Difference between revisions of "What is the "logic" in Buddhist logic? By R. Lance Factor"
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[[File:Bud 0.jpg|thumb|250px|]] | [[File:Bud 0.jpg|thumb|250px|]] | ||
<poem> | <poem> | ||
− | The history of Indian logic is usually divided into | + | The {{Wiki|history}} of [[Indian]] [[logic]] is usually divided into |
three periods, Old Nyaaya (circa 250 B.C. ) , | three periods, Old Nyaaya (circa 250 B.C. ) , | ||
− | Buddhist logic (sixth century A.D.) and New Nyaaya. | + | [[Buddhist]] [[logic]] (sixth century A.D.) and New Nyaaya. |
− | The Buddhist logic text, Nyaayaprave`sa | + | The [[Buddhist]] [[logic]] text, Nyaayaprave`sa |
(Introduction to Logical Methods) , had great | (Introduction to Logical Methods) , had great | ||
− | influence upon Indian and Chinese Buddhism and also | + | [[influence]] upon [[Indian]] and [[Chinese Buddhism]] and also |
− | among the Jains. As a pivotal work, the | + | among the {{Wiki|Jains}}. As a pivotal work, the |
− | Nyaayaprave`sa has received critical attention from | + | Nyaayaprave`sa has received critical [[attention]] from |
− | historians of religion, philologists, philosophers, | + | historians of [[religion]], philologists, [[philosophers]], |
− | and logicians. As with all advances in scholarship, | + | and [[logicians]]. As with all advances in {{Wiki|scholarship}}, |
there is controversy over interpretation, but in the | there is controversy over interpretation, but in the | ||
− | case of Buddhist logic, the controversy cuts to the | + | case of [[Buddhist]] [[logic]], the controversy cuts to the |
− | very heart of the issue of whether Buddhist logic is | + | very [[heart]] of the issue of whether [[Buddhist]] [[logic]] is |
− | in any recognizable contemporary sense a "logic." | + | in any recognizable contemporary [[sense]] a "[[logic]]." |
− | The received view holds that Buddhist logic bears | + | The received [[view]] holds that [[Buddhist]] [[logic]] bears |
very close similarities to syllogistic forms and | very close similarities to syllogistic forms and | ||
that it can be represented and analyzed by standard | that it can be represented and analyzed by standard | ||
deductive techniques.(1) A much different and | deductive techniques.(1) A much different and | ||
− | opposing view has been argued by Professor Douglas | + | opposing [[view]] has been argued by Professor Douglas |
Daye in a series of papers. Daye maintains that "... | Daye in a series of papers. Daye maintains that "... | ||
− | the descriptive utility of mathematical logic with | + | the descriptive utility of {{Wiki|mathematical}} [[logic]] with |
early Nyaaya texts has simply been overrated";(2) | early Nyaaya texts has simply been overrated";(2) | ||
that although the Nyaaya texts contain metalogical | that although the Nyaaya texts contain metalogical | ||
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validity and invalidity does not apply;(3) that | validity and invalidity does not apply;(3) that | ||
Nyaaya models are not inferences but "formalistic | Nyaaya models are not inferences but "formalistic | ||
− | explanations"; and that "... Buddhist logic is not | + | explanations"; and that "... [[Buddhist]] [[logic]] is not |
deductive, nor can it be formally valid nor is it an | deductive, nor can it be formally valid nor is it an | ||
inference."(4) | inference."(4) | ||
[[File:Buddha 2sw.jpg|thumb|250px|]] | [[File:Buddha 2sw.jpg|thumb|250px|]] | ||
The cumulative effect of these claims is to | The cumulative effect of these claims is to | ||
− | assert that Buddhist logic is not a "logic" at all, | + | assert that [[Buddhist]] [[logic]] is not a "[[logic]]" at all, |
− | at least not in any sense which is recognized by | + | at least not in any [[sense]] which is recognized by |
− | Western philosophers. There is a radical | + | Western [[philosophers]]. There is a radical |
− | incompatibility between the Nyaaya methods of logic | + | incompatibility between the Nyaaya methods of [[logic]] |
and those of the Prior Analytics or Principia | and those of the Prior Analytics or Principia | ||
Mathematica. Of course, there will be differences, | Mathematica. Of course, there will be differences, | ||
possibly very great differences, between any two | possibly very great differences, between any two | ||
− | traditions so diverse as fourth century (B.C.) | + | [[traditions]] so diverse as fourth century (B.C.) |
