Difference between revisions of "What is the "logic" in Buddhist logic? By R. Lance Factor"
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− | The history of Indian logic is usually | + | The {{Wiki|history}} of [[Indian]] [[logic]] is usually divided into [[three periods]], Old [[Nyaaya]] (circa 250 B.C. ) , [[Buddhist]] [[logic]] (sixth century A.D.) and New [[Nyaaya]]. |
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− | + | The [[Buddhist logic]] text, [[Nyaayaprave`sa]] ([[Introduction to Logical Methods]]) , had great [[influence]] upon [[Indian]] and [[Chinese Buddhism]] and also among the {{Wiki|Jains}}. | |
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− | + | As a pivotal work, the [[Nyaayaprave`sa]] has received critical [[attention]] from {{Wiki|historians}} of [[religion]], philologists, [[philosophers]], and [[logicians]]. | |
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− | + | As with all advances in {{Wiki|scholarship}}, there is [[controversy]] over [[interpretation]], but in the case of [[Buddhist]] [[logic]], the [[controversy]] cuts to the very [[heart]] of the issue of whether [[Buddhist]] [[logic]] is in any recognizable contemporary [[sense]] a "[[logic]]." | |
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− | + | The received [[view]] holds that [[Buddhist]] [[logic]] bears very close similarities to {{Wiki|syllogistic}} [[forms]] and that it can be represented and analyzed by standard {{Wiki|deductive}} techniques.(1) | |
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− | + | A much different and opposing [[view]] has been argued by {{Wiki|Professor}} [[Douglas Daye]] in a series of papers. | |
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− | + | Daye maintains that "... the descriptive utility of {{Wiki|mathematical}} [[logic]] with early [[Nyaaya]] texts has simply been overrated"; | |
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− | + | (2) that although the [[Nyaaya]] texts contain [[Wikipedia:metalogic|metalogical]] {{Wiki|rules}} for evaluating the "legitimacy or illegitimacy" of arguments, the {{Wiki|distinction}} between validity and invalidity does not apply; | |
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− | + | (3) that [[Nyaaya]] models are not inferences but "formalistic explanations"; and that "... [[Buddhist]] [[logic]] is not {{Wiki|deductive}}, nor can it be formally valid nor is it an {{Wiki|inference}}." | |
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− | + | (4) [[File:Buddha 2sw.jpg|thumb|250px|]] The cumulative effect of these claims is to assert that [[Buddhist]] [[logic]] is not a "[[logic]]" at all, at least not in any [[sense]] which is [[recognized]] by {{Wiki|Western}} [[philosophers]]. | |
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− | + | There is a radical incompatibility between the [[Nyaaya]] methods of [[logic]] and those of the Prior Analytics or Principia Mathematica. | |
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− | + | Of course, there will be differences, possibly very great differences, between any two [[traditions]] so diverse as fourth century (B.C.) {{Wiki|Greece}} and sixth century (A.D.) [[India]], but are we to go so far as to say that the [[Nyaaya]] does not contain inferences? | |
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− | + | The radical incompatibility {{Wiki|thesis}} is, I maintain, a mistake; moreover, it is a mistake which can readily be uncovered by examining the typical [[Nyaaya]] {{Wiki|inference}} scheme. | |
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− | + | Of the notion that a [[Nyaaya]] scheme could be a "formalistic explanation" without [[being]] an {{Wiki|inference}}, I shall say very little because I do not see how anything which functions as an explanation could not involve inferences of some kind or other. | |
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− | [[File:Buddha 2sw.jpg|thumb|250px|]] | + | It is important to know whether the [[Nyaaya]] scheme is {{Wiki|deductive}} or not, and if it is, whether all of its parts are [[essential]] to the deduction. |
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− | + | I will demonstrate that there are two ways of reading the [[Nyaaya]] [[form]]: one which is straightforwardly {{Wiki|deductive}} and a second which is best understood by what the American {{Wiki|pragmatist}}, [[.S. Peirce]], and later [[Norwood Hanson]], call "retroduction." | |
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[[File:Bud4.jpeg|thumb|250px|]] | [[File:Bud4.jpeg|thumb|250px|]] | ||
To begin with, consider this representative | To begin with, consider this representative | ||
− | example from the Nyaaya:(5) | + | example from the [[Nyaaya]]:(5) |
− | 1. pak.sa (thesis) Sound is imprrmanrne | + | 1. [[pak.sa]] ({{Wiki|thesis}}) [[Sound]] is imprrmanrne |
− | 2. hetu (mark or Reason) - Because of its | + | 2. [[hetu]] (mark or [[Reason]]) - Because of its |
− | property of being produced | + | property of [[being]] produced |
− | + | ||
3. d.r.s.taanta (Exemplification)--Whatever is | 3. d.r.s.taanta (Exemplification)--Whatever is | ||
− | produced, is impermanent | + | produced, is [[impermanent]] |
− | 4. sapak.sa (similar case)- As with a pot, and | + | 4. [[sapak.sa]] (similar case)- As with a pot, and |
so forth | so forth | ||
− | 5. vipak.sa (dissimilar case)- As (not with the | + | 5. [[vipak.sa]] (dissimilar case)- As (not with the |
− | case) of space, and so forth | + | case) of [[space]], and so forth |
− | Tachikawa proposes the following scheme for what | + | [[Tachikawa]] proposes the following scheme for what |
− | he calls the "three-membered Indian syllogism:(6) | + | he calls the "three-membered [[Indian]] syllogism:(6) |
