Logical Reasoning

Proposition or Statement is a declarative sentence that is either True or False. Argument: An argument is a group of statements including one or more premises and one and only one conclusion. Validity and soundness are properties of an argument. Premise: A premise is a statement in an argument that provides reason or support for the conclusion. There can be one or many premises in a single argument. Truth and falsity are properties of premises. Conclusion: A conclusion is a statement in an argument that indicates of what the arguer is trying to convince the reader/listener. What is the argument trying to prove? There can be only one conclusion in a single argument. Distinction between premises and conclusions: The foolproof way to do this is to ask yourself what the author of the argument is trying to get you to believe. The answer to this question is the conclusion. There must also be at least one reason and possibly many. These are your premises. Reasoning: the process of thinking about something in a logical way in order to form a conclusion or judgment. Inference: An inference is a process of drawing conclusions based on the evidence. On the basis of some evidence or a “premise,” you infer a conclusion. Consider the following example. Premise: Weather forecast says 80% chance of thunderstorms. Inference: It’s a good idea to bring an umbrella Logic: It is the systematic study of applying reasoning that leads to the acceptance of one proposition, the conclusion, on the basis of a set of other propositions, the premises. In other word, logic is the science that evaluates arguments. Analytical Reasoning: Refers to the ability to look at information, be it qualitative or quantitative in nature, and discern patterns within the information. In other words, analytical reasoning is the act of carefully considering a problem, claim, question or situation in order to determine the best solution. Applying analytical reasoning also means seeing things from your

point view, there may be some subjectivity also. It also represents judgments made upon statements that are based on the virtue of the statement's own content. Analytical reasoning involves deductive reasoning with no specialised knowledge, such as: comprehending the basic structure of a set of relationships; recognizing logically equivalent statements; and inferring what could be true or must be true from given facts and rules. Analytical reasoning is axiomatic in that its truth is self-evident. Logical Reasoning is the process of using a rational, systematic series of steps based on sound mathematical procedures and given statements to arrive at a conclusion, without any ambiguity. Logical reasoning can be categorised in three branches: deduction, induction and abduction.

Deductive reasoning determines whether the truth of a conclusion can be determined for that rule, based solely on the truth of the premises. Deduction is an inference based on logical certainty. It usually starts from a general principle and then infers something about specific cases. Example: Grapes are poisonous to all dogs. This allows you to infer that grapes are poisonous for your dog, too. If the premise is true, then the conclusion has to be true. There’s no other possibility. Notice, however, that this doesn’t really tell you anything new: once you say, “grapes are poisonous to all dogs,” you already know that grapes are poisonous for your specific dog. Deduction has the advantage of certainty, but it doesn’t generate new knowledge. Mathematical logic and philosophical logic are commonly associated with this type of reasoning.

Deductive inference is further categorised into “immediate“ in which conclusion is drawn from a single statement and “mediate” in which conclusion is drawn from two statements, known as “syllogism”

Inductive reasoning attempts to support a determination of the rule. It hypothesizes a rule after numerous examples are taken to be a conclusion that follows from a precondition in terms of such a rule. Induction is an inference based on probability. It usually starts from specific information and then infers the more general principle.

Example: For the last two years, Amanda has woken up at 6 am every day”

This allows you to infer that Amanda will probably wake up at 6 am tomorrow, too. You would probably be right, and it’s a reasonable inference but it’s not certain! Tomorrow could be the first day that Amanda decides to sleep in. While they may be persuasive, these arguments are not deductively valid. Despite this uncertainty, however, induction does offer the possibility of predicting future events and creating new knowledge. Science is associated with this type of reasoning.

Abductive reasoning infers to the best explanation, selects a cogent set of preconditions. Given a true conclusion and a rule, it attempts to select some possible premises that, if true also, can support the conclusion, though not uniquely. Example: "When it rains, the grass gets wet. The grass is wet. Therefore, it might have rained." This kind of reasoning can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data. Diagnosticians, detectives, and scientists often use this type of reasoning. Within the context of a mathematical model, the three kinds of reasoning can be described as follows. The construction/creation of the structure of the model is abduction. Assigning values (or probability distributions) to the parameters of the model is induction. Executing/running the model is deduction.