− | Greece and sixth century (A.D.) India, but are we to | + | Greece and sixth century (A.D.) [[India]], but are we to |
go so far as to say that the Nyaaya does not contain | go so far as to say that the Nyaaya does not contain | ||
inferences? The radical incompatibility thesis is, I | inferences? The radical incompatibility thesis is, I | ||
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Nyaaya inference scheme. Of the notion that a Nyaaya | Nyaaya inference scheme. Of the notion that a Nyaaya | ||
scheme could be a "formalistic explanation" | scheme could be a "formalistic explanation" | ||
− | without being an inference, I shall say very little | + | without [[being]] an inference, I shall say very little |
because I do not see how anything which functions as | because I do not see how anything which functions as | ||
an explanation could not involve inferences of some | an explanation could not involve inferences of some | ||
− | kind or other. It is important to know whether the | + | kind or other. It is important [[to know]] whether the |
Nyaaya scheme is deductive or not, and if it is, | Nyaaya scheme is deductive or not, and if it is, | ||
− | whether all of its parts are essential to the | + | whether all of its parts are [[essential]] to the |
deduction. I will demonstrate that there are two | deduction. I will demonstrate that there are two | ||
− | ways of reading the Nyaaya form: one which is | + | ways of reading the Nyaaya [[form]]: one which is |
straightforwardly deductive and a second which is | straightforwardly deductive and a second which is | ||
best understood by what the American pragmatist, | best understood by what the American pragmatist, | ||
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example from the Nyaaya:(5) | example from the Nyaaya:(5) | ||
− | 1. pak.sa (thesis) Sound is imprrmanrne | + | 1. pak.sa (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 |
P.184 | P.184 | ||
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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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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]]. |
Why is this instance of modus ponens a matter of | Why is this instance of modus ponens a matter of | ||
dispute? The incompatibilists point out that the | dispute? The incompatibilists point out that the | ||
relationship between the thesis (pak.sa) and the | relationship between the thesis (pak.sa) and the | ||
− | justification (hetu) is always expressed in the | + | justification ([[hetu]]) is always expressed in the |
− | Sanskrit ablative case and that this relationship | + | [[Sanskrit]] ablative case and that this relationship |
cannot be represented or translated as the English | cannot be represented or translated as the English | ||
"therefore" (or ergo). Its best translation is | "therefore" (or ergo). Its best translation is | ||
− | "because." Thus, for the incompatibilist, the | + | "because." [[Thus]], for the incompatibilist, the |
− | primary objection to identifying the Nyaaya scheme | + | [[primary]] objection to identifying the Nyaaya scheme |
as a deductive inference is the familiar one of | as a deductive inference is the familiar one of | ||
− | ordinary language philosophers who resist the | + | ordinary [[language]] [[philosophers]] who resist the |
translation of expressions as `q because p' into `p | translation of expressions as `q because p' into `p | ||
− | ) q' on the grounds that the causal or explanatory | + | ) q' on the grounds that the [[causal]] or explanatory |
meaning of "because" is lost in the | meaning of "because" is lost in the | ||
truth-functional conditional. | truth-functional conditional. | ||
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deductive relationship between propositions within | deductive relationship between propositions within | ||
the Nyaaya scheme. It is the latter which the | the Nyaaya scheme. It is the latter which the | ||
− | received view upholds: it is the former which the | + | received [[view]] upholds: it is the former which the |
incompatibilist vehemently opposes. The issue is not | incompatibilist vehemently opposes. The issue is not | ||
joined, because surely one can maintain that there | joined, because surely one can maintain that there | ||
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meaning of or even approaches synonymy with the | meaning of or even approaches synonymy with the | ||
original. In sum, the issue between the received | original. In sum, the issue between the received | ||
