Wednesday, July 8, 2015

Analogical reasoning and postulation

Like postulation (arthāpatti), the pramāṇa or instrument of knowledge known as upamāna, often translated as "analogy," is both fascinating and underdeveloped in contemporary analysis. There are few stand-alone books focusing just on upamāna, although it is frequently treated along with testimony and perception. I suspect this is because, as with postulation, upamāna is often reduced to another more well-accepted pramāṇa--usually verbal testimony, inference, or perception.

Two books devoted only to upamāna are:
Chattopadhyay, Uma. Dishonoured by Philosophers: Upamana in Indian Epistemology. New Delhi, D.K. Printworld, 2009. 
Kumar, Shiv. Upamāna in Indian Philosophy. Delhi: Eastern Book Linkers, 1994.
I have been reading just Kumar's book, since I am waiting for an inter-library loan of Chattopadhyay to arrive. In doing so, I came across a debate about the relationship between postulation and upamāna. By the way, I am not translating the latter term since I am not sure whether "analogy" quite captures what is going on. The question is whether we can explain upamāna as merely an instance of postulation. The target of this discussion is frequently this famous stock example (version updated a bit for color):
Suppose I live in the city of Singapore and while I have seen cows, I have little experience with other animals. A rancher tells me that the gavaya is an animal that's like the cow. I venture into the forests of Malaysia one day and happen upon an animal that looks like a cow, but isn't a cow. I remember what this rancher told me and I realize that the animal in front of me is a gavaya. (Or I think, "That is the animal called 'gavaya.') 
It's important to note that upamāna is implicated in language-learning, although that is not its only role for Indian thinkers. I learn what the denotation of 'gavaya' is through testimony, perception, and memory. While pretty much everyone agrees that I have knowledge at the end of this stock example, not everyone thinks that this knowledge is due to some sui generis source, like (most of) the Nyāya and Mīmāṃsā. For instance, the Advaitan Ānandapūrṇa, in his Nyāyacandrikā (who also agrees it is sui generis) argues against an opponent who thinks upamāna is just postulation:
नोपमानं मानान्ताराम् अर्थापततितस्तत्सिदधे: । यद्यनेन सदृशी सा न स्यात् ततस्तया सदृसो ऽयं नोपलभ्यत सदृशस्योभयनिष्ठत्वात् । उपलभ्यते चायं तया सदृशः ।
Upamāna is not another means of knowledge because it is established that it is postulation. If it were not the case that (the cow) is similar (to the gavaya), then this similarity would not be acquired since the similarity is grounded in both (cow and gavaya). Since this similarity (to the gavaya), there is similarity (in the cow). 
In reply, Ānandapūrṇa says:
तदसत् असन्निहितसादृश्यधीः समृतिरिति प्रतिज्ञाविरोधात् ।
That is not right, because this contradicts the (opponent's own) assertion: the thought of similarity which is not present is memory.
In other words, the opponent has earlier said that when I encounter the gavaya in the woods, I remember the earlier testimony that the gavaya is similar to the cow. But here the claim is that I know this similarity through postulation. Only one of these can be correct. Further, Kumar notes that Ānandapūrṇa argues that since the similarity which is remembered is not similarity that is currently present to my senses (when I see the gavaya), it is not able to be established. For most Indian philosophers, the Jaina excluded, smṛti or memory is not a source of knowledge. It is implicated in inference and other pramāṇa, but it is itself not a knowledge-source.

Who might argue that upamāna is postulation? We know at least that Udayana argues for this position in his Kiraṇāvali. As a Naiyāyika, he further thinks that postulation is reducible to inference (anumāna) of a particular sub-variety (it seems that Ānandapūrṇa's interlocutor does as well, given what Kumar says about other counter-arguments involving a discussion of invariable concommitance or vyāpti). This view is not the standard view of Nyāya, however, as many them prefer to hold that upamāna is sui generis (Jayantabhaṭṭa is another exception, agreeing with the Mīmāṃsā that upamāna is a matter of inference).

This discussion is interesting to me, since I find plausible Mukulabhaṭṭa's arguments that the cognition of (at least some varieties of) figurative language are driven by postulation. When one thinks of figurative language, analogy is central. Poetic thought is about juxtapositions which point at similarities or contrasts, as well as explicit statements of these connections, through similes and the like. Analogical reasoning, too, is important in legal theory, scientific thought, and so on.

In Western philosophical thought, analogy is often characterized something like this:

  1. S is similar to T in at least one respect.
  2. S has another feature, P.
  3. Therefore, T has the feature P, or a feature similar to P in some respect.