Structure of Arguments (Deduction and Induction)

The following is an indicative representation of the structure of a typical argument.

Validity and Soundness of Arguments: • A deductive argument is said to be valid if and only if premises are true and the conclusion is also true. In other words, a valid argument cannot have true premises and false conclusion. Otherwise, a deductive argument is said to be invalid. • In effect, an argument is valid if the truth of the premises logically guarantees the truth of the conclusion. The following argument is valid, because it is impossible for the premises to be true and the conclusion nevertheless to be false: Anil owns either a Honda or a Saturn. Anil does not own a Honda. Therefore, Anil owns a Saturn.

• It is important to stress that the premises of an argument do not have actually to be true in order for the argument to be valid. An argument is valid if the premises and conclusion are related to each other in the right way so that if the premises were true, then the conclusion would have to be true as well. In other words, the validity of argument depends, however,

not on the actual truth or falsity of the premises and conclusion, but solely on whether argument has a valid logical form. Consider, the following argument:

All toasters are items made of gold. All items made of gold are time-travel devices. Therefore, all toasters are time-travel devices.

A deductive argument is sound if and only if it is both valid, and all its premises are actually true. Otherwise, a deductive argument is unsound. The following argument is both valid and sound:

In some states, no criminals are eligible voters. In those states, some professional athletes are criminals. Therefore, in some states, some professional athletes are not eligible voters.

• In short, a deductive argument must be evaluated in two ways. First, one must ask if the premises provide support for the conclusion by examining the form of the argument. If they do, then the argument is valid. Then, one must ask whether the premises are true or false in actuality. Only if an argument passes both these tests is it sound. However, if an argument does not pass these tests, its conclusion may still be true, despite that no support for its truth is given by the argument.

• An inductive argument is an argument that is intended by the arguer to be strong enough that, if the premises were to be true, then it would be unlikely that the conclusion is false. So, an inductive argument’s success or strength is a matter of degree, unlike with deductive arguments. There is no standard term for a successful inductive argument, but this article uses the term “strong.” Inductive arguments that are not strong are said to be weak.

Here is a mildly strong inductive argument:

Every time I’ve walked by that dog, it hasn’t tried to bite me. So, the next time I walk by that dog it won’t try to bite me.

• Analogical Argument is a special type of inductive argument, whereby perceived similarities are used as a basis to infer some further similarity that has yet to be observed. Analogical reasoning is one of the most common methods by which human beings attempt to understand the world and make decisions.

• The following diagram gives pictorial depiction of validity and soundness of various kind of arguments.

Analysis of A Proposition

A proposition is a sentence that makes a statement and gives relation between two or more terms.

• A proposition is assumed to be true and from which a conclusion can be drawn.

• The statement, ‘all books are apples’ is assumed to be true as a proposition (or premise), but actually we all know that books and apples are entirely different entities.

In standard form of a proposition consists of four parts as shown below:

Quantifier + Subject + Copula + Predicate

1. Quantifier: The words 'all', 'no' and 'some' are called quantifiers because they specify a quantity 'All' and 'no' are universal quantifiers because they refer to every object in a certain set, while the quantifier 'some' is a particular quantifier because it refers to at least one existing object in a certain set. 2. Subject (denoted by 'S'): The subject is that about which something is said. 3. Predicate (denoted by 'P'): The predicate is the part of the proposition denoting that which is affirmed or denied about the subject. 4. Copula: The copula is that part of the proposition which denotes the relation between the subject and the predicate. Examples:

Four-Fold Classification of Propositions:

A proposition is said to have a universal quantity if it begins with a universal quantifier, and a particular quantity if it begins with a particular quantifier. Besides, propositions which assert something about the inclusion of the whole or a part of one set in the other are said to have affirmative quality, while those which deny the inclusion of the whole or a part of one set in the other are said to have a negative quality. Also, a term is distributed in a proposition if it refers to all

members of the set of objects denoted by that term. Otherwise, it is said to be undistributed. Based on the above facts, propositions can be classified into four types:

• Universal Affirmative Proposition (denoted by A): It distributes only the subject i.e. the predicate is not interchangeable with the subject while maintaining the validity of the proposition. Example: All snakes are reptiles. This is proposition A since we cannot say 'All reptiles are snakes'.

