Examining the Relevance of Indian Logical Traditions and Present-day AI Developments

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Examining the Relevance of Indian Logical Traditions and Present-Examining the Relevance of Indian Logical Traditions and Present-

day AI Developments day AI Developments

Ramesh Subramanian

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Examining the Relevance of Indian Logical

Traditions and Present-day AI Developments

Ramesh Subramanian

Quinnipiac University

Hamden, Connecticut, USA 06518 rsubram[email protected]

ABSTRACT

This paper is an essay on the differences between “formal” Western logic and

Indian logical traditions and how the latter impacts present-day AI developments.

Upon the colonization of India, Western philosophers often dismissed Indian

logical constructs as being underdeveloped or clumsy. Others, however, saw such

denigration as emanating from Western racial prejudice rather than objectivity.

This debate has persisted. I discuss the salient aspects of this debate, and then focus

on the inductive aspects of Indian logic. This is especially relevant to the present,

when there is an explosion of artificial intelligence based applications. I discuss

the salient features of the new developments in Generative AI, and then attempt to

show how the models in Generative AI are connected to Indian logic with its focus

on inductive reasoning rather then deductive reasoning. It is useful for students and

researchers of present-day AI to be aware of alternate systems of logic, which may

be useful in developing newer AI models and applications.

Keywords: Indian Logic; Generative AI; AI Development; Aristotelian logic;

Nyaya sutra; Indian syllogism; AI Education

Examining Indian Logical Traditions and AI Developments Ramesh Subramanian

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INTRODUCTION AND MOTIVATION

Artificial Intelligence is all the rage at the moment. AI applications abound in

almost every sphere of human endeavor. Innovations in AI have led to a

mushrooming of AI related startups. The global market size for AI applications was

estimated by Bloomberg Business at around USD 500 Billion in 2022 and is

expected to grow at a compound annual growth rate exceeding 38%, and is

estimated to reach about USD 1.5 Trillion by 2030 (Catsaros, 2023). University

courses in AI and Machine Learning are very popular across a wide spectrum of

students. Newer and better models of AI, known as Generative AI are emerging.

This has led to passionate discussions on the ethics of AI and ML, their impact on

privacy, law, and society, among the sociological and legal community, such as the

Yale Law School’s “Information Society Project” in which the author is a Fellow.

This paper examines Indian logical traditions in comparison to Western logical

traditions, and discusses how it is relevant to today’s developments in AI, especially

Generative AI. My motivation for this is as follows: To my knowledge, there is very

little, if any, work done in examining the history of logical traditions from across

the globe and then relating those traditions to present-day developments in AI. As

a researcher interested in the history of technology, I am interested in the logical

foundations of AI. As an academic, I am interested in what present-day students

need to know about logic. I often ask to myself: Do students know enough about

the history of logic that underlies the study of AI? If so, to what extent? If not, then

what needs to be taught? What do application designers and analysts know about

logic as a subject? This paper therefore addresses at least some of these questions

on how logical traditions have developed in India in comparison to the West, and

how one should understand and apply the Indian logical traditions, which I argue is

primarily inductive rather than deductive, so that we can see how and where the

Indian perspective becomes relevant when we study new developments in AI.

The paper is written in an essay format. It uses as sources published literature on

topics of logic and well as modern developments in AI. It then compares the logical

approaches, focusing on the main objective, which is to show how Indian logical

traditions are relevant to today’s AI. It is hoped that the contribution of this paper

will be a deeper understanding of logical traditions as well as new developments in

AI and show the relevance of alternative logical approaches such as Indian logical

traditions in gaining a deeper understand for present-day AI.

Examining Indian Logical Traditions and AI Developments Ramesh Subramanian

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GREEK VERSUS INDIAN LOGIC: COLONIAL

PERCEPTIONS GREEK

Most discussions on the history of logic revert to the ancient Greeks, such as

Aristotle, Plato, Diodorus, and Philo, to name a few (Bobzien, 2020). Aristotle and

the development of syllogism is considered to be one of the best intellectual

achievements of the period (Smith, 2022). But is that the only basis for logical

thinking, or is there room for other versions of logic? When the West colonized

the Indian sub-continent, the colonizers naturally sought to accentuate their

intellectual superiority over the colonized. As philosopher Jonardon Ganeri noted

with great precision, “the assumption that the West, and the West alone, had

developed a science of reason was a fundamental axiom in the justification of the

colonial enterprise as a civilizational process (Ganeri, 2004).”