6. There is property p in locus L | 6. There is property p in locus L | ||
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property p, as in locus w | property p, as in locus w | ||
[[File:Buddha 21226.jpg|thumb|250px|]] | [[File:Buddha 21226.jpg|thumb|250px|]] | ||
− | Clearly, if this schema is reversed, (8) and (7) | + | Clearly, if this {{Wiki|schema}} is reversed, (8) and (7) |
− | become premises for a valid deductive inference of | + | become premises for a valid {{Wiki|deductive}} {{Wiki|inference}} of |
(6) as the conclusion. The reverse of our example | (6) as the conclusion. The reverse of our example | ||
becomes an instance of modus ponens. | becomes an instance of modus ponens. | ||
9. d.r.s.taanta - Whatever is created is | 9. d.r.s.taanta - Whatever is created is | ||
− | impermanent. | + | [[impermanent]]. |
− | 10. hetu - Sound is created. | + | 10. [[hetu]] - [[Sound]] is created. |
− | 11. pak.sa - Sound is impermanent. | + | 11. [[pak.sa]] - [[Sound]] is [[impermanent]]. |
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+ | Why is this instance of modus ponens a {{Wiki|matter}} of dispute? | ||
− | + | The incompatibilists point out that the relationship between the {{Wiki|thesis}} ([[pak.sa]]) and the {{Wiki|justification}} ([[hetu]]) is always expressed in the [[Sanskrit]] {{Wiki|ablative}} case and that this relationship cannot be represented or translated as the English "therefore" (or ergo). | |
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− | + | Its best translation is "because." | |
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− | + | [[Thus]], for the incompatibilist, the [[primary]] objection to identifying the [[Nyaaya]] scheme as a {{Wiki|deductive}} {{Wiki|inference}} is the familiar one of ordinary [[language]] [[philosophers]] who resist the translation of {{Wiki|expressions}} as `q because p' into `p ) q' on the grounds that the [[causal]] or explanatory meaning of "because" is lost in the truth-functional [[conditional]]. | |
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[[File:Buddha121xs.JPG|thumb|250px|]] | [[File:Buddha121xs.JPG|thumb|250px|]] | ||
− | This | + | |
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− | + | This objection has force, but one must distinguish between the [[assertion]] that truth-functional connectives preserve or capture the meaning of `q because p' and the claim that truth-functional connectives can represent a {{Wiki|deductive}} relationship between propositions within the [[Nyaaya]] scheme. It is the [[latter]] which the received [[view]] upholds: it is the former which the incompatibilist vehemently opposes. | |
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− | + | The issue is not joined, because surely one can maintain that there is a {{Wiki|deductive}} {{Wiki|inference}} in the [[inversion]] [[Nyaaya]] scheme without maintaining that it captures the meaning of or even approaches synonymy with the original. | |
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− | + | In sum, the issue between the received [[view]] and the incompatibilist pivots on the former's willingness to invert the [[Nyaaya]] [[form]] and read it as a valid deduction and the latter's insistence that the [[form]] cannot be so reversed without losing the special relationship of the [[hetu]]. | |
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− | + | Given the [[merits]] of both [[views]] and given the fact that both positions are not explicit contradictories of one another, there is a way to understand the [[Nyaaya]] scheme which allows both sides to have their cake and eat it too. | |
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− | + | I believe that the three-membered [[Nyaaya]] is best understood as a retroductivc {{Wiki|inference}}. | |
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− | + | A retroduction, as it has been described by [[C. S. Peirce]] and | |
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[[File:Buddha20i.jpg|thumb|250px|]] | [[File:Buddha20i.jpg|thumb|250px|]] | ||
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− | + | [[Norwood Hanson]] is a pattern of {{Wiki|reasoning}} which leads from some [[phenomenon]] or [[perception]] to an explanatory {{Wiki|hypothesis}} of that [[phenomenon]]. | |
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− | + | Its [[form]] is not truth-functional nor are the relationships of that premises completely rulegoverned. | |
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− | + | Peirce said, "It must be remembered that retroduction, although hampered very little by [[logical]] {{Wiki|rules}}, nevertheless, is [[logical]] {{Wiki|inference}}, asserting its conclusion only problematically or conjecturally...."(7) | |
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+ | Retroduction does have a recognizable pattern, and indeed it is very close to the three-membered [[syllogism]] of [[Indian]] [[logic]]. | ||
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+ | Its [[form]], according to Peirce, is: | ||
12. The surprizing fact Q is observed. | 12. The surprizing fact Q is observed. | ||
− | 13. But if P were true, Q would be a matter of | + | 13. But if P were true, Q would be a {{Wiki|matter}} of |
course. | course. | ||
− | 14. Hence, there is reason to suspect that P is | + | 14. Hence, there is [[reason]] to suspect that P is |
true. | true. | ||
− | As a schema, for retroduction we have: | + | As a {{Wiki|schema}}, for retroduction we have: |
[[File:Buddha444.jpg|thumb|250px|]] | [[File:Buddha444.jpg|thumb|250px|]] | ||
(12') q | (12') q | ||
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(14')p | (14')p | ||
− | + | which is {{Wiki|isomorphic}} with that of the [[Nyaaya]] (that is, [[pak.sa]], because [[hetu]] and d.r.s.taanta; hence there is {{Wiki|evidence}} for the [[pak.sa]]). | |
