenced byAdolf Jellinek. The latter speculated that Aristotelian logic may have inspired the Talmudic hermeneutic principles of Hillel (via his teachers Shemaiah and Abtalion). Jacobs affirms that Jellinek’s hypothesis “has since won wide acceptance;” but I beg to differ. (a) Although such influence may well have occurred indirectly by a process of cultural osmosis and in a very watered-down echo, I very much doubt that Hillel or his teachers actually ever studied Aristotelian logic. Had they done so, the impact of his teaching on their way of thinking would have been much more apparent. (b) We must also take into consideration the fact that Aristotle did notinventthe syllogism – he onlydiscoveredit, i.e. he merely noticed that human beings used it in their thinking (and of course went on to analyze it). If syllogistic thinking is found in other cultures after Aristotle’s discovery, it does not mean that such thinking is due to Aristotelian influence.
Another argument that Jacobs attempts in refutation of Schwarz is that “an analogous mode to the Syllogism is used in the Talmudic literature [ha-kol], but it is not aqal wa-homer. This mode is found frequently when the Talmud attempts to show that a given case falls under the heading of a more general principle” (p. 7). But here again we can contend that showing that the Talmud has another tool (viz. theha-kolformula) for subsuming particular cases under more general principles does not in itself demonstrate that a fortiori argument is not also essentially syllogistic. Even if we largely agree with Jacobs’ conclusion that a fortiori argument is not syllogistic, we must say that his second attempt to refute Schwarz is not very convincing.
Certainly, cases ofha-kolcannot conceivably cover all Talmudic use of syllogistic reasoning. Theha-kollabel is explicitly applied to certain significant cases; but most syllogistic reasoning in the Talmud remains implicit and unacknowledged. Syllogism is a movement of thought that is ubiquitous and unavoidable in human cognitive functioning on a conceptual level; no discourse is possible without it, like it or not. There is no need to have studied Aristotle in order to think syllogistically (though studying Aristotle may well improve one’s syllogistic thinking). Syllogism was in use among human beings in all cultures long before Aristotle appeared on the scene and analyzed and formalized the argument in the 4thCentury BCE.
Jacobs mentions (p. 6) another commentator,Arnold Kunst, who allegedly “finally disposes of Schwarz’ viewpoint” when he remarks that:
“The mistake (in Schwarz’s reasoning) is that Aristotelean Syllogism… is the relation of the species to the genus, both being nothing but names, whilst…qal wa-homerdeal[s] withsentences.”
Kunst is here apparently basing his alleged refutation of Schwarz on comparison between categorical syllogism (e.g. A is B and B is C, therefore A is C) and some here unspecified samples of a fortiori argument (probably e.g. If A is B, then all the more A is C), and saying that whereas the former deals with terms (A, B, C), the latter deals with propositions (A is B, A is C).
But from our point of view Kunst’s objection is in error – he fails to take into account non-categorical forms of syllogism (e.g. A is B implies C is D and C is D implies E is F, therefore A is B implies E is F), which concern “sentences” (i.e. propositions). Furthermore, he has obviously not analyzed a fortiori arguments very carefully, for we could equally say of some of them (viz. the copulative) that they deal in “names” (i.e. terms, in contrast to others – viz. the implicational – which deal in propositions). So Kunst’s critique of Schwarz is also based on the wrong reasons.
Jacobs, by the way, interprets Kunst’s statement differently, as meaning that:
“…in the Syllogism the inference concerns the relationship between genus and species; we are saying that since Socrates belongs to the classmanthen he must share the characteristics of that class. Whereas in theqal wa-homerinference we do not say that a weighty precept belongs to the classlight precepts; it obviously does not. We say that what is true of light precepts is true of weighty precepts.”
Jacobs here shows a better understanding of both forms of argument than Kunst. Earlier, too, he stresses that “the element of ‘how much more so’ is lacking in the Syllogism.” However, to repeat, I will show further on that he does not fully understand a fortiori argument, because his approach to it is – though somewhat formal – not formal enough.
