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Jonardon
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 Posted: Mon Oct 03, 2005 3:58 pm Post subject: Inference from mist misperceived as smoke |
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The so-called "baaspaanumana" - an inference to fire from mist wrongly perceived as smoke - seems to cause the Indian logicians many problems. For if "pramaa" is knowledge, and "pramaa" is also pramaa.na-generated true cognition, then there seem only two possibilities (on the assumption that it is true, by chance, that there is a fire).
1. The apparent inference is not in fact a genuine case of inference, and so not a pramaa.na.
2. That the inferrer does really know that there is a fire.
Neither option, however, seems attractive. It cannot be the outcome which decides whether a process is or is not of a certain type. Nor does it seem at all plausible that true cognition is sufficient for knowledge.
In view of the fact that the possibility of using reason to argue one's way out of a false conception of the world is central to many Indian philosophical projects, this type of inference from falsity to truth is hotly contested in the work of Kumaarila, Raamanuja, S'riihar.sa and others. Recent scholars (Stephen Phillips, Sukharanjan Saha) have sharply contrasting views about Ga.nges'a's take on the issue. Therefore, a discussion would be very welcome.
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Jonardon Ganeri
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Plamen
Age: 54 Gender:
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| Posted: Mon Oct 03, 2005 9:49 pm Post subject: |
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My first move was to say that this is not a correct inference because, being a means for reaching pramā (episteme as opposed to doxa), pramāṇa should be but free of all defects. The defect in the pratijñā, however, does not invalidate the inference as it is a perceptual defect rather than logical doṣa. There are many examples of correct syllogisms that start with defective premises and end up with true conclusion.
On the other hand, does anumДЃna-vДЃda require material rather than formal validity of the minor premise? Evidently not, because this is the province of pratyakб№Јa. This make me think along the pragmatist line about the criterion of truth when reading about the successful activity as the driving teleology of cognition in NyДЃya.
Not much different from what I found in VedДЃnta:
| Quote: | Meditation on Brahman leads to its realisation, as in the case of Samvadi-bhrama, or erroneous notion of a thing leading to a successful result in relation to that thing. Hence in the Upanishads various kinds of Upasanas, or meditations, are described. Take the instance of a person seeing from a distance the ray of a light, situated within the walls of a room. He sees a gleam of light passing through the window of a house and getting reflected outside, and mistakes the ray of the light seen outside for a gem shining. He commits this error in his mind because he has not seen the source of the light, but only its reflection outside. Suppose this person runs after that reflection thinking that it is a gem. We can imagine the mistake that he is making in cherishing that notion. But, suppose, at another place, there is a gem kept inside a room at a distance and the light emanating from it through an aperture is also reflected outside. If this reflection of light outside is mistaken for the gem itself, there is, naturally an erroneous perception, for the light of the gem is not the gem. In the two instances cited, where one person sees the gleam of the lamp and takes it for a gem, and another where one sees the ray of light emanating from a gem and thinks it is the gem itself, though there is similarity in so far as there is a mistaken notion regarding the gem, yet, there is a difference in the results that they would achieve in pursuing the objects of their quests. While the one who has mistaken the light of the lamp for the gem would not acquire the gem by approaching it, the other who has mistaken the light of the gem for the gem itself would, by going near it, obtain it. This is an illusion in perception called Samvadi, because, though initial perception is a mistake, the end reached is the desired one. Where the end reached is something quite different from the desired one, the mistaken perception is called Visamvadi-bhrama.
We have also instances of Samvadi error in inference and also acts based on scriptural injunctions. It is likely that by seeing mist at some place we may mistake it for smoke emanating from fire and move towards it in search of fire, and by chance, find fire there, though what was perceived originally was not the smoke emanating from the fire. This is an instance where there is Samvadi in inference. If a person sprinkles some water over himself thinking that it is from the holy Ganga, and gets purified, but it so happens that the water is not of the Ganga but of the Godavari, which is also holy, it is again the mistake known as Samvadi, where the mind thinks something different from the actual fact and yet reaches the desired result. If one is affected by high fever and utters in a delirious mood the holy name of Narayana, and reaches spiritual exaltation in the higher planes of existence thereby, it should be considered as an instance of Samvadi error. And so on, there can be hundreds of instances of such errors in respect of perception, inference and scriptural testimony, which lead to the desired end, nevertheless. |
- The Philosophy of the Panchadasi
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Phillips
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| Posted: Tue Oct 04, 2005 6:11 pm Post subject: |
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Both of Jonardon's options are available.