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− | + | The similarity ([[sapak.sa]]) and dissimilarity ([[vipak.sa]]) cases serve as further {{Wiki|evidence}} in support of the explanatory {{Wiki|justification}}. | |
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− | + | The [[philosopher]] of [[science]], [[Norwood Hanson]], argued that retroduction was a "[[logic]] of discovery" which led to deductive-nomological explanations. | |
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+ | Like Peirce, Hanson pointed out that the [[reversal]] of a retroduction was a {{Wiki|deductive}} {{Wiki|inference}} 'q, q because p', becomes 'p, if p, then q, hence q'. | ||
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+ | The notion of [[reversal]]" or inverting" a retroduction is not a technique or {{Wiki|rule}} of formal [[logic]], but rather a simple [[psychological]] description of changing the [[order]] of premises. | ||
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[[File:Buddhagarden.jpg|thumb|250px|]] | [[File:Buddhagarden.jpg|thumb|250px|]] | ||
− | If the three-membered | + | If the three-membered [[syllogism]] is retroduction and if a retroduction is part of a retroductive-deductive pair, one should expect to find internal {{Wiki|evidence}} for the presence or absence of a {{Wiki|deductive}} fragment. |
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− | + | To return to the [[Nyaaya]] and its commentary on this three-membered [[syllogism]], is there internal {{Wiki|evidence}} to treat it as a retroduction-cum-deduction? | |
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− | + | A crucial point of philological [[interpretation]] is the [[function]] of the {{Wiki|ablative}} "because" and the meaning of "[[hetu]]" itself. | |
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− | [[ | + | The weakness of the standard [[view]] is that it disregards the special features of the {{Wiki|ablative}} "because" and translates the three-membered [[syllogism]] as if it contained conditionals. |
− | + | Following Daye, I suggest that that move is too hasty, and that we must regard the {{Wiki|ablative}} "because" as an operator connecting the [[hetu]] and d.r.s.taanta to the {{Wiki|thesis}}. | |
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− | + | Since the [[Sanskrit]] {{Wiki|ablative}} expresses a [[relation]] of [[physical]] or {{Wiki|conceptual}} removal, separation, {{Wiki|distinction}}, or origin, it was used to convey the notion of [[causal]] explanation. | |
− | + | [[File:Buddhas.jpg|thumb|250px|]] | |
− | + | This fact gives [[Wikipedia:Prima facie|prima facie]] {{Wiki|evidence}} for interpreting it in the [[sense]] of "a [[reason]] for." Such an [[understanding]] is reinforced by the meaning of "[[hetu]]," which is the [[name]] of the explanatory part of the three membered [[syllogism]]. | |
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+ | According to [[Tachikawa]], "[[hetu]]" primarily means 'reason'.(8) | ||
− | + | This is solid ground for reading 'q because p' as: 'p is the [[reason]] for q', 'p is the explanatory {{Wiki|hypothesis}} for q', or even the Peircean 'if p were true, q would be a {{Wiki|matter}} of course'. | |
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− | + | Beyond points of translation, one of the strongest [[reasons]] for [[seeing]] the three-membered [[syllogism]] of the [[Nyaayaprave`sa]] as a retroduction-deduction is the [[existence]] of the five-membered [[syllogism]] in the earlier [[Nyaaya tradition]], particularly the [[Nyaaya Suutra]].(9) | |
− | 17. Exemplification (d.r.s.taata) - Wherever | + | The five-membered [[syllogism]] of the [[Nyaaya Suutra]] is perfectly symmetrical between its three initial retroductive steps and its two culminating {{Wiki|deductive}} steps: |
− | there is smoke. there is fire, as (for | + | |
+ | |||
+ | 15. {{Wiki|Thesis}}([[pratij~naa]]) for example, there is | ||
+ | [[fire]] on the mountain. | ||
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+ | 16. [[Reason]] ([[hetu]])- The mountain smokes. | ||
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+ | 17. {{Wiki|Exemplification}} (d.r.s.taata) - Wherever | ||
+ | there is smoke. there is [[fire]], as (for | ||
example) on the hearth in the kitchen. | example) on the hearth in the kitchen. | ||
− | 18. Recapitulation of the reason (upanaya) - The | + | 18. Recapitulation of the [[reason]] ([[upanaya]]) - The |
mountain smokes. | mountain smokes. | ||
− | 19. Conclusion (nigamana) There is fire on the | + | 19. Conclusion ([[nigamana]]) There is [[fire]] on the |
mountain. | mountain. | ||
[[File:BuddhaTwang.jpg|thumb|250px|]] | [[File:BuddhaTwang.jpg|thumb|250px|]] | ||
− | + | If one were to picture this pattern as an isosceles triangle, one side would represent the retroduction from [15] the pratij~naa {{Wiki|reasoning}} through the [16] [[hetu]] to [17] the d.r.s.taanta, and the opposing side of the triangle would represent the deduction beginning with [17] the d.r.s.taanta to [18] [[upanaya]] and inferring the [[nigamana]]. | |
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− | + | The {{Wiki|French}} {{Wiki|Indologist}} [[Wikipedia:René Guénon|Rene Guenon]] pointed out that after the [[appearance]] of the [[Nyaaya Suutra]], there were two abridged [[forms]] of the five-membered [[syllogism]], (10) in which either the first three [15-17] or the last three [17-19] parts appeared alone. | |
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− | + | Gutnon also pointed out that the [[latter]] {{Wiki|abridgment}} resembles the [[syllogism]] of Aristolle; the former {{Wiki|abridgment}}, of course, is precisely the one found in the 6th century [[Nyaayaprave`sa]] and indeed the same smoke-fire example occurs there also. | |