As the process of colonization unfolded across the sub-continent, Western colonial

scholars eagerly researched cultures of the colonized, to see if there were any

similarities or “proofs” of intellectual growth. Imagine their surprise, when they

discovered that the Indian sub-continent actually possessed a long and active

history of logical thought! Upon discovering Indian or “Hindu” logic, these

philosophers then sought to discredit it and prove its weaknesses compared to

“Western” logical reasoning. The selective occlusion of Indian logic became

prevalent among Western philosophers during the nineteenth century, as

exemplified by Henry T. Colebrooke, who “discovered” Indian logic (or “Hindu

syllogism”) and presented it at the Royal Asiatic Society on February 21, 1824

(Colebrooke, 1824); and Heinrich Ritter, who discussed Hindu syllogism in his

1846 History of Ancient Philosophy vol. 4. (Ritter, 1846)”

These scholars zeroed in on the Nyaya Sutras, authored by the philosopher

Aksapada Gautama anywhere from 600 BCE to 150 CE. This was a classic text on

logical foundations that emerged from or existed in the Indian sub-continent. So

here was something that they could compare with “Western logical foundations.”

They soon noticed that the Nyaya Sutra contained descriptions of syllogisms. But

the syllogisms therein were different from Aristotle’s in that they contained five

members or parts, rather than Aristotelian syllogism that had three members. Thus,

the syllogisms found in the Nyaya sutra consisted of: the proposition, the reason,

the instance, the application, and the conclusion or inference. The most famous and

oft-quoted example of this is the following presentation of “Indian syllogism:”

1. This hill is fiery:

2. For it smokes.

3. What smokes is fiery: as a culinary hearth.

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4. Accordingly, the hill is smoking:

5. Therefore it is fiery.

The immediate reaction of the Western philosophers was: Aha! This is clumsy! To

them, the conclusion, that the hill is on fire, should follow from just two premises,

that the hill is smoky (minor premise), and that where there is smoke, there is fire

(major premise). Syllogism could be formed by just using the first three, or the last

three parts of the above form. Thus two parts were superfluous, or, as noted by

Heinrich Ritter, “.in its exposition the Nyaya is tedious, loose and unmethodical.

Indeed the whole form of this philosophy is a proof of the incapacity of its

expositors to enter into the intrinsic development of ideas, whatever knowledge

they may have possessed of the external laws of composition (Ritter, 1838).” Ritter

based his conclusions on Colebrooke as well as Karl Windischmann, who published

his Die Philosophie im Fortgang der Weltgeschichte between 1827 and 1834. In

fact, Ritter quotes Windischmann thus: "Windischmann concludes that the Hindoos

possessed only the fundamental principles of the logic which the Greeks

cultivated." Another eminent logician, Sir William Hamilton referred to “Hindu

syllogism” as “merely a clumsy agglutination of . .. counter-forms, being enounced,

1st, analytically, 2nd, synthetically” in his Discussions on Philosophy (Appendix 1

‘On Syllogism’ page 604) (Hamilton, 1853).

While the term “Hindu syllogism” was introduced to the West by Colebrooke, it

was not as though Western philosophers were unaware of Indian syllogism until

Colebrooke’s talk in 1824. Max Muller, who wrote an Appendix to William

Thomson’s Outline of the Laws of Thought (Oxford, 1842), quotes the German

historian Barthold Niebuhr as stating much earlier, that there were great similarities

between Greek and Indian logic, and it was possible that these logical traditions

borrowed concepts from each other. The British mathematician and logician

Augustus De Morgan saw parallels between Grecian and Indian logic, and but

remarked that they must have independently formed these systems of logic. There

is some legitimacy to the assertion that Grecian and Indian logic are autochthonous.

The ancient Buddhist text Digha Nikaya Vol 1, which translates to “long

discourses” by Buddhas, some of them preceding Gautama Buddha, and dated at

around 500 BCE, also contains syllogisms similar in structure to Aristotle’s, as seen

below (Vidyabhusana, 1920 pp500):

1. My being wrong is a hindrance to me

2. The sense of remorse is due to my being wrong.

3. The sense of remorse is a hindrance to me

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This has even led some Indian scholars to debate whether Indian syllogism predates

Aristotelian syllogism. In an interesting refutation of Colebrooke’s “discovery” of

Indian syllogism, logician George Boole’s wife Mary Everest Boole, in an article

titled “Indian thought and Western science in the nineteenth century (Mary Everest

Boole, 1901),” noted that in addition to George Boole, other logicians such as De

Morgan and Charles Babbage were certainly familiar with the Indian body of work

in logic at the same time as Colebrooke. Given this, Colebrooke’s motivation in

claiming that he discovered India’s logical traditions (or “Hindu syllogism”) is

questionable.

