Is Judaic logic used in the Talmud for inferring Judaic laws analytic? Is it a priori?
Judaism differs considerably from other theistic religions. One of the main features is that Jewish religious laws are not dogmatic but based on specific legal reasoning. This reasoning was already used by the first Judaic commentators of the Bible (Tannaim) for inferring Judaic laws from the Pentateuch. Hence, Judaic logic that was aimed to be a methodology for deducing religious laws has been developed in Judaism. Rambam claimed that this logic was invented by nobody, but it is a part of the Torah. Indeed, this logic differs from other formal systems (Stoic propositional logic, Aristotelean syllogistic, etc.). On the one hand, Judaic logic is analytic as well as other systems. On the other hand, it contains so many ad hoc rules that we may ask whether it is a prpiori in fact?
The paper by Curtis Franks http://www.nd.edu/~cfranks/frankssacredinference.pdf considers cases when we may not draw an inference from something which itself has been inferred. Under these circumstances, we could assume that Judaic logic is analytic a posteriori. The status of analytic a posteriori was grounded first by Saul Kripke and Stephen Palmquis. Also, we could attempt to answer, whether the Lord is analytic a posteriori? As we know, in Kant’s opinion, the Lord is a construction a priori. This means that God exists just in our thoughts and nowhere else. According to modern logicians, there is analytic a posteriori. Perhaps the Lord is analytic a posteriori, too? This means that we could investigate His Will logically, i.e. analytically, and at the same time He is in reality, i.e. a posteriori.
I think it might help me understand some of the issues at play if someone could please help me with the following question: are the hermeneutic tools of binyan av, gezeirah shava, kal ve'chomer, hekesh rules of inference or not? In the first instance, I had always thought of these rules as ways by which laws that were already known could be connected/related to the some physical point in the text. Franks seems to be pointing to this understanding of these rules in the first paragraph of Section 2. I'm then confused: if these rules are mandated ways of hooking laws onto textual points in a non-truth conducive way, then I don't see why there should be any restriction on using the results of one tool as a premise in a second. But I admit that I may be radically misconceiving the nature of Talmudic dispute and debate, in which case I would love to hear why it matters how laws are connected to textual points.
Weeding out Distinctions
For the sake of clarifying our terms in the forthcoming discussion, I thought I would write up some helpful background.
There are several philosophical distinctions that have long been associated with the a priori/a posteriori distinction. It is necessary to weed out these distinctions so as to make clear what, if anything, makes the a priori distinct from the a posteriori.
Some have thought that a priori justification is infallible—infallibility being “a mode of justification that always leads to truth” (Goldman 1999:5). If a priori justification were infallible, then for every belief p justified a priori for S, p would be true. Laurence BonJour, the leading contemporary advocate of a priori knowledge, denies that a priori justification is so characterized. For example, one could perform a mathematical calculation in one’s head and have a priori warrant for the belief in the result only to realize later, with the aid of a calculator, that one’s calculation was incorrect owing to haste. A second case proving this point is the case of Euclidean geometry “regarded for centuries as describing the necessary character of space, but apparently refuted by … General Relativity” (BonJour 1998: 111-2). Assumedly beliefs about the nature of space based on the Euclidean conception of space were justified a priori though proven false. One can thus be justified a priori in believing a proposition that is false.
Another property popularly thought synonymous with the a priori is that of being unrevisable regardless of the agent’s future experience (Putnam 1979: 433). Take the case of Sam, a first-year mathematics student, who carefully goes through a mathematical proof and comes to believe p, the conclusion of the proof. Sam’s belief p is supposedly a priori justified. Consequently, Sam’s mathematics professor, whom Sam trusts, deceives Sam into thinking p false to prove to her associates how gullible first-year mathematics students can be. Owing to his trust in his professor, Sam now believes that p is false. Sam’s belief p surely is no longer a priori justified once he comes to believe, incorrectly so, that it is false and that he has perhaps misunderstood the proof or taken some incorrect step in the process of proving p. In this instance there is a belief that is justified a priori at t1 which is subsequently revised due to the agent’s future experience at t2.
W.V. Quine is another who thinks that the a priori is characterized by unrevisablity in light of experience. Quine argued against the a priori category by showing that “no statement is immune to revision” (1963: 43). If no statement is immune to revision in light of experience then there can be no category of beliefs unrevisable in the face of future experience; in other words, there can be no such category as a priori knowledge. But Quine’s argument only works if we understand a priori justification along the lines of unrevisablity. The a priori, however, is not thus characterized. So Quine was wrong in thinking he had shelved the a priori with his revision thesis.