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− | + | Given the [[interpretation]] I have [[offered]], it is not surprising that there should be two abridgments of the five-membered [[syllogism]]. | |
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− | + | One {{Wiki|abridgment}} captures the retroductive move; the second captures the {{Wiki|deductive}} move. Deduction and retroduction are inversions of one another, and they can be separated by positioning the property-locus statement. One {{Wiki|abridgment}} [[reasons]] from the {{Wiki|thesis}} statement to an explanatory generalization; the other {{Wiki|abridgment}} deduces the {{Wiki|thesis}} from the generalization. | |
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− | + | The [[Buddhist]] [[logicians]] Mere quite emphatic about which {{Wiki|abridgment}} they favored. The [[Nyaaya]] quite explicitly says, "We say that these three statements make the members of the [[syllogism]] and no more! "(11) [[Tachikwa's]] gloss on this statement indicates that it is an [[assertion]] that only three statements are necessary for an {{Wiki|inference}}. | |
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[[File:Buddhism-2.jpg|thumb|250px|]] | [[File:Buddhism-2.jpg|thumb|250px|]] | ||
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+ | We may conclude that what "{{Wiki|inference}}" primarily meant to the [[Buddhist]] [[logicians]] was "{{Wiki|reasoning}} to an explanatory [[causal]] {{Wiki|hypothesis}}"; however, it would be wrong to further conclude that they had no [[appreciation]] of the {{Wiki|deductive}} {{Wiki|abridgment}}. | ||
− | + | To them [[logic]] was a means of bringing others to a [[recognition]] of particular statements; it was an [[upaaya]], a {{Wiki|heuristic}} [[teaching]] device. | |
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− | + | The retroductive {{Wiki|abridgment}} of the [[five-membered syllogism]] clearly teaches in the sence that it brings the [[hearer]] to an [[awareness]] of a [[causal]] or {{Wiki|conceptual}} connection. | |
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− | + | The {{Wiki|deductive}} {{Wiki|abridgment}} does not "teach" in this [[sense]] because like all deductions its conclusion does not contain [[information]] nor already found in the premises, | |
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− | + | [[Thus]], from the standpoint of an [[upaaya]] the retroductive {{Wiki|inference}} is enough, or, as the author of the [[Nyaayaprave`sa]] put it, "...these three members make the [retroductive] [[syllogism]] and no more." | |
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[[File:Buddhism-Mongolia.jpg|thumb|250px|]] | [[File:Buddhism-Mongolia.jpg|thumb|250px|]] | ||
− | A further | + | |
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− | + | A further point in favour of reading the [[Nyaaya]] {{Wiki|inference}} {{Wiki|schema}} as a retroduction is that it makes the remainder of the manual on [[logical]] methods, especially the detailed [[sections]] on kinds of fallacies, more intelligible and [[enlightening]]. | |
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− | + | More than two thirds of the text covers identification and {{Wiki|classification}} of fallacies, but none bear any resemblance to the formal fallacies of deduction such as [[affirming]] the consequent or denying the antecedent, nor does the system resemble {{Wiki|Western}} notions of an informal [[fallacy]]. | |
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− | + | Fallacies of irrelevance such as the ad hominem or post hoc propter hoc call [[attention]] to the lack of support between premises and putative conclusion. In [[Buddhist]] [[logic]] the {{Wiki|classification}} of fallacies does not attempt to circumscribe the ways premises can be irrelevant; on the contrary it fives criteria for grading the strength or weakness of the explanatory {{Wiki|hypotheses}}. | |
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− | + | This is precisely what is required for retroductive accuracy. | |
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− | + | Weak {{Wiki|hypotheses}} emerge in three circumstances: | |
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− | + | (1) the [[hetu]] is unrecognized by proponent or opponent, | |
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− | + | (2) the [[hetu]] is inconclusive, or | |
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− | + | (3) it is contradicted. Inconclusive [[hetus]] are those which are not supported by further {{Wiki|evidence}} from the similarity and dissimilarity cases; contradicted [[hetus]] are those which prove the opposite of the [[pak.sa]]. | |
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− | + | Such a {{Wiki|contradiction}} is established by deducing the opposite property-locus [[assertion]]. | |
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− | + | A [[hetu]] can fail to be [[recognized]], that is, it can fail as a [[teaching]] device by not making the auditor (or speaker) {{Wiki|aware}} of the connection between the [[assertion]] statement and its warranting [[hetu]]. | |
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− | + | [[Thus]], when {{Wiki|hypotheses}} fail to be understood, they engender fallacies of [[recognition]], but when they fail in evidential support they engender fallacies of {{Wiki|contradiction}} or inconclusivity. On the whole, this {{Wiki|classification}} of fallacies reflects a sophisticated, but also a commonsensical, means of evaluating {{Wiki|hypotheses}}. | |
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− | + | It is open textured as retroductive {{Wiki|reasoning}} must be, and more importantly it does not attempt (as the {{Wiki|Western}} notion of fallac does) to classify fallacious {{Wiki|reasoning}} as a kind of {{Wiki|deductive}} argument gone awry. | |