Allen Wiseman, it seems, has not (to date) actually read Schwarz, since he speaks of “how Schwarz might have seen the matter”. He supposes that Schwarz argued that a fortiori argument was “a form of” the categorical syllogism, because the former “resembles” the latter. However, Wiseman is careful to avoid a definite judgment, saying (QC and CS are his abbreviations forqal vachomerand categorical syllogism): “Whether Schwarz’s actual claim was that the QC can only be a CS is a matter for further study,”adding: “I shall… only focus on it as a possible CS.”
Wiseman places Schwarz’s apparent position in a historical context, with reference to early 20thcentury issues ofMind, where there was an ongoing debate as to “whether one needs to assume a universal ‘all’ to make thea fortiorivalid” or alternatively “one can dispense with it (as in transitivity) and just accept theparticular terms as sufficient.” The matter was not finally resolved and just drops out of sight (by about 1920), perhaps because the new, quantificational predicate forms expanded what constituted logic. In particular, it changed the nature of the classical paradigm of logic, the categorical syllogism, to become just a part of the newer, more generalized understanding.”
As regards this discussion, I have shown in an earlier chapter (3.2) that a fortiori argument may either concern individuals or classes, and I have there detailed in formal terms the various ways the singular argument can be quantified. The issue is not very difficult to resolve, once the form of a fortiori argument is identified. The reason why the issue was hotly debated inMindis simply that the argument had not yet been formalized. If as Wiseman suggests the debate petered out due to a change of paradigm in logic, it was only (I would say) because attentions were drawn to other topics. For classical logic, which refers to ordinary language, was in fact as capable as the new, symbolic logic, of resolving the issue. Indeed more so, since as it turns out modern logic was not the first to resolve it but classical logic was.
In any event, Wiseman suggests that “Schwarzrealized that with the latent, universal premise, one could construct some valid QC‘s as CS‘s.” But this of course only means that Schwarz may have realized that some correlations are possible between the two argument forms, without going so far as to claim that they can be equated. In this regard, I again refer the reader to my own work, earlier in the present volume, where all the ways the two argument forms can be formally correlated are analyzed. Thus, I do not think that Wiseman is right in relating Schwarz’s presumed syllogistic posture with the said debate inMind(all the more so since that debate occurred later).
Note that Wiseman’s own position is that the two arguments “relate only in part.”Wiseman speculates that Schwarz may have taken his cue from mathematics, and reasoned by analogy from the hierarchy of natural numbers that “if a lower caseon a continuum within a special category has an inherent feature, every like, higher case has it too.” Apparently he sees that reasoning as syllogistic, since he adds “Since a CS is not valid with particular premises, one needs a universal.” But in fact syllogismispossible with singular premises; for example: Joan’s husband is the man who built this house, and Tom is Joan’s husband, therefore Tom is the man who built this house. So, if Schwarz’s reasoning was as Wiseman has it, it was not accurate.
More interesting is Wiseman’s suggestion, “in Schwarz’s defense” that “if his standard was mathematical proof, perhaps he saw in the CS the strongest form of deductive logic possible for the a fortioriat the time of the Rabbis.Even if he was familiar with quantificational predicate relations, the Biblical writers and later Rabbis did not likely argue in those terms. To propose such an advanced grasp of logic might be anachronistic.” Now, that is a good point. We should not forget that Schwarz’s books on the subject were primarily concerned with rabbinical logic, and not logic in general. Many contemporary commentators fail to make this distinction, and think that by makingqal vachomercomprehensible to themselves (by means of intricate symbolic logic) they explain how it was understood by the rabbis.
Finally, let me make the following clear.
We have in an earlier chapter called Comparisons and Correlations (5), investigated in great detail the exact relationship between a fortiori argument and syllogism. We saw there that there have historically been many viewpoints on this issue; we made theoretical enquiries into the possible correlations between any two forms of argument; we engaged in structural comparisons between the two forms here of interest to us; we looked into the formal possibilities of turning syllogisms into a fortiori arguments and, conversely, a fortiori arguments into syllogism, and even followed through with reiteration of such translations. Our conclusions, after this thorough research work, were the following:
“Syllogism and a fortiori argument are very different movements of thought. They are structurally different, and each serves a different rational purpose; so they are not equivalent or interchangeable. Although they can be formally interrelated in various ways, they remain logically distinct and irreplaceable in important ways. Syllogism orders terms or theses by reference to the inclusions (or exclusions) between them, while a fortiori argument orders them by reference to the measures or degrees of some property they have (or do not have) in common. Neither function can be substituted for the other. We can (however awkwardly) reword one form of argument into the other; but such translations are not exactly transformations, because significant information cannot be passed on from one form to the other; therefore, neither form of argument can be fully reduced to the other. Thus, both forms are needed by reason to pursue its business; they are complementary instruments of reasoning.”