1. This is a case of pseudo-inference (anumAna-AbhAsa) because mist not being smoke there is the fallacy of a-siddhi (failure of pakSa-dharmatA).
2. Proabably we do not want to distinguish pramANa-ja-pramA from pramANa-AbhAsa-ja-pramA, but if we do, only the former is knowledge. Or the cognition of fire from misperceived mist does not count as pramA BECAUSE it is not pramANa-ja.
stavana (Stephen Phillips)
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Plamen
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| Posted: Thu May 18, 2006 12:31 pm Post subject: |
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Mahalakshmi G.S. asked me to provide an example of "correct syllogisms that start with defective premises and end up with true conclusion".
Here is the classical one:
My handkerchief is on the moon.
The moon is in my pocket.
Hence, my handkerchief is in my pocket.
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Avi Sion
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| Posted: Wed May 24, 2006 11:19 am Post subject: Inferences |
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Concerning the first topic:
| Quote: | | an inference to fire from mist wrongly perceived as smoke |
Perhaps because I do not know the Indian terms you use, I do not see in this discussion a clear distinction between inductive and deductive inference.
I see something that looks like smoke and infer from it fire? Such inference is inductive, not deductive.
It is based on an empirical observation of fire, that this phenomenon is (usually if not always) accompanied by "smoke". We generalize to "If fire, then smoke". The reverse if-then statement "if smoke, then fire" does not formally follow - because we have also on occasion observe smoke without fire. Thus, the best we can say here is: "If smoke, possibly fire".
Now, with regard to the mist mistaken as smoke, that is an additional complication, distinct form the inference of fire from smoke. The issue in this case is one of accuracy of observation and classification (and naming) of what one has observed. Smoke and mist look very similar in some cases, at least at first sight. To distinguish them accurately, empirically, we might have to make a chemical analysis. If it is H2O - it is mist. If there are e.g. carbon molecules, it is smoke.
Here, too, then, the issue is one of induction. It seems to me that the Indian philosophers you discuss do not make a clear distinction between such logic and deductive logic - so that they wrongly conclude such reasoning is illogical.
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Avi Sion
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| Posted: Wed May 24, 2006 11:47 am Post subject: Syllogisms |
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Concerning now the example Plamen offers of "correct syllogisms that start with defective premises and end up with true conclusion".
| Quote: | My handkerchief is on the moon.
The moon is in my pocket.
Hence, my handkerchief is in my pocket. |
This is not a correct syllogism, except very superficially. Its form is, notice well:
X is on Y - Y is in Z - therefore, X is in Z.
As is more evident now, the major and minor premise used do not have the same copulae (i.e. relationships). The following syllogisms would be valid, but the above, mixed-form syllogism is not valid.
X is Y - Y is Z - therefore, X is Z.
X is on Y - Y is on Z - therefore, X is on Z.
X is in Y - Y is in Z - therefore, X is in Z.
We can analyze this error more deeply, by pointing out the logical process of permutation tacitly involved in the thinking that makes Plamen's sample syllogism seem "correct" at first.
Just because the word "is" is present in expressions like "is in", "is out of", "is on top of", "is under", "is next to", etc., or again in "is greater than", "is less than", "is equal to", etc. - and all such compound expressions - does not mean that we can at will separate the word "is" from the other words attached to it (like "in", "on", etc.).
The use of "is" in such compounds is intended to mean "existence" (in, on, etc. - or bigger, etc.) -, and it is not to be confused with the solitary use of the word "is" as in: "She is beautiful" (attributing a quality) or (a later conceptual development no doubt) "She is a beautiful woman" (classifying an individual in a group). The latter two lone "is" words can be related by permutation. We can always permute "She is beautiful" to "She is [a beautiful thing]". On the other hand, we cannot freely permute "X is in Y" to "X is [in Y]" - firstly, because this loses some of the logical potential of "is in", and secondly because it on occasion leads to logical errors (as in the example Plamen gives).
You can study a more detailed example of illicit permutation in my website www.thelogician.net, in my book Future Logic, chapter 45, regarding the Russell Paradox.