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[[File:Buddhism.jpg|thumb|250px|]] | [[File:Buddhism.jpg|thumb|250px|]] | ||
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+ | In this paper I have attempted to enlarge the {{Wiki|dialogue}} about the [[nature]] of [[Buddhist]] [[logic]] by arguing that it is [[essentially]] retroductive. | ||
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+ | As [[philosophers]] and {{Wiki|psychologists}} continue to investigate the {{Wiki|conceptual}} and {{Wiki|factual}} aspects of {{Wiki|hypothesis}} formation, the study of [[Buddhist]] [[logic]] will increase in importance because, unlike other [[logical]] treatises, the [[Nyaayaprave`sa]] is an historyically significant document about ways of {{Wiki|reasoning}} and misreasoning to an explanatory | ||
+ | {{Wiki|hypothesis}}. | ||
+ | |||
+ | |||
NOTES | NOTES | ||
1. Daniel H. H. Ingalls, Material for the Study | 1. Daniel H. H. Ingalls, Material for the Study | ||
− | of Navya-Nyaya Logic, Harvard Oriental Series, vol. | + | of [[Navya-Nyaya]] [[Logic]], {{Wiki|Harvard}} {{Wiki|Oriental}} Series, vol. |
− | 40 (Cambridge: Harvard | + | 40 ({{Wiki|Cambridge}}: {{Wiki|Harvard University}} Press, 1951); |
− | Hajime Nakamura, "Buddhist Logic Expounded by Means | + | [[Hajime Nakamura]], "[[Buddhist]] [[Logic]] Expounded by Means |
− | of Symbolic Logic," Indogku Bukkyogaku Kenkyu 7 | + | of [[Symbolic]] [[Logic]]," Indogku Bukkyogaku Kenkyu 7 |
(1958) : 375-395; J. F. Staal, "Means of | (1958) : 375-395; J. F. Staal, "Means of | ||
− | Formalization of Indian and Western Thought," Logic, | + | Formalization of [[Indian]] and {{Wiki|Western}} [[Thought]]," [[Logic]], |
− | Metlzodology and Philosophy of Science, Proceedings | + | Metlzodology and [[Philosophy]] of [[Science]], Proceedings |
− | of the XIIth International Congress of Philosophy, | + | of the XIIth International Congress of [[Philosophy]], |
Venice, 1958; H. Kitagawa, "A Note on the | Venice, 1958; H. Kitagawa, "A Note on the | ||
− | Methodology in the Study of Indian Logic," Indogaku | + | {{Wiki|Methodology}} in the Study of [[Indian]] [[Logic]]," Indogaku |
Bukkyogaku Kenkyu 8 (1960) : 380-390; S. S. | Bukkyogaku Kenkyu 8 (1960) : 380-390; S. S. | ||
− | Barlingay, A Modern Introduction to Indian Logic | + | Barlingay, A {{Wiki|Modern}} Introduction to [[Indian]] [[Logic]] |
− | (Delhi: National Publishing House, 1965) : A. | + | ({{Wiki|Delhi}}: National Publishing House, 1965) : A. |
− | Charlene S. McDermott, An Eleventh-Century Buddhist | + | Charlene S. McDermott, An Eleventh-Century [[Buddhist]] |
− | Logic of "Exists, " Foundations of Language, | + | [[Logic]] of "[[Exists]], " Foundations of [[Language]], |
− | Supplementary Series, vol. 2 (Dordrecht, Holland: D. | + | Supplementary Series, vol. 2 (Dordrecht, [[Holland]]: D. |
Reidel, 1970); B. K. Matilal, The Navya-Nyaaya | Reidel, 1970); B. K. Matilal, The Navya-Nyaaya | ||
− | Doctrine of Negation, Harvard Oriental Series, vol. | + | [[Doctrine]] of {{Wiki|Negation}}, {{Wiki|Harvard}} {{Wiki|Oriental}} Series, vol. |
− | 46 (Cambridge: Harvard University Press. 1968): and | + | 46 ({{Wiki|Cambridge}}: {{Wiki|Harvard University}} Press. 1968): and |
− | particularly Epistemology, Logic and Grammar in | + | particularly {{Wiki|Epistemology}}, [[Logic]] and [[Grammar]] in |
− | Indian Philosophical Analysis, Janua Linguarum, | + | [[Indian]] [[Philosophical]] Analysis, Janua Linguarum, |
Series Minor, 111 (Mouton: The Hague, 1971). | Series Minor, 111 (Mouton: The Hague, 1971). | ||
[[File:Buddhism47gf.jpg|thumb|250px|]] | [[File:Buddhism47gf.jpg|thumb|250px|]] | ||
2. Douglas Daye, "Metalogical Incompatibilities | 2. Douglas Daye, "Metalogical Incompatibilities | ||
− | In the Formal Description of Buddhist Logic | + | In the Formal Description of [[Buddhist]] [[Logic]] |
− | (Nyaaya)," Notre Dame Journal of Logic 28, no. 2 | + | ([[Nyaaya]])," Notre Dame Journal of [[Logic]] 28, no. 2 |
(1977): 231. | (1977): 231. | ||
− | 3. Douglas Daye, "Empirical Falsifiability and | + | 3. Douglas Daye, "[[Empirical]] Falsifiability and |
the Frequence of Dar`sana Relevance in the Sixth | the Frequence of Dar`sana Relevance in the Sixth | ||
− | Century Buddhist Logic of Sankaravamin," Logique et | + | Century [[Buddhist]] [[Logic]] of Sankaravamin," Logique et |
Analyse 86 (June 1979): 221. | Analyse 86 (June 1979): 221. | ||
− | 4. Douglas Daye, Comparative Issues in Buddhist | + | 4. Douglas Daye, Comparative Issues in [[Buddhist]] |
− | and Angle-European Formal Logics (unpublished | + | and Angle-European Formal [[Logics]] (unpublished |
− | manuscript), p. 121. | + | {{Wiki|manuscript}}), p. 121. |
− | 5. Musashi Tachikawa, trans., "A Sixth Century | + | 5. [[Musashi]] [[Tachikawa]], trans., "A Sixth Century |
− | Manual of Indian Logic (the Nyaayaprave`sa) ," | + | Manual of [[Indian]] [[Logic]] (the [[Nyaayaprave`sa]]) ," |
− | Journal of Indian Philosophy 1, no. 2 (1971): 114. | + | Journal of [[Indian Philosophy]] 1, no. 2 (1971): 114. |
6. Ibid., p. 115, Norwood R. Hanson, Patterns of | 6. Ibid., p. 115, Norwood R. Hanson, Patterns of | ||
− | Discovery (Cambridge: Cambridge University Press, | + | Discovery ({{Wiki|Cambridge}}: {{Wiki|Cambridge}} {{Wiki|University}} Press, |
1958), pp. 93-105. | 1958), pp. 93-105. | ||
− | "Is There A Logic of Discovery," Current Issues | + | "Is There A [[Logic]] of Discovery," Current Issues |
− | in Philosophy of Science, edited by H. Fergland and | + | in [[Philosophy]] of [[Science]], edited by H. Fergland and |
− | G. Maxwell (New | + | G. Maxwell ({{Wiki|New York}}: Holt-Rinehart & Winston, |