− | view and the incompatibilist pivots on the former's | + | [[view]] and the incompatibilist pivots on the former's |
− | willingness to invert the Nyaaya form and read it as | + | willingness to invert the Nyaaya [[form]] and read it as |
a valid deduction and the latter's insistence that | a valid deduction and the latter's insistence that | ||
− | the form cannot be so reversed without losing the | + | the [[form]] cannot be so reversed without losing the |
− | special relationship of the hetu. Given the merits | + | special relationship of the [[hetu]]. Given the [[merits]] |
− | of both views and given the fact that both positions | + | of both [[views]] and given the fact that both positions |
are not explicit contradictories of one another, | are not explicit contradictories of one another, | ||
− | there is a way to understand the Nyaaya scheme which | + | there is a way [[to understand]] the Nyaaya scheme which |
allows both sides to have their cake and eat it too. | allows both sides to have their cake and eat it too. | ||
I believe that the three-membered Nyaaya is best | I believe that the three-membered Nyaaya is best | ||
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P.185 | P.185 | ||
− | Norwood Hansonl is a pattern of reasoning which | + | Norwood Hansonl is a pattern of {{Wiki|reasoning}} which |
− | leads from some phenomenon or perception to an | + | leads from some [[phenomenon]] or [[perception]] to an |
− | explanatory hypothesis of that phenomenon. Its form | + | explanatory {{Wiki|hypothesis}} of that [[phenomenon]]. Its [[form]] |
is not truth-functional nor are the relationships of | is not truth-functional nor are the relationships of | ||
that premises completely rulegoverned. Peirce said, | that premises completely rulegoverned. Peirce said, | ||
"It must be remembered that retroduction, although | "It must be remembered that retroduction, although | ||
− | hampered very little by logical rules, nevertheless, | + | hampered very little by [[logical]] rules, nevertheless, |
− | is logical inference, asserting its conclusion only | + | is [[logical]] inference, asserting its conclusion only |
problematically or conjecturally...."(7) | problematically or conjecturally...."(7) | ||
Retroduction does have a recognizable pattern, | Retroduction does have a recognizable pattern, | ||
and indeed it is very close to the three-membered | and indeed it is very close to the three-membered | ||
− | syllogism of Indian logic. Its form, according to | + | [[syllogism]] of [[Indian]] [[logic]]. Its [[form]], according to |
Peirce, is: | Peirce, is: | ||
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course. | course. | ||
− | 14. Hence, there is reason to suspect that P is | + | 14. Hence, there is [[reason]] to suspect that P is |
true. | true. | ||
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which is isomorphic with that of the Nyaaya (that | which is isomorphic with that of the Nyaaya (that | ||
− | is, pak.sa, because hetu and d.r.s.taanta; hence | + | is, pak.sa, because [[hetu]] and d.r.s.taanta; hence |
there is evidence for the pak.sa). The similarity | there is evidence for the pak.sa). The similarity | ||
(sapak.sa) and dissimilarity (vipak.sa) cases serve | (sapak.sa) and dissimilarity (vipak.sa) cases serve | ||
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justification. | justification. | ||
− | The philosopher of science, Norwood Hanson, | + | The [[philosopher]] of [[science]], Norwood Hanson, |
− | argued that retroduction was a "logic of discovery" | + | argued that retroduction was a "[[logic]] of discovery" |
which led to deductive-nomological explanations. | which led to deductive-nomological explanations. | ||
Like Peirce, Hanson pointed out that the reversal of | Like Peirce, Hanson pointed out that the reversal of | ||
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because p', becomes 'p, if p, then q, hence q'. The | because p', becomes 'p, if p, then q, hence q'. The | ||
notion of reversal" or inverting" a retroduction is | notion of reversal" or inverting" a retroduction is | ||
− | not a technique or rule of formal logic, but rather | + | not a technique or rule of formal [[logic]], but rather |
− | a simple psychological description of changing the | + | a simple [[psychological]] description of changing the |
− | order of premises. | + | [[order]] of premises. |
[[File:Buddhagarden.jpg|thumb|250px|]] | [[File:Buddhagarden.jpg|thumb|250px|]] | ||