To be fair, it is apparent that there were certainly other Western philosophers and

logicians in the nineteenth century who were aware of, and recognized that India

indeed possessed a long history of reasoning and logic. However, in the late

nineteenth century, this, however, just resulted in back-handed methods of

acknowledging the same. In some instances, Western logicians found tedious ways

to explain the need for five, rather than three parts, so as to make Indian logic look

more like Aristotelian logic. These are discussed in great detail by Ganeri (Ganeri,

2004). I do not discuss these various attempts here, except to note that these

attempts did not do much to lessen Western skepticism of Indian logic.

Other researchers simply avoided such explanations, and simply sought to portray

Indian logic as some “other.” A prime example is philosopher H. H. Price, who in

a 1957 article on “The present relations between Eastern and Western philosophy”

published in Philosophy Today, expressed his belief that a “vast chasm” separated

the two traditions, in which one “looks outward and is concerned with logic and

with the presuppositions of scientific knowledge; the other inward, into the 'deep

yet dazzling darkness' of the mystical consciousness (Price, 1957).” Thus, while

Indian philosophy was interesting and important, it could not be compared to

Western systems of logical thought which were more scientific in nature. In this

“othering,” Price was apparently helped along by Indian philosophers such as

Sarvepalli Radhakrishnan and the social reformist Swami Vivekananda.

They portrayed Indian philosophy more from its spiritual persuasions as embodied

in Vedic texts such as the Upanishads and the Brahmasutras rather than from the

logical constructs embedded within. The historian Tapan Raychaudhuri suggested

that this selective veneration of the Hindu culture was done on purpose, in the

background of emerging nationalist consciousness in India during the late 19

and

early 20

centuries.

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From the above, we see, not surprisingly, the persistence of Western cultural

imperialism that sought to attribute more importance to Western logical systems,

and that which seeks to “other” the development of logic in the East. The

hierarchical superiority of deductive reasoning (i.e. through Aristotle-style

syllogism) over inductive reasoning (i.e. a syllogistic style that uses examples as

emphasis or explanation) is thus sought to be perpetuated.

HOW TO UNDERSTAND INDIAN LOGIC

This brings us to the question of how, or, more importantly, whether to judge the

soundness of Indian logic. There are two avenues of thought on this. The first is

that the original, oft-cited example of Indian syllogism, i.e. “There is fire on the

hill, because there is smoke…” is simply a rhetorical exercise, and emanates from

the ancient Indian culture of debate and argumentation. This was the view of

Scottish orientalist James Ballantyne, who was also the first superintendent of the

Sanskrit College in Benares started by the British government). Ballantyne, along

with others with similar views proposed instead the following interpretation of the

syllogism example in a debate format, as a debate between a questioner and

responder (Ganeri, 2001, pp10):

(1) What is your thesis? That the hill has fire on it.

(2) Why? Because there is smoke there.

(3) So what? Where there is smoke, there is fire: e.g. the kitchen.

(4) And? The hill is such a smokey place.

(5) So? Therefore, it has fire.

In this form, the example is more akin to rhetoric, rather than formal logic. This

form also seems to exemplify some of the debates between Hindu and Buddhist

philosophers of the Nyaya period. Another influential analysis and interpretation of

Indian Nyaya syllogism is due to Stanislaw Schayer, who studied both Indian and

Western philosophies. Schayer saw Indian syllogism as really a proof that exploited

two rules of inference. He represented the five steps as follows (excerpted from

(Ganeri, 2001 pp25; Schayer, 2001):

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Seen from this perspective, Indian syllogism embodies more inductive reasoning

rather than deductive reasoning.

In the next section, we move closer into how the study of logic has changed over

time, and how the emergence of “Logical Relativism” helps to understand different

systems of logic, and where especially Indian logic fits into this newer way of

looking at logic, and how and where it fits into present-day AI developments.

EMERGENCE OF LOGICAL RELATIVISM

Starting in the middle of the 20

century, there has been gradual change in the

approach to the examination of logical traditions. Led mostly by sociologists, this

trend focuses on the notion that examination and understanding of logic has a

cultural component. That is, logical reasoning is relative, and is predicated on its

cultural context. A well-known and oft-cited example is the one by British

sociologist David Bloor, who discussed the “Azande logic” in his 1976 book

Knowledge and Social Imagery.” In the book, Bloor uses the example of the

Azande tribe in Central Africa who were studied by anthropologists. Members of

this tribe believe that witchcraft is inherited. And since the tribe is small enough,

the logical conclusion is that every member of the tribe possesses witchcraft. Yet,

Bloor notes that members of the tribe sincerely believe that some members do not

possess witchcraft, contrary to common logical assumptions, without in any way

rejecting the original assumptions. Bloor cites the Azande logic as an example of

how logic could be treated differently in different cultural contexts (Bloor, 1991).