• Universal Negative Proposition (denoted by E): It distributes both the subject and the predicate i.e. an entire class of predicate term is denied to the entire class of the subject term, as in the proposition. Example: No boy is intelligent.

• Particular Affirmative Proposition (denoted by I): It distributes neither the subject nor the predicate. Example: Some men are foolish. Here, the subject term 'men' is used not for all but only for some men and similarly the predicate term 'foolish' is affirmed for a part of subject class. So, both are undistributed.

• Particular Negative Proposition (denoted by O): It distributes only the predicate. Example: Some animals are not wild. Here, the subject term 'animals' is used only for a part of its class and hence is undistributed while the predicate term 'wild' is denied in entirety to the subject term and hence is distributed. These facts can be summarized as follows:

Statement Form Quantity Quality Distributed (A): All S is P. Universal Affirmative S only

(E): No S is P. Universal Negative Both S and P (I): Some S is P. Particular Affirmative Neither S nor P (O): Some S is not P Particular Negative P only

Classical Square of Opposition (AEIO Rule of Syllogism): The categorical proposition having the same subject and predicate terms may differ in quality and quantity or in both. This differing is called opposition.

Following relations are possible among the propositions:

1. Contradictories 2. Contraries 3. Sub Altern 4. Sub Contraries

The relations of the given four propositions-A, E, I, O amongst one another are usually depicted in the following scheme— Square of opposition.

It is a chart that was introduced within classical logic to represent the logical relationships existing between the various propositions

1. Contradictory: Contradictory opposition is the relation between two proposition having the same subject but differs in both quality and quantity. The relation between A and O, E and I are called contradictory. In order to refute the truth of the proposition All mangoes are apples, it would be enough to show that some mangoes (or even one mango) are not apple. One exception would disprove the truth of the universal affirmative proposition.

2. Contrary: Contrary opposition exists between two proposition when both have universal quantity, but one affirms and the other denies its predicate of the subject. The relationship between A and E is called contraries.

Ex: (A) All mangoes are apples. This statement is universal affirmative.

The contrary of this proposition will be: (E) No mangoes are apples. This statement is universal negative.

3. Sub contraries: The relation between two particular propositions having the same subject and predicate but differing in quality is sub contrary opposition. The relation between particular affirmative (I) and particular negative (O) is called sub contraries.

Ex. Some mangoes are apples (I). This is a particular positive proposition. Sub contrary to the proposition will be: Some mangoes are are apples (O): This is a particular negative proposition.

4. Sub alternation: Sub alternation opposition is the relation between two propositions having the same subject and predicate but differing in quantity only. The relation between universal negative (E) and particular negative (O) is called sub alternation.

Check table below to see the differences between Square of Opposition Terms

Contradictory Contrary If one is true, then the other will be false It is always between a. definitely. universal. Both statements can not If one is false, then the other will be true b. be true at the same time definitely. but both can be false. If one is true, then the Both can not be true or false at the same c. other will be false time. definitely. If one is false, then the d. - other will be doubtful. Sub-contrary Sub alternation It is between universal a. It is always between particular. and particular If universal is true, then b. Opposite to contrary. particular will be true definitely.

If universal is false, then Both statements can not be false at the c. particular will be same time but both can be true. doubtful. If particular is false, then If one is false, then the other will be true d. universal will be false definitely. definitely. If particular is true, then universal will be If one is true, then the other will be e. doubtful. doubtful. Truth downward, false upward.

Argument

An argument is a series of statements, called the premises, intended to determine the degree of truth of another statement, the conclusion.

For example:

Premises: All musician can read music Ram is a musician

Conclusion: Ram can read music.

Types of Arguments

There are generally two types of arguments as follows:

1. Deductive Argument/Deductive Reasoning 2. Inductive Argument/ Inductive Reasoning 3. Abductive (or Hypothetico-Deductive) Argument/ Abductive Reasoning

1. Deductive Argument:

• Deductive argument starts out with a general statement and examines the possibilities to reach a specific, logical conclusion..

• It is considered as from general to particular. • In this, the premises are intended to provide support for the conclusion that is so strong that, if the premises are true, it would be impossible for the conclusion to be false.

Example:

Premises All dogs have long ears Tuffy is a dog

Conclusion Therefore, Tuffy has long ears.