− | If the three-membered syllogism is retroduction | + | If the three-membered [[syllogism]] is retroduction |
and if a retroduction is part of a | and if a retroduction is part of a | ||
retroductive-deductive pair, one should expect to | retroductive-deductive pair, one should expect to | ||
find internal evidence for the presence or absence | find internal evidence for the presence or absence | ||
of a deductive fragment. To return to the Nyaaya and | of a deductive fragment. To return to the Nyaaya and | ||
− | its commentary on this three-membered syllogism, is | + | its commentary on this three-membered [[syllogism]], is |
there internal evidence to treat it as a | there internal evidence to treat it as a | ||
retroduction-cum-deduction? A crucial point of | retroduction-cum-deduction? A crucial point of | ||
− | philological interpretation is the function of the | + | philological interpretation is the [[function]] of the |
− | ablative "because" and the meaning of "hetu" | + | ablative "because" and the meaning of "[[hetu]]" |
− | itself. The weakness of the standard view is that it | + | itself. The weakness of the standard [[view]] is that it |
disregards the special features of the ablative | disregards the special features of the ablative | ||
"because" and translates the three-membered | "because" and translates the three-membered | ||
− | syllogism as if it contained conditionals. Following | + | [[syllogism]] as if it contained conditionals. Following |
Daye, I suggest that that move is too hasty, and | Daye, I suggest that that move is too hasty, and | ||
that we must regard the ablative "because" as an | that we must regard the ablative "because" as an | ||
− | operator connecting the hetu and d.r.s.taanta to the | + | operator connecting the [[hetu]] and d.r.s.taanta to the |
− | thesis. Since the Sanskrit ablative expresses a | + | thesis. Since the [[Sanskrit]] ablative expresses a |
− | relation of physical or conceptual removal, | + | relation of [[physical]] or {{Wiki|conceptual}} removal, |
separation, distinction, or origin, it was used to | separation, distinction, or origin, it was used to | ||
− | convey the notion of causal explanation. This fact | + | convey the notion of [[causal]] explanation. This fact |
gives prima facie evidence for interpreting it in | gives prima facie evidence for interpreting it in | ||
− | the sense of "a reason for." Such an understanding | + | the [[sense]] of "a [[reason]] for." Such an understanding |
− | is reinforced by the meaning of "hetu," which is the | + | is reinforced by the meaning of "[[hetu]]," which is the |
name of the explanatory part of the three- | name of the explanatory part of the three- | ||
[[File:Buddhas.jpg|thumb|250px|]] P.186 | [[File:Buddhas.jpg|thumb|250px|]] P.186 | ||
− | membered syllogism. According to Tachikawa, "hetu" | + | membered [[syllogism]]. According to Tachikawa, "[[hetu]]" |
primarily means 'reason'.(8) This is solid ground | primarily means 'reason'.(8) This is solid ground | ||
− | for reading 'q because p' as: 'p is the reason for | + | for reading 'q because p' as: 'p is the [[reason]] for |
− | q', 'p is the explanatory hypothesis for q', or even | + | q', 'p is the explanatory {{Wiki|hypothesis}} for q', or even |
the Peircean 'if p were true, q would be a matter of | the Peircean 'if p were true, q would be a matter of | ||
course'. | course'. | ||
Beyond points of translation, one of the | Beyond points of translation, one of the | ||
− | strongest reasons for seeing the three-membered | + | strongest [[reasons]] for [[seeing]] the three-membered |
− | syllogism of the Nyaayaprave`sa as a | + | [[syllogism]] of the Nyaayaprave`sa as a |
− | retroduction-deduction is the existence of the | + | retroduction-deduction is the [[existence]] of the |
− | five-membered syllogism in the earlier Nyaaya | + | five-membered [[syllogism]] in the earlier Nyaaya |
− | tradition, particularly the Nyaaya Suutra.(9) The | + | [[tradition]], particularly the Nyaaya Suutra.(9) The |
− | five-membered syllogism of the Nyaaya Suutra is | + | five-membered [[syllogism]] of the Nyaaya Suutra is |
perfectly symmetrical between its three initial | perfectly symmetrical between its three initial | ||
retroductive steps and its two culminating deductive | retroductive steps and its two culminating deductive | ||
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15. Thesis(pratij~naa) for example, there is | 15. Thesis(pratij~naa) for example, there is | ||