Bloor’s book caused serious ripples among philosophers, sociologists, and

historians of science, by challenging the established position and role of Western

conceptualizations of logic.

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It gave rise to a whole sub-field known as “Logical Relativism.” Predictably, this

development led to protests, and reasoned refutations by logicians, who asserted

that Azande logic was just another form of, or could be folded into Aristotelian

logic (Triplett, 1988).

Nevertheless, Logical Relativism has gained ground. It is seen as the answer to

Western cultural imperialism, and the belief that other cultures may subscribe to

alternate forms of logic. Sociologists Christian Greiffenhagen and Wes Sharrock

characterize Logical Relativism into two sub-groups, “alternative logic” and

“symmetric treatment.” The Azande logic is an example of the former. Symmetric

treatment, on the other hand, seeks to show how forms of classical logic does not

apply in all cases. For example, if murderers are those who deliberately kill people,

then bomber pilots are murderers, as they deliberately kill people. Yet, society does

not consider them that way (even though it is quite conceivable that the Azande

may not see a difference).

Similar discussions on alternative logic extend to the work of early Chinese

philosophers. Some Western philosophers, such as Massimo Pigliucci of the City

University of New York have argued that Eastern philosophers “do not attempt to

argue for a position by using logic and evidence.” This in turn has been refuted by

philosophers and students of Chinese philosophy such as Brian Van Norden, who

point to logical constructs prevalent the Mohist School founded by Mozi in the fifth

century BCE in China (Cleary, 2016). This tension is ongoing.

Coming back to Indian logic, the approaches of Ballantyne and Schayer can be

considered to fall within the realm of alternate considerations of logic. They seek

to move away from strictly deductive reasoning. They posit that Indian logic is

instead inductive in nature. Western philosophers who sought to compare Indian

syllogism to Aristotelian syllogism, with the former’s emphasis on deductive

reasoning, naturally found it wanting. Deductive reasoning is truth-preserving,

whereas inductive reasoning is empirical, as noted by Amin Afrouzi (A. Afrouzi,

personal communication, February 16, 2023). It is important to note that one is not

superior to the other. The efforts to undertake an exact comparison of Indian

syllogism with Aristotelian syllogism, and finding the former wanting and ill-

developed, is thus not useful, and perhaps disingenuous.

Studies in analyzing and interpreting the actual nature of Indian logic continues.

More recently, philosophers such as Sibajiban Bhattacharyya, Bimal Krishna

Matilal, and Jonardon Ganeri have proposed new alternative approaches to studying

Indian logic.

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Ganeri argues that Indian logic should be considered as a theory of case-based

reasoning, rather than as one that aims towards providing a general rule. The Nyaya

Sutra defines the rules of good debate. Thus, the interlocutors must (1) be able to

draw upon a common and accepted body of information, and based on that (2) there

is no need for the interlocutors to understand the underlying general rule in order to

arrive at a conclusion (Ganeri, 2003). Both of these “conditions” seem to be aligned

with the new developments in present day developments in AI, as discussed below.

HOW DOES THIS APPLY TO PRESENT DAY AI

DEVELOPMENT

What we can see from the above is the changing nature of logic itself, or what is

considered to be “logic.” The logic of present-day AI is mostly inductive, not

deductive. Interpretations change constantly, and are context-driven. We posit that

the hierarchy of deductive versus inductive reasoning is changed by the way we

develop present-day AI applications. The newest avatar of AI development,

“Generative AI” is a case in point. It is briefly introduced below.

GENERATIVE AI: A BRIEF INTRODUCTION

In recent years AI Generated Content (AIGC) and applications have generated

widespread interest. Products such as ChatGPT and DALL-E are much talked about

and offer promise for the introduction of very innovative applications (McKinsey,

2023). AIGC refers to taking a given human content and instructions to complete a

given task, using Generative AI (GAI) algorithms. The process involves two steps:

the first is to extract intent information from human instructions, and the second is

to generate content according to the extracted intentions (Cao et al., 2023). While

this basic approach has existed for several years, recent advancements in computing

processing power as well as newer modeling frameworks have caused major

ripples. They have enabled the development of new training models, the ability to

process vast amounts of training data, and development of very large “foundation

models” that can then be used for processing new “prompts” or queries in real-time.