− | 1961), pp. 20-35. Also Aristotle, Prior Analytics II, | + | 1961), pp. 20-35. Also {{Wiki|Aristotle}}, Prior Analytics II, |
25. | 25. | ||
[[File:BuddhistTriad.JPG|thumb|250px|]] | [[File:BuddhistTriad.JPG|thumb|250px|]] | ||
− | 7. C. S. Peirce, Collected Works (Cambridge: | + | 7. C. S. Peirce, Collected Works ({{Wiki|Cambridge}}: |
− | Harvard | + | {{Wiki|Harvard University}} Press, 1933), vol. 1, p. 188. |
Also vol. 6, pp. 522-28. | Also vol. 6, pp. 522-28. | ||
− | 8. Tachikawa, p. 116. | + | 8. [[Tachikawa]], p. 116. |
− | 9. A. B. Keith, Indian Logic and Atomism | + | 9. A. B. Keith, [[Indian]] [[Logic]] and {{Wiki|Atomism}} |
− | (Oxford: 1921), p. 21. The author dates the Nyaaya | + | ({{Wiki|Oxford}}: 1921), p. 21. The author dates the [[Nyaaya Suutra]] at 200-450 A.D. |
− | |||
− | 10. Rene Guenon, Introduction generale a l'etude | + | 10. [[Wikipedia:René Guénon|Rene Guenon]], Introduction generale a l'etude |
− | des doctrines hindous(Paris: 1930), pp. 226-227. | + | des [[doctrines]] hindous(Paris: 1930), pp. 226-227. |
− | 11. Tachikawa, p. 122. | + | 11. [[Tachikawa]], p. 122. |
</poem> | </poem> | ||
{{R}} | {{R}} |
Latest revision as of 15:08, 8 March 2015
The history of Indian logic is usually divided into three periods, Old Nyaaya (circa 250 B.C. ) , Buddhist logic (sixth century A.D.) and New Nyaaya.
The Buddhist logic text, Nyaayaprave`sa (Introduction to Logical Methods) , had great influence upon Indian and Chinese Buddhism and also among the Jains.
As a pivotal work, the Nyaayaprave`sa has received critical attention from historians of religion, philologists, philosophers, and logicians.
As with all advances in scholarship, there is controversy over interpretation, but in the case of Buddhist logic, the controversy cuts to the very heart of the issue of whether Buddhist logic is in any recognizable contemporary sense a "logic."
The received view holds that Buddhist logic bears very close similarities to syllogistic forms and that it can be represented and analyzed by standard deductive techniques.(1)
A much different and opposing view has been argued by Professor Douglas Daye in a series of papers.
Daye maintains that "... the descriptive utility of mathematical logic with early Nyaaya texts has simply been overrated";
(2) that although the Nyaaya texts contain metalogical rules for evaluating the "legitimacy or illegitimacy" of arguments, the distinction between validity and invalidity does not apply;
(3) that Nyaaya models are not inferences but "formalistic explanations"; and that "... Buddhist logic is not deductive, nor can it be formally valid nor is it an inference."
There is a radical incompatibility between the Nyaaya methods of logic and those of the Prior Analytics or Principia Mathematica.
Of course, there will be differences, possibly very great differences, between any two traditions so diverse as fourth century (B.C.) Greece and sixth century (A.D.) India, but are we to go so far as to say that the Nyaaya does not contain inferences?
The radical incompatibility thesis is, I maintain, a mistake; moreover, it is a mistake which can readily be uncovered by examining the typical Nyaaya inference scheme.
Of the notion that a Nyaaya scheme could be a "formalistic explanation" without being an inference, I shall say very little because I do not see how anything which functions as an explanation could not involve inferences of some kind or other.
It is important to know whether the Nyaaya scheme is deductive or not, and if it is, whether all of its parts are essential to the deduction.
I will demonstrate that there are two ways of reading the Nyaaya form: one which is straightforwardly deductive and a second which is best understood by what the American pragmatist, .S. Peirce, and later Norwood Hanson, call "retroduction."
To begin with, consider this representative
example from the Nyaaya:(5)
1. pak.sa (thesis) Sound is imprrmanrne
2. hetu (mark or Reason) - Because of its
property of being produced
3. d.r.s.taanta (Exemplification)--Whatever is
produced, is impermanent
4. sapak.sa (similar case)- As with a pot, and
so forth
5. vipak.sa (dissimilar case)- As (not with the
case) of space, and so forth
Tachikawa proposes the following scheme for what
he calls the "three-membered Indian syllogism:(6)
6. There is property p in locus L
7. (because) there is property q (in L).
8. Wherever there is property q, there is
property p, as in locus w
Clearly, if this schema is reversed, (8) and (7)
become premises for a valid deductive inference of
(6) as the conclusion. The reverse of our example
becomes an instance of modus ponens.
9. d.r.s.taanta - Whatever is created is
impermanent.
10. hetu - Sound is created.
11. pak.sa - Sound is impermanent.
Why is this instance of modus ponens a matter of dispute?
The incompatibilists point out that the relationship between the thesis (pak.sa) and the justification (hetu) is always expressed in the Sanskrit ablative case and that this relationship cannot be represented or translated as the English "therefore" (or ergo).
Its best translation is "because."
Thus, for the incompatibilist, the primary objection to identifying the Nyaaya scheme as a deductive inference is the familiar one of ordinary language philosophers who resist the translation of expressions as `q because p' into `p ) q' on the grounds that the causal or explanatory meaning of "because" is lost in the truth-functional conditional.
This objection has force, but one must distinguish between the assertion that truth-functional connectives preserve or capture the meaning of `q because p' and the claim that truth-functional connectives can represent a deductive relationship between propositions within the Nyaaya scheme. It is the latter which the received view upholds: it is the former which the incompatibilist vehemently opposes.