An important question, as in Indian philosophical thought, is how to analyze the structure of this argument. Unlike Indian philosophical thought, there is not necessarily a reference to a thinker who is having a mental episode, moving from testimony to perception to memory of the testimony and finally to knowledge of the similarity. Further, the conception of analogy in Western philosophy is inductive: (3) is not a necessary conclusion drawn from (1) and (2) but is probabilistic (or some other model). In contrast, for Indian philosophers, a pramāna results in secure knowledge, not belief to a degree or the like. However, this knowledge need not be secure because it is inferential. After all,  anumāna or inference requires a necessary pervasion relationship (vyāpti) between a sign and what it establishes. This relationship is difficult to characterize adequately for upamāna. Here is how Jayantabhaṭṭa analyzes it in the Nyāyamañjarī:

  1. Sādhya (what is to be established): the cow remembered is similar to the gavaya.
  2. Hetu (inferential sign): the cow has the same kind of limbs as the gavaya. 
  3. Pakṣa (location relating sādhya and hetu): the cow remembered in the forest.

Here, though, in contrast to the Western characterization, what is being discovered is the initial similarity between source S and target T. At least as Jayantabhaṭṭa wants to put it, what comes to be known is that the cow and the gavaya are similar. This poses a problem since it seems as if this was already known through testimony! Further, if the paradigmatic example of a hetu is smoke which indicates fire's presence, (1) we need to have multiple instances of this in order to make a universal generalization, and (2) for the hetu to be valid, we also need its absence--smoke should not exist where there is not fire. But in this example, I have only seen one instance of a gavaya and there are other animals with limbs like a cow that are not gavaya-s.

There is much more to say about upamāna, postulation, inference, testimony, and their interrelations, as well as the connections between these topics and analogical thought. However, this should give a sense of the topic in brief.

Cross-posted to the Indian Philosophy Blog.

Edited for error: “Jayantabhaṭṭa is another exception, agreeing with the Mīmāṃsā that upamāna is a matter of inference” should read “Jayantabhaṭṭa is another exception, arguing against the Mīmāṃsā that upamāna is a matter of inference.”

Friday, July 3, 2015

On writing a prospectus for a dissertation

The closest approximation to my dissertation-writing process I could find online.
Recently, I was talking with a few grad students from my PhD program about the process for writing a dissertation prospectus. At UT-Austin, the prospectus process is fairly rigorous (possibly in part because there are no qualifying exams to move on to ABD status). These students are at the beginning stages of prospectus work and wanted to know how others went about their year of committee-selection, writing, and research.

Hindsight is, as they say 20-20, and looking back at my prospectus year, I think I could have spent a bit longer refining my project. However, the benefit of defending at the end of year three (the suggested time frame for a projected five-year PhD) was that I could take advantage of being in candidacy for teaching within the university for a longer time, and I had a mental block removed to dissertation-writing. While the details of how a dissertation proposal works will vary among institutions, below are a few reflections I had for these students. In a cursory search of the philosophy blogosphere, I didn't find a lot of links on the topic. If I find some, I'll put them up.

In retrospect, I defended (a bit) too early. I could have used an extra semester to sharpen my focus. Some of that was because I hadn't dug deeply enough into the relevant literature to see the challenge that I was taking on -- the initial project was very wide-ranging. That was the major criticism I got at the defense--I had too much. It was right. 
However, I wouldn't have put it off that much longer, perhaps only asked more direct questions of my committee earlier on, such as (1) do you think that the project is feasible in this form? (2) is the project making a contribution? (3) what gaps in the relevant literature do I have?  
In terms of the committee, you are (as I understand) able to change your committee after the prospectus, so consider it provisional. What I did was set up conference courses with some potential members and used the time as a way to develop my bibliography. I then chose other members who I thought would give good feedback and met with them on a relatively regular basis. For the dissertation committee, I changed one member for an outside committee member. 
What worked for me may not work for you, but I think having a goal of when you want to defend and working backwards by setting rough draft dates for your various pieces is the way to go. Then figure out which faculty members you think you might be able to work with, see if they're on board, and find a way to meet regularly and have them actually looking at your work. 
Ultimately, they shouldn't let you defend a prospectus if you aren't ready (some outliers exist, but I think usually that's what happens) and the defense will be hard, but even if you pass with changes, remember that the goal is for you to have a strong project that will give you publishable pieces of work and a contribution that will help you get a job--so you will have to keep revising!
I'd like to hear what others have to say about their dissertation proposal process. What would you have done differently? What would you recommend to those just starting out? One thing I didn't say which I would also emphasize is that it is easy to get paralyzed by having to read everything. At a certain point, you ought to just start writing. There is time to revise, but revising doesn't happen without something, not matter how rough.