Examining Indian Logical Traditions and AI Developments Ramesh Subramanian

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There are multiple families of generative AI models, such as Diffusion models,

Variational Autoencoders (VAEs), and Generative Adversarial Networks (GANs)

(AltexSoft, 2022). By combining two or more of these models, it has been

demonstrated that better (i.e. more human-like) results can be produced. Large

“foundation models” are built using trillions of human-generated data, with

hundreds of contextual parameters that are then trained and retrained until they

reach accuracy levels and performances that are close to human accuracy and

performance (AltexSoft, 2022),(McKinsey, 2023). Thus there is constant learning

and re-learning within these models. Examples of some foundation models are

GPT, Llama, BLOOM, FLAN-T5, BERT, etc (Slashdot Media, 2023).

Interaction with these models typically involve:

• A Prompt (such as a question like “What is Titan?”), which is fed into

• A Model (such as the ones above), which processes the question and outputs

• A Completion, which is the response (such as “Titan is the largest moon of

Saturn…”)

This example uses a large language model (LLM). Generative AI applications

using LLMs can be used to write essays, summarize text, translate sentences to

other languages, translate text to machine code, extract information given the names

of people, etc. The important point here is the training of these LLMs. That process

involves trillions of data, each with billions of parameters which represent contexts,

collected and trained over several months. The training typically uses a model

known as the “Transformer Model,” introduced by Google engineers in 2017

(Vaswani et al., 2017a). The model basically “learns” the strength of relationships

between word-pairs in texts, using the concept of “attention weights,” as well as

positional encoding of the words. In this manner, the model is able to predict the

“next word,” given a prompt.

A more detailed discussion of the LLM models and the Transformer architecture is

outside the scope of this paper. For interested readers, a good place to start is the

2017 seminal paper “Attention is all you need” by Ashish Vaswani et al (Vaswani

et al., 2017b). However, the important takeaways from this discussion on

Generative AI are the following:

• The “next word” that is predicted by the models is dependent on the context,

and does not follow any hierarchical process of deduction

• This context is determined by how “close” a word is to other words in

ndimensional space (i.e. with numerous parameters)

• Very large amounts of data, with large numbers of parameters are required for

building and training these models

Examining Indian Logical Traditions and AI Developments Ramesh Subramanian

GENERATIVE AI AND THE INDIAN-LOGIC CONNECTION

Some experts have observed that India’s inherent complexity, in terms of its

varying cultural norms, religions, languages and scripts, positions it to be an ideal

locational resource to develop large language models (Aggarwal, 2018). The data

that can be collected is potentially vast, and the parameters that relate to or inter-

connect the data points are numerous. The contextual reasoning that is an aspect of

the Indian logical tradition is also aligned with Recurrent Neural Networks and the

more recent Generative AI models.

Thus, today, as AI application development is at an inflection point, poised to take

off, India is at the center of this development – not only from the point of view of

its induction-oriented logical traditions, but also from the point of view of the

trillions of data points that are required to develop large language models (LLMs).

Along with the availability of technical manpower, this has led to a big impetus for

developing AI models and applications in India. We can already see the result of

this alignment in some of the research in AI vision. A case in point is the prevalent

use of the “Mahalanobis Distance” in various image recognition systems used

today. Mahalanobis, the Indian statistician and father of modern computing

practices in India, developed this concept of measuring the distance between

“groupings” – which is contextual in nature. He in turn based his work on ancient

Indian mathematical and logical works (Mahalanobis, 1936).

CONCLUSION

In summary, in this paper I have first shown how Indian logical systems were

dismissed by Western philosophers and scientists early on. Yet, as we have seen,

these systems have persisted and are very relevant to today’s AI development. I

have discussed the debates between deductive and inductive logic, and how Indian

logic falls under the latter. I have discussed the initial rejection of Indian logical

systems by the several Western logicians, and some efforts by others to counter

those rejections.

While that debate is bound to continue into the future without any clear “winner,”

I posit that India has a lot to offer in present-day Generative AI models, LLMs, and

AI applications. I have tried to show how Indian systems of logic, with their strong

emphasis on rhetoric, examples, and induction rather than formal deduction, offer

a natural basis for new developments in AI. We can see the relevance of inductive

logic in present-day AI systems, which depends on building very large models, such

Examining Indian Logical Traditions and AI Developments Ramesh Subramanian

as language models, that take into account numerous contexts and nuances that are

present in natural language.

In the future, it would be useful to study other logical traditions to see what they

can offer to these newer developments in AI. It would also be useful to investigate

specific works of scientists and researchers who have have worked in the area of

inductive logic and with respect to Generative AI applications. Finally, I hope that

this paper will be useful for students and developers of AI and AI-based information

systems. Learning about some of the histories and interpretations of logic in

different cultural traditions will positively impact the applications that they

develop, which will be deployed around the world and will impact all human

development in the years to come.

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