The issue is not joined, because surely one can maintain that there is a deductive inference in the inversion Nyaaya scheme without maintaining that it captures the meaning of or even approaches synonymy with the original.
In sum, the issue between the received view and the incompatibilist pivots on the former's willingness to invert the Nyaaya form and read it as a valid deduction and the latter's insistence that the form cannot be so reversed without losing the special relationship of the hetu.
Given the merits of both views and given the fact that both positions are not explicit contradictories of one another, there is a way to understand the Nyaaya scheme which allows both sides to have their cake and eat it too.
I believe that the three-membered Nyaaya is best understood as a retroductivc inference.
A retroduction, as it has been described by C. S. Peirce and
Norwood Hanson is a pattern of reasoning which leads from some phenomenon or perception to an explanatory hypothesis of that phenomenon.
Its form is not truth-functional nor are the relationships of that premises completely rulegoverned.
Peirce said, "It must be remembered that retroduction, although hampered very little by logical rules, nevertheless, is logical inference, asserting its conclusion only problematically or conjecturally...."(7)
Retroduction does have a recognizable pattern, and indeed it is very close to the three-membered syllogism of Indian logic.
Its form, according to Peirce, is:
12. The surprizing fact Q is observed.
13. But if P were true, Q would be a matter of
course.
14. Hence, there is reason to suspect that P is
true.
As a schema, for retroduction we have:
(12') q
(13') q because p
(14')p
which is isomorphic with that of the Nyaaya (that is, pak.sa, because hetu and d.r.s.taanta; hence there is evidence for the pak.sa).
The similarity (sapak.sa) and dissimilarity (vipak.sa) cases serve as further evidence in support of the explanatory justification.
The philosopher of science, Norwood Hanson, argued that retroduction was a "logic of discovery" which led to deductive-nomological explanations.
Like Peirce, Hanson pointed out that the reversal of a retroduction was a deductive inference 'q, q because p', becomes 'p, if p, then q, hence q'.
The notion of reversal" or inverting" a retroduction is not a technique or rule of formal logic, but rather a simple psychological description of changing the order of premises.
If the three-membered syllogism is retroduction and if a retroduction is part of a retroductive-deductive pair, one should expect to find internal evidence for the presence or absence of a deductive fragment.
To return to the Nyaaya and its commentary on this three-membered syllogism, is there internal evidence to treat it as a retroduction-cum-deduction?
A crucial point of philological interpretation is the function of the ablative "because" and the meaning of "hetu" itself.
The weakness of the standard view is that it disregards the special features of the ablative "because" and translates the three-membered syllogism as if it contained conditionals.
Following Daye, I suggest that that move is too hasty, and that we must regard the ablative "because" as an operator connecting the hetu and d.r.s.taanta to the thesis.
Since the Sanskrit ablative expresses a relation of physical or conceptual removal, separation, distinction, or origin, it was used to convey the notion of causal explanation.
This fact gives prima facie evidence for interpreting it in the sense of "a reason for." Such an understanding is reinforced by the meaning of "hetu," which is the name of the explanatory part of the three membered syllogism.
According to Tachikawa, "hetu" primarily means 'reason'.(8)
This is solid ground for reading 'q because p' as: 'p is the reason for q', 'p is the explanatory hypothesis for q', or even the Peircean 'if p were true, q would be a matter of course'.
Beyond points of translation, one of the strongest reasons for seeing the three-membered syllogism of the Nyaayaprave`sa as a retroduction-deduction is the existence of the five-membered syllogism in the earlier Nyaaya tradition, particularly the Nyaaya Suutra.(9)
The five-membered syllogism of the Nyaaya Suutra is perfectly symmetrical between its three initial retroductive steps and its two culminating deductive steps:
15. Thesis(pratij~naa) for example, there is
fire on the mountain.
16. Reason (hetu)- The mountain smokes.
17. Exemplification (d.r.s.taata) - Wherever
there is smoke. there is fire, as (for
example) on the hearth in the kitchen.
18. Recapitulation of the reason (upanaya) - The
mountain smokes.
19. Conclusion (nigamana) There is fire on the
mountain.
If one were to picture this pattern as an isosceles triangle, one side would represent the retroduction from [15] the pratij~naa reasoning through the [16] hetu to [17] the d.r.s.taanta, and the opposing side of the triangle would represent the deduction beginning with [17] the d.r.s.taanta to [18] upanaya and inferring the nigamana.
The French Indologist Rene Guenon pointed out that after the appearance of the Nyaaya Suutra, there were two abridged forms of the five-membered syllogism, (10) in which either the first three [15-17] or the last three [17-19] parts appeared alone.
Gutnon also pointed out that the latter abridgment resembles the syllogism of Aristolle; the former abridgment, of course, is precisely the one found in the 6th century Nyaayaprave`sa and indeed the same smoke-fire example occurs there also.
Given the interpretation I have offered, it is not surprising that there should be two abridgments of the five-membered syllogism.
One abridgment captures the retroductive move; the second captures the deductive move. Deduction and retroduction are inversions of one another, and they can be separated by positioning the property-locus statement. One abridgment reasons from the thesis statement to an explanatory generalization; the other abridgment deduces the thesis from the generalization.
The Buddhist logicians Mere quite emphatic about which abridgment they favored. The Nyaaya quite explicitly says, "We say that these three statements make the members of the syllogism and no more! "(11) Tachikwa's gloss on this statement indicates that it is an assertion that only three statements are necessary for an inference.
We may conclude that what "inference" primarily meant to the Buddhist logicians was "reasoning to an explanatory causal hypothesis"; however, it would be wrong to further conclude that they had no appreciation of the deductive abridgment.