Some take the a priori to be coextensive with the analytic and the a posteriori with the synthetic. Kant is responsible for viewing the a priori semantically (Critique of Pure Reason (A6, B10). A proposition is analytic if the meaning of its predicate is contained in the meaning of its subject. If the meaning of the predicate extends beyond the meaning of the subject, then the proposition is synthetic. On this account, all analytic propositions are known a priori. George Bealer (1999: 244) argues that on the assumption that definitions are analytic and that scientific definitions qualify as analytic definitions, then there are scientific definitions that require empirical investigation or experience to be known, e.g. water =def. H2O. Such analytic propositions came to be known only after empirical investigation into the chemical structure of water and thus qualify as known a posteriori. The semantic property “analytic” and the epistemic property “a priori” are thus not coextensive. Quine also made the mistake of conflating these two distinctions. By arguing that there are no propositions known merely in virtue of their meaning (1963: 29), some take Quine to have argued against the existence of a priori knowledge. But given that the two are not coextensive, it is incorrect to conclude anything about the a priori from Quine’s arguments against the analytic category.
The a priori is also confused with having the highest possible degree of justification. Philip Kitcher (1983: 24) is an example of someone who thinks that beliefs justified a priori are certain, that is, justified to the highest degree. Alvin Goldman (1999:7) thinks that it follows from there being a priori warrant for beliefs held fallibly that such warrant is not required to reach the level of certainty. If a priori warrant is characterized by certainty, then assumedly a posteriori warrant never enjoys this level of warrant. However, as we have seen above, S can believe p with a priori warrant yet p be proven false. So the fallibility of a priori warrant entails that it is not characterized by certainty. So the a priori cannot be distinguished from the a posteriori along the lines of the relative degree of justification.
The final distinction, which proves harder to separate from the epistemic distinction at hand, is the metaphysical distinction between the necessary and the contingent. A proposition is necessarily true if true in all possible worlds and contingently true if true in at least this world. Are only necessary truths known a priori? Alvin Plantinga (1974; 1993), and BonJour (1998), think so. Gareth Evans (1979), Timothy Williamson (1986), Albert Casullo (2003), John Hawthorne (2002), and Goldman (1999) disagree. The substance of the disagreement between these camps turns, amongst other things, on the cogency of Saul Kripke’s argument allowing for contingent a priori knowledge. In Naming and Necessity (1980: 55), Saul Kripke argues that it is possible to know a priori the contingently true proposition that “the standard meter stick is one meter long.” Given certain conditions, such as the application of heat to that stick such that its length changes, that proposition would no longer be true at a future time.
It is clear that some necessary truths can be known a posteriori. For example, if I learn Pythagoras’s theorem by testimony from my mathematics teacher or from a computer tutorial without understanding each step in the proof, then I know that mathematical theory a posteriori. It takes perceptual experience to learn some necessary truths, e.g., that water is H20 and that Hesperus is Phosporus. It is less clear that only necessary truths can be known a priori. Besides Kripke’s example, there are two further considerations in favor of the contingent a priori. First, it seems apparent that an agent can have a priori justification at t1 for a proposition p only for the agent to realize at t2 that the said proposition p is contingently true (Casullo 2003: 168). As being a priori justified in believing that p is compatible with fallibility, as shown above, it follows that the agent could be wrong about the modal status of p though be justified in believing that p a priori. In such cases it is possible for contingently true propositions to be justifiedly believed a priori.
Secondly, there is another manner in which to argue for the contingent a priori. Williamson (1986: 114) argues that using the method (M), described below, one can come to have a priori knowledge of a contingent truth:
(M) Given a valid deduction from the premise that someone believes that P to the conclusion that P, believe that P.
If “P” is replaced by “There is at least one believer,” then one can know a priori the contingently true proposition “There is at least one believer.” The foregoing three examples are adequate grounds for the contingent a priori.
BonJour and Plantinga nevertheless insist that the propositions known a priori be necessarily true because they connect a priori knowledge with rational insight or reason. Their accounts become untenable, however, when they make the additional claim that not only must the proposition known a priori be necessarily true but that the agent also recognize the modal status of the known proposition as necessarily true:
[R]ational insight … must involve a genuine awareness by the person in question of the necessity or apparent necessity of the proposition in something like the strong logical or metaphysical sense (BonJour 1998: 114).
To see that a proposition p is true—in the way in which we see that a priori truths are true—is to apprehend not only that things are a certain way but that they must be that way (Plantinga 1993: 105).
This surely amounts to a stringency not satisfied by most. It is obvious that most people do not realize that necessarily “7 + 5 = 12” as the possession of modal concepts is limited to the philosophical few (Boghossian 2001: 638). If cognizance of a proposition’s modal status as necessarily true is a necessary condition for a priori justification and knowledge, then either only a minority of people who have an eye for the modal status of propositions have beliefs justified a priori or the condition is unnecessarily strong. Neither alternative bodes well for establishing a unique kind of justification or knowledge. If rationalists stick to their guns on this one, then this further necessary condition for a priori justification would surely deprive the mathematical knowledge of most people of its supposed a priori status. (For other problems facing BonJour and Plantinga on this score, see Casullo (2003: 15ff)).
