Philosophy With Selvi #2 – Understanding Logic

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This is part-II of the Philosophy With Selvi series. Part-I is here. This series is written for children of ages 10 – 14 years.

When Saturday arrived, mother and daughter took Puli to the park and tossed around a stick for him to fetch. Selvi loved the weekends because she got to spend more time playing with Puli and talking to Sandanam. Today, Selvi was her usual inquisitive self and the fresh air provoked deep thoughts.

“Ma”, she said as she watched Puli dash after the stick. “You told me the other day about justification of knowledge. Tell me more about how that works. “

Sandanam, was not entirely unprepared since she had spent the past few nights thinking about how she should deal with her daughter’s intense curiosity. But there was no simple formula. Perhaps Selvi needed formal training… someone who could teach her properly what she wanted to understand…

“OK, let’s start at the beginning” Sandanam began. “Justification of knowledge involves making arguments and dismissing or accepting them. The formal study of this process is called Logic”.

“Is common-sense the same thing as logic?”

“Depending on the definition, common-sense can be described during conversation as a type of logic. But it is not a formal system of logic. It is not comprised of a formal set of rules for evaluating arguments.”

Puli was racing back with the stick in his mouth. On reaching the two women he spun around them and circled back with Selvi laughing wildly, chasing after him.

Sandanam resumed her mental monologue. She’s just a little girl, she thought. Shouldn’t Selvi be worrying about things girls her age are concerned about?… But then again, why should she?.. Indeed, why should any girl only care about clothes, or movies …

Puli let Selvi catch up with him and grab hold of one end of the stick around which he still had his jaws clamped firmly shut. He dug in and would not let Selvi pry it from his mouth. An impromptu game of tug-o-war ensued. Selvi yelled at Puli to let go, which he did promptly, sending her somersaulting backwards on the grass. Puli came over immediately and licked Selvi’s face as she sat up. The look of surprise on her face turned to amusement. When Puli saw Selvi smile he jumped back, tail wagging, concern for Selvi abated and his undivided attention directed once again at the inexplicably fascinating object Selvi was holding in front of him. Selvi stood up on her feet, wound back, and threw the stick as far as she could. Then she turned back to her mother with an expression that said “Go on, then!”

Sandanam had made up her mind. She was going to present Selvi with a historical account of logic. She began to talk.

“There are three classical philosophical traditions of formal logic- the Greek, the Chinese and the Indian traditions. The Greek tradition influenced the thinkers of the enlightenment, which led to the development of the modern scientific tradition.”

She paused. Selvi was looking at the ground, standing with her weight almost all on her left foot. Sandanam knew a question was on its way, but she pressed on.

The study of logic in India began at about the same time as the Greeks in Europe. Broadly speaking, there were 5 schools of Indian logical thinking, each influencing the others over the centuries. (1) The oldest school of Indian logic dealt with Grammar, which influenced all of Indian philosophy because of the predominance of the Sanskrit language in philosophical discussion in ancient India. One of the earliest influential Sanskrit grammarians was Panini who lived in the 4th century BCE. (2) Vaisesika was a form of natural philosophy that viewed the world as composed of atoms. It is considered one of the six orthodox schools in the Astika tradition of Indian philosophy. Its proponents built a system of categories, and devised syllogism and methods of inference, to inform their epistemology. These syllogisms and methods of inference were developed further within the subsequent schools of Indian logic. The logical categories created by the proponents of the Vaisesika school of thought formed the foundations of the old Nyaya school of logic. (3) Formally recognized as the orthodox logical tradition in Astika philosophy, old Nyaya is often simply referred to as Vedic logic. Proponents of the old Nyaya school of logic assimilated elements of Vaisesika logic and further developed formal systematic analyses of perception and inference. However, old Nyaya and Vaisesika were doomed from the start because of their deference to Vedic authority as infallible truth. Many proponents of the old Nyaya school wasted their efforts developing complicated but flawed arguments for the existence of god. (4) Buddhist logic was partly a reaction against the old Nyaya school. In Buddhist logic we begin to see a formal logic that is distinct from epistemological and ontological concerns, and almost completely dependent on syllogism and inference. Buddhist logic strongly influenced Chinese logic. (5) Navya-Nyaya (New Nyaya) was the final phase of classical Indian logic. It began in the 13th century fueled by the work of Gangesopadhyàya. It further refined concepts from the old Nyaya tradition. The Navya-Nyaya school has produced many thinkers over the last few centuries and their influence is felt to the present day.