− | fire on the mountain. | + | [[fire]] on the mountain. |
− | 16. Reason (hetu)- The mountain smokes. | + | 16. [[Reason]] ([[hetu]])- The mountain smokes. |
17. Exemplification (d.r.s.taata) - Wherever | 17. Exemplification (d.r.s.taata) - Wherever | ||
− | there is smoke. there is fire, as (for | + | 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|]] | ||
Line 255: | Line 255: | ||
If one were to picture this pattern as an isosceles | If one were to picture this pattern as an isosceles | ||
triangle, one side would represent the retroduction | triangle, one side would represent the retroduction | ||
− | from [15] the pratij~naa reasoning through the [16] | + | from [15] the pratij~naa {{Wiki|reasoning}} through the [16] |
− | hetu to [17] the d.r.s.taanta, and the opposing side | + | [[hetu]] to [17] the d.r.s.taanta, and the opposing side |
of the triangle would represent the deduction | of the triangle would represent the deduction | ||
beginning with [17] the d.r.s.taanta to [18] upanaya | beginning with [17] the d.r.s.taanta to [18] upanaya | ||
and inferring the nigamana. | and inferring the nigamana. | ||
− | The French Indologist Rene Guenon pointed out | + | The French {{Wiki|Indologist}} Rene Guenon pointed out |
that after the appearance of the Nyaaya Suutra, | that after the appearance of the Nyaaya Suutra, | ||
there were two abridged forms of the five-membered | there were two abridged forms of the five-membered | ||
− | syllogism, (10) in which either the first three | + | [[syllogism]], (10) in which either the first three |
[15-17] or the last three [17-19] parts appeared | [15-17] or the last three [17-19] parts appeared | ||
alone. Gutnon also pointed out that the latter | alone. Gutnon also pointed out that the latter | ||
− | abridgment resembles the syllogism of Aristolle; the | + | abridgment resembles the [[syllogism]] of Aristolle; the |
former abridgment, of course, is precisely the one | former abridgment, of course, is precisely the one | ||
found in the 6th century Nyaayaprave`sa and indeed | found in the 6th century Nyaayaprave`sa and indeed | ||
the same smoke-fire example occurs there also. Given | the same smoke-fire example occurs there also. Given | ||
− | the interpretation I have offered, it is not | + | the interpretation I have [[offered]], it is not |
surprising that there should be two abridgments of | surprising that there should be two abridgments of | ||
− | the five-membered syllogism. One abridgment captures | + | the five-membered [[syllogism]]. One abridgment captures |
the retroductive move; the second captures the | the retroductive move; the second captures the | ||
deductive move. Deduction and retroduction are | deductive move. Deduction and retroduction are | ||
inversions of one another, and they can be separated | inversions of one another, and they can be separated | ||
by positioning the property-locus statement. One | by positioning the property-locus statement. One | ||
− | abridgment reasons from the thesis statement to an | + | abridgment [[reasons]] from the thesis statement to an |
explanatory generalization; the other abridgment | explanatory generalization; the other abridgment | ||
deduces the thesis from the generalization. The | deduces the thesis from the generalization. The | ||
− | Buddhist logicians Mere quite emphatic about which | + | [[Buddhist]] [[logicians]] Mere quite emphatic about which |
abridgment they favored. The Nyaaya quite explicitly | abridgment they favored. The Nyaaya quite explicitly | ||
says, "We say that these three statements make the | says, "We say that these three statements make the | ||
− | members of the syllogism and no more! "(11) | + | members of the [[syllogism]] and no more! "(11) |
Tachikwa's gloss on this statement indicates that it | Tachikwa's gloss on this statement indicates that it | ||
is an assertion that only three statements are | is an assertion that only three statements are | ||
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[[File:Buddhism-2.jpg|thumb|250px|]] | [[File:Buddhism-2.jpg|thumb|250px|]] | ||
We may conclude that what "inference" primarily | We may conclude that what "inference" primarily | ||
− | meant to the Buddhist logicians was "reasoning to an | + | meant to the [[Buddhist]] [[logicians]] was "{{Wiki|reasoning}} to an |
− | explanatory causal hypothesis"; however, it would be | + | explanatory [[causal]] {{Wiki|hypothesis}}"; however, it would be |
wrong to further conclude that they had no | wrong to further conclude that they had no | ||