With regard to Schwarz, we can consequently say the following, abstractly. If his thesis was indeed, as many seem to affirm, that a fortiori argument is identical to, or essentially the same as, or equivalent to, or entirely reducible to syllogism – his thesis was demonstrably wrong. If however, his thesis was softer, less extreme, claiming only a web of partial relationships between the two forms, there may have been some truth in it. I would need to see the actual text of his theory in English to judge exactly what his position was and assess it concretely.
Hungary-Austria, 1846-1931. He wrote many works on various aspects of Talmudic logic and methodology. His Hebrew name was Arieh (some of his books appear under this name).
This Hebrew version is available online at:openlibrary.org/works/OL15863565W/Midat_%E1%B8%B3al_%E1%B9%BFa-%E1%B8%A5omer_ba-sifrut_ha-talmudit. Wiseman mentions what might be yet another work on this subject in his bibliography:Midat Kal Vachomer, published in Cracow in 1914/5, unless this is just a later edition of same.
I take this opportunity to loudly recommend the translation into English and publication of Schwarz’s relevant works. They are evidently of permanent interest and value to the field of Talmudic studies.
However, see Jacobs’ comments on this issue, described further down.
In addition to the said books on “Syllogism” (i.e. presumably, a fortiori argument) and “Analogy” (i.e. gezerah shavah, etc.), he produced four similarly named books: on “Induction” (i.e. presumably,binyan av) in 1909, on “Antinomy” in 1913, on “Quantitative Relations” in 1916, and on “Context” in 1921, as well as a number of other works. See list here:openlibrary.org/search?q=adolf+schwarz, where some works are freely available in e-book form (in German and Hebrew).
This is the Hebrew technical term for a fortiori argument. It means ‘light and weighty’ or ‘easy and difficult’ or ‘minor and major’.
Jacobs (p. 19, footnote 3) refers us to two books on this question: “S. Lieberman: ‘Hellenism in Jewish Palestine’ N.Y., pp. 47ff. and D. Daube: ‘Rabbinic Methods of Interpretation and Hellenistic Rhetoric’ inHUCA, Vol. XXII, pp. 239-264.” These are dealt with in later chapters of the present volume (15 and 30.5).
In chapter 2 of the same work.
Poland-England, 1903-1981. See his paper “An Overlooked Type of Inference.” inBulletin of the School of Oriental and African Studies, Vol. X, Part 4, pp. 976-991 (1942).
A Contemporary Examination of the A Fortiori Argument Involving Jewish Traditions(Waterloo, Ont.: University of Waterloo, 2010), pp. 33-6.
On pp. 13-4, Wiseman says: “It is of more than passing interest to see how Schwarz actually argued the matter and was not just understood or misrepresented by his critics.”
Wiseman, on p. 28, tells us of “two opposing views:” that of C. A. Mercier, “that one need not assume or start with a universal, but that a universal (or better, a general) expression for thea fortioriarises onlya posteriorifrom examples,” and the view ofF. C. S. Schillerand others, “that universals are implicitly necessary or involved.”He lists several articles inMind, which are all dated between Oct 1915 and Apr 1919.
The articles inMindmentioned by Wiseman are dated between 1915 and 1918, whereas Schwarz’s works on a fortiori argument are dated 1901 and 1914.
He was, Wiseman tells us on p. 13, a mathematician.
The distinctive feature of such singular syllogism is that the middle term, as well as the minor term, is singular; the major term may be singular (as in this example) or plural (e.g. ‘a great architect’). A singular term may be viewed as a class with only one member. Needless to say, a proposition involving two such terms is not a tautology, but an informative statement equating two such classes. We may not know initially that they correspond. For the same reason, syllogism involving such propositions is useful, and it is commonly used.