The Chinese tradition of logic was started by a contemporary of Confucius (6th century BCE) called Mozi. The Mohist school, as it was called, approached inference with a preference for analogy rather than deduction or induction. A separate school known as the Logicians were the intellectual descendants of the Mohists during the oppressive Warring States Period in Chinese history. After the Mohist school fell out of favor following the Qin dynasty, Buddhist philosophy introduced from India became highly influential. Buddhist philosophy was responsible for reviving the logical tradition in China.

In the Greek tradition, although there was little formal logic before Aristotle in the 3rd century BCE, there existed a great many philosophers who were involved in logical study of the world. The Greeks were the first to use geometry, starting with Pythagoras in the 6th century BCE. Later philosophers like Zeno of Elea and Euclid started what is known as the dialectic tradition in philosophy, which involved resolving arguments through discussion governed by rules of reasoning. These philosophers, many of whom were contemporaries of Plato, established what is known as the Stoic tradition in Greek logic, which contributed many important ideas to the development of the Western tradition of logic. Plato laid the ground-work for Aristotle, who established the most comprehensive system of formal logic in the Greek tradition. In fact, Aristotle is known as the founder of formal logic in the Western tradition. His work on categories and syllogism had a major impact on Western philosophy, and continued to be critiqued and further developed throughout the Roman, Christian and Islamic periods. The influence of Aristotelian ideas in Europe and the Middle East contributed to the development of modern science, as 15th and 16th century enlightenment philosophers, from Francis Bacon to Descartes and Kant, developed the foundations of scientific philosophy through the debate between, and subsequent synthesis of, the schools of rationalist and empiricist logic.

“There are many commonalities between the Eastern and Western schools of logic, such as when dealing with the sources of knowledge, known as ‘Pramanas’ in Indian logic.”

Selvi was at bursting point. But she tempered her eagerness and simply asked “OK, so what are these sources of knowledge?”

Sandanam smiled. She sensed her daughter was filing away her questions for later.

“Most logic traditions agree on two very general sources of knowledge (or pramanas)- perception and inference. Do you know what perception is?”

“Yes. Seeing or hearing something..right?”

“Right. It’s the process of collecting information about the world using our sense organs”.

“OK. What is inference?”

“Inference is the process of following logical arguments and drawing logical conclusions. We all make inferences all the time. As an example consider these statements:

  • When there is smoke, there is fire.
  • There is smoke now.
  • There is fire now.

Using premises and observations we infer logical conclusions. The above statements follow from each other and together form what is known as a ‘syllogism’.”

Selvi was beginning to understand what logic really meant, but there were more questions now than before. She looked at Puli who had made friends with a toddler playing over by the trees. At that moment Puli turned his head to look at her. He stopped prancing around when their eyes met.

Puli stood there, head turned to the side looking at Selvi in the distance. He saw her turn back to her mom, deep in conversation. The toddler let out a squeal and charged him, causing Puli to break pose and jump away, playfully daring the kid to come chasing after him.

“So, inference is important in all schools of logic” Selvi asked.

“Yes. Inference is an essential aspect of all logic systems. In the Indian tradition it was known as ‘anumāna’.”

“Are the different types of inferences also found in different schools of logic?”

Sandanam paused for a bit. There was no avoiding it now.