2. Inductive Argument:

• It refers to an argument that takes specific information and makes a broader generalisation that is considered probable, allowing for the fact that the conclusion may not be accurate. • It observes some common pattern among the premises and conclusion and that observed pattern will hold in general according to this argument. • Inductive arguments make generalisation. • It is considered as from particular to general.

Example:

Premises: We have seen several Americans All of them have fair complexion

Conclusion: All Americans have fair complexion

3. Abductive (or Hypothetico-Deductive) Argument:

• Abductive argument is to take away a logical assumption, inference, conclusion, hypothesis, or best guess from an observation or set of observations. • The conclusion drawn is just a best guess, it may or may not be true.

Example:

A person enters into his room and finds torn up papers lying all over the floor. He realises that dog has been alone in the room all day. The person draws a conclusion that the dog tore up the papers

3. Analogy

Analogy is a type of reasoning in which a comparison is made between things that have similar features, Or in other words, analogy means similarity.

For Example: 1. Tree: Leaf:: Flower : Petal 2. Hammer: Nail :: Comb : Hair

Indian Logic Pramana (Source of Knowledge)

• Pramāṇa is a Sanskrit word which means ‘measure’. • The concept of pramanas is very critical for understanding the laws of Indian Logic and the philosophy of knowledge. • In Indian philosophy, the word represents all the means through which true and accurate knowledge about the world can be obtained. • A different school of thoughts and philosophies have a varied number of means through which one can make the sense of the world. • As per the Vedas philosophy, Pramanas are six in number.

Pratyaksha Pramana (Perception)

• Pratyaksha means knowledge gained through perception. Perception takes place with the help of sensory organs. It can be direct as well as indirect. • Direct perception ➢ It is the cognition of the sense objects by our sense organs alone – smell (nose), touch (skin), form (eyes), sound (ears) and taste (tongue). ➢ Knowledge takes place when the object of knowledge comes in direct contact with objects of sense.

➢ Direct sensory perception is also referred to as “anubhava” (meaning experience). • Indirect perception ➢ It creates knowledge based on memory (Smriti). ➢ Once we have known what an apple looks like, this gets incorporated into our memory or stock of knowledge. ➢ In later instances, whenever we see any red-coloured and round shaped fruit, our previous memory directs us to categorise them as apples.

Anumana Pramana (Inference):

• Knowledge that cannot be gained through sense organs becomes the object of inference. • We infer knowledge of what we don’t see from what we can see. • This is also considered to be the source of valid mediated knowledge. • For example, we can infer fire from the smell of smoke; or we can infer physical or emotional pain when we see the other person crying, etc.

Upamana Pramana (Comparison or Analogy):

• This kind of knowledge is acquired by the perception of similarity between two different objects of knowledge. • It is different from mere perception and inference and is based on a comparison. • Such knowledge is possible when there is a prior familiarity

Arthapatti Pramana (Assumption or Implication):

• Knowledge gained through seeing the relation between cause and effect are Arthapatti pramana. • It includes postulation, supposition, and presumption. • This form of knowledge is either gained from what we have seen or heard and are assuming rightly.

Anupalabdhi Pramana (Non- Apprehension or Mimamsa):

• This is based on the apprehension of a non-existent thing based on non- perception.

• Negative facts are cognized by non-apprehension or unavailability • This means that perception, as well as non-perception, can be the source of valid knowledge.

Shabda Pramana (Word or Verbal Testimony):

• This is gained through verbal testimony. • A lot of knowledge that we gain about the world is through verbal testimony, texts, symbols, or words. • It can be either uttered or written. • A verbal testimony must have a valid source for its object of knowledge to be true. • In ancient times, Vedas were considered to be the most authentic source of knowledge by most of the Indian philosophers. • Some western philosophers totally rejected this idea and called for context- based knowledge. • This also opened the debate that there can be various sources of knowing objects • Its validity and reliability depend on the source as well as the context. • In modern days, we rely on newspapers, books, journals, TV news etc. to form our object of knowledge or opinion.