In conclusion, the example Plamen gives is not problematic because the premises are untrue, yet the conclusion is true (which indeed happens in some cases, of course) - but because of formal incorrectness, mixing "is on" with "is in" inattentively. An example of true conclusion from false premises in a valid syllogism would be, say:
A dog is a cat - a cat is a canine - therefore, a dog is a canine.
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Plamen
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| Posted: Tue Jun 20, 2006 5:30 pm Post subject: |
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Thank you, Avi!
From your explanation, I understand that it is logically incorrect to infer in this way,
1. I am on Earth
2. The Earth is in the Solar system
3. Therefore, I am in the Solar system.
As to the inductive character of misguided inference, I have argued elsewhere that the way we reach the general rule known as invariable concomitance has nothing to do with the nature of the third visualisation of the probans which is the source of our deductive knowledge about the probandum. |
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Avi Sion
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| Posted: Tue Jun 20, 2006 6:05 pm Post subject: Geometrical syllogisms |
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Good one, Plamen!
However, looking at the form of the premises generally, we have:
X is ON Y
Y is IN Z
Therefore, X is ON or IN Z.
The general conclusion we would propose from geometrical considerations is a disjunctive one, not a categorical one. You can easily see this by drawing some Euler diagrams. The case where X falls inside Y and inside Z is indeed one possibility. But another possible case is that X remains on the surface of Z, as it was on the surface of Y - i.e. X is a point at the outer boundary of both Y and Z, where they touch.
For this reason, the "X is in Z" conclusion is not a necessary conclusion, but a contingent conclusion. That is, to affirm it a syllogistic CONCLUSION in the usual sense is logically inaccurate.
Please do not think that I am engaged in a personal contest over this. My motive is purely professional. I had already, after writing my previous post, thought to myself that I should have mentioned the above disjunctive conclusion, but then I thought you would figure it out for yourself.
After all, the issue is minor. Or is it? In fact, my raising this issue in response to your post has awoken me to the need to list all this sort of geometrical syllogism in detail one day in a short essay. So I gained something from it and thank you.
By the way, after I wrote it the example about dogs and cats, I thought that was a farfetched choice, and I should more simply have suggested the following alternative example:
My handkerchief is IN the moon.
The moon is in my pocket.
Hence, my handkerchief is in my pocket.
This being valid syllogism would have illustrated your point acceptably.
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Avi Sion
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| Posted: Tue Jun 20, 2006 6:27 pm Post subject: Induction |
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I do not understand your comment in response to my comment about induction. Perhaps you could tell me where to find your previous remarks on this subject.
The two issues can be related, by the way. That is to say, as I explain in Future Logic (see for instance, in chapter 67) deduction and induction are closely related. We may say that all logic is inductive, with deduction as a particular means within this wide range of means. Or we can say that deduction is logical inference of 100 percent necessity, and all lesser (merely probable) conclusions are induction.
In either case, the example we have above considered can be used to illustrate this issue.
X is ON Y
Y is IN Z
Therefore, X is ON or IN Z.
A syllogism like this, which has two or more alternative conclusions, is deductively invalid (in the sense that neither conclusion can be inferred necessarily - although the disjunction is of course necessary), but inductively possibly valid (in the sense that one or the other conclusion might be hypothesized, and perhaps found correct given further data input).
In the case of your proposed new example, viz.
| Quote: | 1. I am on Earth
2. The Earth is in the Solar system
3. Therefore, I am in the Solar system. |
... it happens to be a good inductive conclusion. Formally, two alternatives were possible: you are either IN the solar system OR ON ITS EDGE. To prove your chosen alternative (which is ab initio a mere scientific hypothesis), you would have to make some additional EMPIRICAL observation, in this case: verify that you are not merely on the outer edge of the solar system, but indeed surrounded by it on all sides.
I hope this clarifies the difference between deduction and induction for readers. Best regards.
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Plamen
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| Posted: Tue Jun 20, 2006 7:20 pm Post subject: |
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I see your point, Avi. Hope you see my also - Y being IN Z is inclusive of X being ON Y, there is no way of Y to be in Z without X to be also in there, because if we assume that X is not on Y while Y is in Z, then Z would not be anymore on Y.
As for the second issue, I would appreciate much your thoughts about this topic
http://nyaya.darsana.org/topic75.html |
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