“Different schools of logic approached inference differently, although they had many core ideas in common. In the Greek tradition, induction and deduction were historically the most debated modes of inference. In India, Nyaya and later schools incorporated a mixed induction-deduction approach, along with other modes of inference such as analogy. The Chinese Logicians were more keen on using analogy than induction-deduction. Today we recognize many types of inferential logic.

“What type of inference is the example of fire and smoke that you used?”

“Deduction. In this method of inference you take general principles as your premises and infer specific conclusions. That is, you go from the general to the specific. Give me an example of a general statement that you believe is true in principle.”

Selvi thought for a moment and said “Crows are black”.

“Good. Now if I told you that there are three crows on that tree, what can you tell me about them?”

“Those three crows are black?”

“That, Selvi, is deductive logic! All logic in pure mathematics is deductive logic. Another important type of logic, inductive logic, is the opposite of deductive logic. In inductive logic, you go from specific observations to general principles.


Consider this syllogism:

  • A dog is chasing a rabbit.
  • All dogs chase rabbits.

Here we go from a specific observation to a general principle. This is the general form of induction. Both induction and deduction are essential inferential techniques in science. Philosophers often discuss each type separately because each needs to be internally consistent, but in practice both types of logical inference are used by us to form coherent ideas about the world.”

Fun Fact: In formal logic an inference might be considered valid or invalid. What constitutes a valid inference is determined by the rules of logic. An invalid inference is called a fallacy.

Selvi seemed to be deep in thought. Puli was back at her side now, and she was stroking his back with a far-away look in her eyes.

Sandanam knew exactly how to lead Selvi around the road-block.

“Imagine you’re a police officer and you’re trying to solve a crime, say, a murder. What type of logical inference would you use?” she asked.

There was a moment of silence followed by a quick intake of breath.

“Both inductive and deductive logical inferences” said Selvi looking up triumphantly.

“Exactly”, said Sandanam. She grabber Puli’s collar and slipped the leash back on. The dog looked down at the ground and his tail went limp. But when Selvi said “We’re going home, boy!”, her enthusiasm prompted him to look up at her with his heavy eyes and give his tail a little wag.

Sandanam picked up where she had left off. “There are also many newer forms of logic, some of which derive from mathematical logic and computational logic. These include interdependence-friendly logic, multimodal logic, game-theoretic semantics and linear logic. Besides, modern science has transcended and re-defined many aspects of traditional logic, and helped create new logically coherent systems.”

“Is science also a philosophy?”

Sandanam looked at her daughter and smiled.

“Science is a methodical practice born out of philosophy. Indeed, some of Aristotle’s ideas from over two millennia ago still inform the scientific method! But science in turn also informs philosophy.

“The foundational ideas behind science have evolved over the years. A good method for studying the history of the philosophy of science is to study the debates between the proponents of two general types of justifications: Rational justifications and Empirical justifications. So can you guess which of these two types of justifications are involved in the justification of science?”

Selvi looked up at mother quizzically, then her face lit up. They were both smiling as they said in unison,

“Both, rational and empirical justifications!”.

Sandanam and her daughter held eye contact for a moment longer and then simultaneously burst out laughing, with Puli joining in braking excitedly.

On the walk back from the park Sandanam made a mental note to design some special experiments for Selvi. Also, she needed a book….an instruction manual on how to raise an extremely inquisitive teenager. This conversation had brought them to science’s doorstep, and her little girl was ready to walk right in.

The sun was going down now and Selvi’s attention seemed to have moved on to other things. It stayed on those other things all the way home.

The phone was ringing as they walked in the door. Selvi ran and grabbed it, saw the number on the caller ID, exclaimed “its for me!”, ran up into her room, and shut the door as her father yelled after her from the living room warning her not to stay on the line for hours.

“Well, at least this is normal”, Sandanam reflected as she sat down at the computer and began her search.

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About the author

Ajita Kamal

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