Indian Logic (Means of Knowledge)

The following diagram shows various means of Indian knowledge

Nyaya Philosophy

• It is described in Nyaya Sutras authored by Gautama, who is founder of this school. • Nyaya school follows a scientific, a rational and logical approach. • Nyaya school recognizes four pramanas (source of knowledge) – Perception, Inference, Comparison and Verbal Testimony - as means to attaining knowledge). • Nyaya system considers God as one who creates, sustains and destroys the universe. • It believes that gaining knowledge through the five senses is the sole way of attaining liberation from the cycle of birth and death.

Vaisheshika Philosophy

• It was founded by the sage Kanada. A significant work on Vaisheshika is “Prashastapada“. • It is an objective and realistic philosophy of the Universe. • It deals with metaphysics and ontology. • It recognizes four pramanas (source of knowledge) – Perception, Inference, Comparison and Verbal Testimony - as means to attaining knowledge).

• The reality to have many categories, which are attribute, action, substance, genus, distinct quality and inference. • Universe are composed of 5 elements: earth, water, air, fire and ether. • It explains the mechanical process of formation of universe i.e. universe composed of atoms and molecules. Brahman being the fundamental force causing consciousness in these atoms. • It considers God to be the guiding principle. • It considers that living beings are rewarded or punished according to law of karma. • The creation and destruction of universe is a cyclic process and occurs according to the wishes of God.

Mimansa Philosophy

• The main text of Mimansa is Sutra of Gaimini, written around 3rd century BC. • It considers the philosophy of Vedas to be eternal and processes all • It recognizes all six four pramanas (source of knowledge) – Perception, Inference, Comparison and Verbal Testimony, Presumption and Non- apprehension - as means to attaining knowledge). • knowledge, and religion means fulfilment of duties prescribed by the Vedas. • Mimansa encompasses the Nyaya-Vaisheshika system. • It emphasizes the concept of valid knowledge. • The essence of the system is Dharma, considered to be a dispenser of fruits of actions. • Mimansa lays stress on ritualistic parts of Vedas.

Sankhya or Samkhya Philosophy

• Sankhya is the oldest of all philosophies put forth by the sage Kapila, who authored Samkhya Sutra. • It recognizes three pramanas (source of knowledge) – Perception, Inference, and Verbal Testimony - as means to attaining knowledge). • It is a dualistic philosophy with Purusha (soul) and Prakriti (nature) in it. • Prakriti and Purusha are supposed to be completely independent and absolute. Purusha: is mere consciousness and cannot be changed or modified. • Prakriti has three attributes- Thought, movement and change/transformation.

• Samkhya philosophy establishes relationship between Purusha and Prakriti to explain creation of Universe. • It also explains phenomenon of evolution. • It emphasizes the attainment of knowledge of self through meditation and concentration.

Yoga Philosophy

• This system was described in Yogasutra written by Patanjali around 2nd century BC. • It recognizes three pramanas (source of knowledge) – Perception, Inference, and Verbal Testimony - as means to attaining knowledge). • Yoga means the union of two principal entities – human spirit and divine spirit. • Emancipation of Purusha from Prakriti by self-awareness through the discipline of body and mind is conceptualized by Yoga • Yoga admits existence of God as a guide and teacher. • It states that practising Ashtanga Yoga is the way to relieve oneself from past sins in order to make way for liberation.

➢ Yama (self-control), ➢ Niyama (observation of rules), ➢ Asana (fixed postures), ➢ Pranayama (breath control), ➢ Pratyahara (choosing an object), ➢ Dharna (fixing the mind), ➢ Dhyana (concentration), ➢ Samadhi (complete dissolution of self by merging mind and object).

Vedanta (Uttara Mimamsa)

• It was propounded by Shankaracharya, who wrote commentaries on Upnishads, Brahma Sutras and Bhagvad Gita. • It refers to the philosophy of the Upnishada (concluding part of Vedas). • Vedanta school is a monoistic school of philosophy that believes that the world is unreal, and the only reality is Brahman. • Ramanuja is considered another important Advaita Scholar. • Vedanta philosophy believes that different religions lead to same goal.

• Its core message is that every action must be governed by intellect. The mistakes are made by the mind, but the intellect tells that action is in our interest or not. • Vedanta allows practitioner to access the realm of spirit through the means of intellect. • The three sub-branches of Vedanta are Advaita of Shankaracharya, Vishishta Advaita of Ramanujacharya and Dvaita of Madhwacharya. • It recognizes all six four pramanas (source of knowledge) – Perception, Inference, Comparison and Verbal Testimony, Presumption and Non- apprehension - as means to attaining knowledge).