Hopefully it is now apparent that the a priori, as a kind of justification, is to be kept separate from the analytic (a semantic concept), the necessary (a metaphysical concept), and is a kind of justification that does not have the properties of being certain, infallible, and indefeasible by experience. Thus laid bare, it is clear that if there is to be a separate kind of a priori justification or knowledge distinct from a posteriori justification or knowledge, the distinction cannot rest on any one of the foregoing distinctions or relative qualities of justification. With this groundwork complete, it is now possible to turn to the literature that argues for the separation of the a priori from the a posteriori along the lines of rational insight and experience independence.
Bealer, G. 1999. “The A Priori”. In: Greco, J. and Sosa, E. (eds.). The Blackwell Guide to Epistemology. Oxford: Blackwell.
Benacerraf, P. 1973. “Mathematical Truth”. In: Journal of Philosophy 70, pp. 661-679.
BonJour, L. 1998. In Defense of Pure Reason. Cambridge: Cambridge University Press.
————–. 2001. “Replies”. Rev. of In Defense of Pure Reason, by Laurence BonJour. In: Philosophy and Phenomenological Research 63 no. 3, pp. 673-698.
Casullo. A. 2003. A Priori Justification. Oxford: Oxford University Press.
Evans, G. 1979. “Reference and Contingency”. In: Monist 62, pp. 161-189.
Goldman, A. 1979. “What is Justified Belief?” In: Pappas, G. (ed.). Justification and Knowledge. Dordrecht: D. Reidel.
————–. 1999. “A Priori Warrant and Naturalistic Epistemology”. In: Nous 33, pp. 1-28.
Hawthorne, J. 2002. “Deeply Contingent A Priori Knowledge”. In: Philosophy and Phenomenological Research 65 no. 2, pp. 247-270.
Kitcher, P. 1983. The Nature of Mathematical Knowledge. New York: Oxford University Press.
Kripke, S. 1980. Naming and Necessity. Cambridge, Mass.: Harvard University Press.
Plantinga, A. 1974. The Nature of Necessity. Oxford: Clarendon Press.
————–. 1993. Warrant and Proper Function. Oxford: Oxford University Press.
Putnam, H. 1979. “Analyticity and Apriority: Beyond Wittgenstein and Quine”. In: Midwest Studies in Philosophy 4, pp. 423-441.
Quine, W. 1963. “Two Dogmas of Empiricism.” In: From a Logical Point of View. 2nd ed. rev. New York: Harper & Row.
Williamson, T. 1986. “The Contingent A Priori: Does it have anything to do with indexicals?” In: Analysis 46 no. 3, pp. 113-117.
The hermeneutic tools (middot) including binyan av, gezeirah shava, kal ve'chomer, hekesh are rather rules of inference. First of all, Rambam claims so in the Introduction to his Seder Zraim. Some references are cited in Aviram Ravitsky's contribution to the book Judaic Logic (Gorgias Press, 2011) edited by me. For instance:
1. The author of Ša‘arey ẓedeq: "The reason [Rabbi Ishmael] began with this principle [i.e. qal wa-ḥomer] is that it features self-explanatory truth more than the other principles, alike the first figure of logical syllogism that is more self-evident than the rest of the figures".
2. Rabbi Hillel Ben-Samuel of Verona: "And anyone who understands the sayings of our Sages of blessed memory, in the thirteen principles by which the Torah is expounded, and knows the methods of syllogism and their modes, and the me-thods of demonstration, it will be clear to him that the Sages of the Talmud established all of their scrutinies on the methods of syllogism and demonstration".
3. Rabbi Abraham Shalom: "That the qal wa-ḥomer [קל וחומר] ('a fortiori argument') and the gezerah šawah [גזרה שווה] ('argument by analogy') […] are the edges of the methods of logic".
I apologize for coming to the symposium so late. I certainly appreciate your attention to this paper.
In response to Dani's first question, I am not sure what turns on the classification of the principles of Talmudic exegesis as inference rules. The restriction on iteration and composition of these rules doesn't seem to me any more or less natural or expected whether we think of them as ways of establishing laws from the text or as ways of attaching known laws to textual sources. I have this to say, however: I'm not sure if the distinction you have in mind is really a distinction about the nature of these principles themselves, as opposed to a distinction about how one should read Talmudic debate. Traditionally, most passages are read as discussion among the sages about how the halachah that they agree about originates from the Torah. So they are proposing ways to "hook laws onto text," as you say. We do not read them as "inferring" laws from the text in real time. Despite this council on how to read a sugya, one reads a proposal of how to hook a particular law onto a particular text as a proposal for where the law derives from, even if the Amoraim making the proposal are not engaged in an act of deriving the law.