− | appreciation of the | + | [[appreciation]] of the |
P.187 | P.187 | ||
− | deductive abridgment. To them logic was a means of | + | deductive abridgment. To them [[logic]] was a means of |
− | bringing others to a recognition of particular | + | bringing others to a [[recognition]] of particular |
− | statements; it was an upaaya, a heuristic teaching | + | statements; it was an upaaya, a heuristic [[teaching]] |
device. The retroductive abridgment of the | device. The retroductive abridgment of the | ||
− | five-membered syllogism clearly teaches in the sence | + | five-membered [[syllogism]] clearly teaches in the sence |
− | that it brings the hearer to an awareness of a causal | + | that it brings the [[hearer]] to an [[awareness]] of a [[causal]] |
− | or conceptual connection. The deductive abridgment | + | or {{Wiki|conceptual}} connection. The deductive abridgment |
− | does not "teach" in this sense because like all | + | does not "teach" in this [[sense]] because like all |
deductions its conclusion does not contain | deductions its conclusion does not contain | ||
− | information nor already found in the premises, Thus, | + | [[information]] nor already found in the premises, [[Thus]], |
from the standpoint of an upaaya the retroductive | from the standpoint of an upaaya the retroductive | ||
inference is enough, or, as the author of the | inference is enough, or, as the author of the | ||
Nyaayaprave`sa put it, "...these three members make | Nyaayaprave`sa put it, "...these three members make | ||
− | the [retroductive] syllogism and no more." | + | the [retroductive] [[syllogism]] and no more." |
[[File:Buddhism-Mongolia.jpg|thumb|250px|]] | [[File:Buddhism-Mongolia.jpg|thumb|250px|]] | ||
A further point in favour of reading the Nyaaya | A further point in favour of reading the Nyaaya | ||
inference schema as a retroduction is that it makes | inference schema as a retroduction is that it makes | ||
− | the remainder of the manual on logical methods, | + | the remainder of the manual on [[logical]] methods, |
especially the detailed sections on kinds of | especially the detailed sections on kinds of | ||
fallacies, more intelligible and enljghtening. More | fallacies, more intelligible and enljghtening. More | ||
Line 325: | Line 325: | ||
notions of an informal fallacy. Fallacies of | notions of an informal fallacy. Fallacies of | ||
irrelevance such as the ad hominem or post hoc | irrelevance such as the ad hominem or post hoc | ||
− | propter hoc call attention to the lack of support | + | propter hoc call [[attention]] to the lack of support |
between premises and putative conclusion. In | between premises and putative conclusion. In | ||
− | Buddhist logic the classification of fallacies does | + | [[Buddhist]] [[logic]] the classification of fallacies does |
not attempt to circumscribe the ways premises can be | not attempt to circumscribe the ways premises can be | ||
irrelevant; on the contrary it fives criteria for | irrelevant; on the contrary it fives criteria for | ||
Line 333: | Line 333: | ||
hypotheses. This is precisely what is required for | hypotheses. This is precisely what is required for | ||
retroductive accuracy. Weak hypotheses emerge in | retroductive accuracy. Weak hypotheses emerge in | ||
− | three circumstances: (1) the hetu is unrecognized by | + | three circumstances: (1) the [[hetu]] is unrecognized by |
− | proponent or opponent, (2) the hetu is inconclusive, | + | proponent or opponent, (2) the [[hetu]] is inconclusive, |
− | or (3) it is contradicted. Inconclusive hetus are | + | or (3) it is contradicted. Inconclusive [[hetus]] are |
those which are not supported by further evidence | those which are not supported by further evidence | ||
from the similarity and dissimilarity cases; | from the similarity and dissimilarity cases; | ||
− | contradicted hetus are those which prove the | + | contradicted [[hetus]] are those which prove the |
opposite of the pak.sa. Such a contradiction is | opposite of the pak.sa. Such a contradiction is | ||
established by deducing the opposite property-locus | established by deducing the opposite property-locus | ||
− | assertion. A hetu can fail to be recognized, that | + | assertion. A [[hetu]] can fail to be recognized, that |
− | is, it can fail as a teaching device by not making | + | is, it can fail as a [[teaching]] device by not making |
the auditor (or speaker) aware of the connection | the auditor (or speaker) aware of the connection | ||