To them logic was a means of bringing others to a recognition of particular statements; it was an upaaya, a heuristic teaching device.
The retroductive abridgment of the five-membered syllogism clearly teaches in the sence that it brings the hearer to an awareness of a causal or conceptual connection.
The deductive abridgment does not "teach" in this sense because like all deductions its conclusion does not contain information nor already found in the premises,
Thus, from the standpoint of an upaaya the retroductive inference is enough, or, as the author of the Nyaayaprave`sa put it, "...these three members make the [retroductive] syllogism and no more."
A further point in favour of reading the Nyaaya inference schema as a retroduction is that it makes the remainder of the manual on logical methods, especially the detailed sections on kinds of fallacies, more intelligible and enlightening.
More than two thirds of the text covers identification and classification of fallacies, but none bear any resemblance to the formal fallacies of deduction such as affirming the consequent or denying the antecedent, nor does the system resemble Western notions of an informal fallacy.
Fallacies of irrelevance such as the ad hominem or post hoc propter hoc call attention to the lack of support between premises and putative conclusion. In Buddhist logic the classification of fallacies does not attempt to circumscribe the ways premises can be irrelevant; on the contrary it fives criteria for grading the strength or weakness of the explanatory hypotheses.
This is precisely what is required for retroductive accuracy.
Weak hypotheses emerge in three circumstances:
(1) the hetu is unrecognized by proponent or opponent,
(2) the hetu is inconclusive, or
(3) it is contradicted. Inconclusive hetus are those which are not supported by further evidence from the similarity and dissimilarity cases; contradicted hetus are those which prove the opposite of the pak.sa.
Such a contradiction is established by deducing the opposite property-locus assertion.
A hetu can fail to be recognized, that is, it can fail as a teaching device by not making the auditor (or speaker) aware of the connection between the assertion statement and its warranting hetu.
Thus, when hypotheses fail to be understood, they engender fallacies of recognition, but when they fail in evidential support they engender fallacies of contradiction or inconclusivity. On the whole, this classification of fallacies reflects a sophisticated, but also a commonsensical, means of evaluating hypotheses.
It is open textured as retroductive reasoning must be, and more importantly it does not attempt (as the Western notion of fallac does) to classify fallacious reasoning as a kind of deductive argument gone awry.
In this paper I have attempted to enlarge the dialogue about the nature of Buddhist logic by arguing that it is essentially retroductive.
As philosophers and psychologists continue to investigate the conceptual and factual aspects of hypothesis formation, the study of Buddhist logic will increase in importance because, unlike other logical treatises, the Nyaayaprave`sa is an historyically significant document about ways of reasoning and misreasoning to an explanatory
hypothesis.
NOTES
1. Daniel H. H. Ingalls, Material for the Study
of Navya-Nyaya Logic, Harvard Oriental Series, vol.
40 (Cambridge: Harvard University Press, 1951);
Hajime Nakamura, "Buddhist Logic Expounded by Means
of Symbolic Logic," Indogku Bukkyogaku Kenkyu 7
(1958) : 375-395; J. F. Staal, "Means of
Formalization of Indian and Western Thought," Logic,
Metlzodology and Philosophy of Science, Proceedings
of the XIIth International Congress of Philosophy,
Venice, 1958; H. Kitagawa, "A Note on the
Methodology in the Study of Indian Logic," Indogaku
Bukkyogaku Kenkyu 8 (1960) : 380-390; S. S.
Barlingay, A Modern Introduction to Indian Logic
(Delhi: National Publishing House, 1965) : A.
Charlene S. McDermott, An Eleventh-Century Buddhist
Logic of "Exists, " Foundations of Language,
Supplementary Series, vol. 2 (Dordrecht, Holland: D.
Reidel, 1970); B. K. Matilal, The Navya-Nyaaya
Doctrine of Negation, Harvard Oriental Series, vol.
46 (Cambridge: Harvard University Press. 1968): and
particularly Epistemology, Logic and Grammar in
Indian Philosophical Analysis, Janua Linguarum,
Series Minor, 111 (Mouton: The Hague, 1971).
2. Douglas Daye, "Metalogical Incompatibilities
In the Formal Description of Buddhist Logic
(Nyaaya)," Notre Dame Journal of Logic 28, no. 2
(1977): 231.
3. Douglas Daye, "Empirical Falsifiability and
the Frequence of Dar`sana Relevance in the Sixth
Century Buddhist Logic of Sankaravamin," Logique et
Analyse 86 (June 1979): 221.
4. Douglas Daye, Comparative Issues in Buddhist
and Angle-European Formal Logics (unpublished
manuscript), p. 121.
5. Musashi Tachikawa, trans., "A Sixth Century
Manual of Indian Logic (the Nyaayaprave`sa) ,"
Journal of Indian Philosophy 1, no. 2 (1971): 114.
6. Ibid., p. 115, Norwood R. Hanson, Patterns of
Discovery (Cambridge: Cambridge University Press,
1958), pp. 93-105.
"Is There A Logic of Discovery," Current Issues
in Philosophy of Science, edited by H. Fergland and
G. Maxwell (New York: Holt-Rinehart & Winston,
1961), pp. 20-35. Also Aristotle, Prior Analytics II,
25.
7. C. S. Peirce, Collected Works (Cambridge:
Harvard University Press, 1933), vol. 1, p. 188.
Also vol. 6, pp. 522-28.
8. Tachikawa, p. 116.
9. A. B. Keith, Indian Logic and Atomism
(Oxford: 1921), p. 21. The author dates the Nyaaya Suutra at 200-450 A.D.
10. Rene Guenon, Introduction generale a l'etude
des doctrines hindous(Paris: 1930), pp. 226-227.
11. Tachikawa, p. 122.