One point that I did not belabor in this paper, but which might interest a broadly philosophical audience, is the analogy to the Lewis Carroll puzzle. Carroll proposed an infinite regress argument for why the rule that a particular inference instantiates cannot be counted as a premise of that inference. The idea is that if you don't think the explicit premises warrant the conclusion on their own, then this same skepticism can rear its head again when the new "rule premise" is added.
There are a few good philosophical discussions of Carroll's puzzle. Barry Stroud distinguishes a few possible interpretations of Carroll's point, and argues that one of these is both what Carroll had in mind and is a good point to make. Peter Winch connects the puzzle to an aspect of Wittgenstein's remarks about rule-following from the /Philosophical Investigations/. It is worth pointing out that Carroll did not introduce this puzzle. It appears, together with the infinite regress argument, in section 199 of Bolzano's /Wissenschaftlerhe/. Bolzano has two notions of logical consequence, and it is interesting that the puzzle comes up in his discussion of /Abfolge/ rather than in his discussion of /Ableitbarkeit/—thus his conclusion is that the rule underlying an inference cannot be part of the grounds of that inference's conclusion. This has a little less to do with rule-skepticism and more to do with Bolzano's peculiar ontological system.
Against this background, it is interesting that in the Zevachim sugya, the chachomim treat the principle that says that two rules can be composed as a premise of an inference that depends on such a composition. So in order to infer one law from another, I would also have to know that the inference principle is allowed at that moment. This is different from the type of knowledge that Carroll discussed, knowledge about the general validity of a rule, but it is still analogous. It also seems remarkable that the "substructural" considerations in the hermeneutics of kodashim provide a good reason for the fact of compositionality to be treated as a premise of the second in a chain of two inferences.
I will now share something oriented in the opposite direction: a list of the 9 insights into the sugya itself that are put forward in this paper, perhaps mostly of interest to Talmudic scholars rather than philosophers. The points most relevant to a basic understanding of the sugya are labeled with an *. The sixth point perhaps has some theological interest. The list follows the order in which the points are established in the paper.
First, some background. The sages use three different argument forms in their application of kal vachomer to establish which rules compose with one another. In the paper, these are labeled PRINCIPLES 1, 2, and 3, which I present here in the "teaching/learning" idiom.
P1: if x teaches y, then so too must everyone who teaches someone x does not teach
P2: if x teaches y, then so too must everyone who learns from someone from whom x does not learn
P3: if someone who doesn't teach himself teaches y, then so too must everyone who does teach himself
1. P1 and P2 are logically independent. They are two different types of kal vachomer argument.
2*. The seemingly unusual P3 is not needed at all. In the sugya, P3 is used to establish "g teaches k." But there is a very simple argument based on P1 that establishes "g teaches k" that could have been used instead.
3*. P3 is implied by P2. So while it seems unusual and gives the sugya something of a bizarre feel, the sages's use of P3 is not a departure from what they have already been doing.
4. There is a single idea about the range of application of the tools k, g, h, b that is captured by P1 and P2. It is thus possible to understand all the uses of kal vachomer in this sugya as based on this idea.
5*. According to Rashi, the reference of the expression "a kal vachomer, the son of a kal vachomer" is different from the reference of the rejoinder "a kal vachomer, the son of the son of a kal vachomer." According to Tosafos, the two expressions refer to the same proposed inference.
6. Claims about which rules compose with which other rules are themselves treated as claims in the realm of kodashim. (This is not really a chiddush. The Shitah Mechubetzes at least implicitly acknowledges this.)
7*. The kasha of the Birkas HaZevach is this: Why do the sages even ask about the self-iterability of kal vachomer? It is never necessary to iterate this rule, because it is transitive. The teretz is this: In kodashim, kal vachomer sometimes has two premises, an explicit one and a hidden one. For example, if the explicit premise of a kal vachomer (K1) is a law that is derived with gezeira shava, then K1, according to all Rishonim, also depends on the premise "G teaches K." But "G teaches K" is derived with a kal vachomer (K2). This chain, K1 composed with K2, violates transitivity. Therefore, occasionally one has to know that kal vochomer is self-iterable.
8*. The first attempted proof of "K teaches K," which the sages reject at what I called the sugya's "high water mark," is unacceptable for another reason as well: together with the proof of "G teaches K," this proof exhibits circularity.
9. The kind of circularity pointed out in 8 has a lot of potential to arise in a discussion like this one, but it turns out that none of the proofs that the sages do not explicitly reject engender circularity of this form.