between the assertion statement and its warranting | between the assertion statement and its warranting | ||
− | hetu. Thus, when hypotheses fail to be understood, | + | [[hetu]]. [[Thus]], when hypotheses fail to be understood, |
− | they engender fallacies of recognition, but when they | + | they engender fallacies of [[recognition]], but when they |
fail in evidential support they engender fallacies | fail in evidential support they engender fallacies | ||
of contradiction or inconclusivity. On the whole, | of contradiction or inconclusivity. On the whole, | ||
Line 352: | Line 352: | ||
sophisticated, but also a commonsensical, means of | sophisticated, but also a commonsensical, means of | ||
evaluating hypotheses. It is open textured as | evaluating hypotheses. It is open textured as | ||
− | retroductive reasoning must be, and more importantly | + | retroductive {{Wiki|reasoning}} must be, and more importantly |
it does not attempt (as the Western notion of fallac | it does not attempt (as the Western notion of fallac | ||
− | does) to classify fallacious reasoning as a kind of | + | does) to classify fallacious {{Wiki|reasoning}} as a kind of |
deductive argument gone awry. | deductive argument gone awry. | ||
[[File:Buddhism.jpg|thumb|250px|]] | [[File:Buddhism.jpg|thumb|250px|]] | ||
In this paper I have attempted to enlarge the | In this paper I have attempted to enlarge the | ||
− | dialogue about the nature of Buddhist logic by | + | dialogue about the nature of [[Buddhist]] [[logic]] by |
− | arguing that it is essentially retroductive. As | + | arguing that it is [[essentially]] retroductive. As |
− | philosophers and psychologists continue to | + | [[philosophers]] and {{Wiki|psychologists}} continue to |
− | investigate the conceptual and factual aspects of | + | investigate the {{Wiki|conceptual}} and factual aspects of |
− | hypothesis formation, the study of Buddhist logic | + | {{Wiki|hypothesis}} formation, the study of [[Buddhist]] [[logic]] |
will increase in importance because, unlike other | will increase in importance because, unlike other | ||
− | logical treatises, the Nyaayaprave`sa is an | + | [[logical]] treatises, the Nyaayaprave`sa is an |
historyically significant document about ways of | historyically significant document about ways of | ||
− | reasoning and misreasoning to an explanatory | + | {{Wiki|reasoning}} and misreasoning to an explanatory |
− | hypothesis. | + | {{Wiki|hypothesis}}. |
P.188 | P.188 | ||
Line 374: | Line 374: | ||
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]], Harvard Oriental Series, vol. |
− | 40 (Cambridge: Harvard University Press, 1951); | + | 40 ({{Wiki|Cambridge}}: 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 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 | + | 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 Modern Introduction to [[Indian]] [[Logic]] |
(Delhi: National Publishing House, 1965) : A. | (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 Negation, Harvard Oriental Series, vol. |
− | 46 (Cambridge: Harvard University Press. 1968): and | + | 46 ({{Wiki|Cambridge}}: 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. | 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}} 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 University Press, 1933), vol. 1, p. 188. | Harvard University Press, 1933), vol. 1, p. 188. | ||
Also vol. 6, pp. 522-28. | Also vol. 6, pp. 522-28. | ||
Line 431: | Line 431: | ||
8. Tachikawa, p. 116. | 8. Tachikawa, p. 116. | ||
− | 9. A. B. Keith, Indian Logic and Atomism | + | 9. A. B. Keith, [[Indian]] [[Logic]] and Atomism |
(Oxford: 1921), p. 21. The author dates the Nyaaya | (Oxford: 1921), p. 21. The author dates the Nyaaya | ||
Suutra at 200-450 A.D. | Suutra at 200-450 A.D. | ||
10. Rene Guenon, Introduction generale a l'etude | 10. 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. |
Revision as of 22:44, 1 September 2013
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."(4)
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
Western philosophers. 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,
C.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
P.184
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
P.185
Norwood Hansonl 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
P.187
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 enljghtening. 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.
P.188
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.