Heterodox (Nastik) Schools of Indian Philosophy

Schools that do not accept the authority of Vedas are by definition unorthodox (nastika) systems

Carvaka or Lokayata

• Its founder was Carvaka, author of the Barhaspatya Sutras. • It is a materialistic school of thought. • It holds that one should do whatever gives one pleasure, without any regard to social conventions or morality. • The basic premise of Charvakas is that the proof of anything is its verifiability. • Perception is, therefore, the only valid source of knowledge • All other presumed means of knowledge – inference, mystic insight, authority of the scriptures, and so on, recognized by the orthodox schools – are invalid. • The notions of god, afterlife, karma and so on are all absurd • Nothing survives death.

Buddhism

• It is a system of beliefs based on the teachings of Siddhartha Gautma. • Buddhism is a non-theistic philosophy whose tenets are not especially concerned with the existence or non-existence of God. • Four Noble Truths in Buddhism are the following.

➢ There is suffering ➢ There is a cause of suffering ➢ There is a cessation of suffering ➢ There is a way to the cessation of suffering • Buddhists philosophy of life to get ‘Nirvana’ from suffering is based on the following eight principles: ➢ Right Faith (Samyak Dristi) ➢ Right Resolve (Samyak Sankalpa) ➢ Right Speech (Samyak Vakya) ➢ Right Action (Samyak Karmanta) ➢ Right Living (Samyak Ajiva) ➢ Right Thought (Samyak Smriti) ➢ Right concentration (Samyak Samadhi) ➢ Right Effort (Samyak Vyayama) • It recognizes two pramanas (source of knowledge) – Perception and Inference - - as means to attaining knowledge). • In Theravada (Hinyana), each person has to work out his salvation all by himself • Mahayana this is an interdependent activity in which each seeker receives the aid and support of other seekers, as well as the aid of sages and deities.

Jain Philosophy

• Mahavira, the 24th Jain Tirthankara, is considered to be most important character in Jain Philosophy • According to Jainism, Nirvana or liberation is obtained through three jewels (Tri-ratna).: ➢ Right Philosophy ➢ Right Knowledge ➢ Right Conduct • Right conduct implies 5 abstinence: ➢ not to lie ➢ not to steal ➢ not to strive for luxury and not to strive for possessions ➢ not to be unchaste ➢ not to injure (Ahimsa). • It recognizes three pramanas (source of knowledge) – Perception, Inference and Verbal Testimony -- as means to attaining knowledge).

Structure of Anumana (Inference)

• The word anumana is combination of ‘ANU’ which means after and ‘MANA’ which means knowledge, so the combined meaning of the word is ‘after knowledge’ • Let us take the following example: The hill is fiery. Because the hill is smoky. Whatever has fire has smoke. In the above example, we pass from the perception of smoke in the hill to the knowledge of the existence of fire in it on the ground of our previous knowledge of the universal relation between smoke and fire.

• As per Aristotelian syllogism, an inference must have three terms given below.

➢ Major term (sâdhya) ➢ Middle term (hetu) ➢ Minor term (paka) • The hill is fiery. Because the hill is smoky. Smoke on distant hill reminds us of the universal concomitance (Vyapti) between smoke and fire and help concludes that there is fire on the distant hill. ➢ Inferred (fire) → sadhya ➢ Reason/strength of inference → hetu (smoke) ➢ The subject where the character is inferred → paksa (hill)

• As per Nyâya theory of perception, an inference(anumâna) consists of five propositions.

➢ These propositions are known as avayavas.

➢ These avayavas are: pratijñâ, hetu, udâharana, upanaya and nigamana. ➢ ❖ This hill has fire (pratijna = the logical statement which is to be proved), ❖ Because it has smoke (hetu = reason for the establishment of the proposition), ❖ Whatever has smoke has fire e.g. an oven (udaharana = the universal concomitance together with example), ❖ This hill as smoke which is invariably associated with fire (upanaya = application of the universal concomitance to the present case), ❖ Therefore, this hill has fire (nigamana = conclusion drawn from the preceding propositions).

Vyapti

• Vyâpti is the logical ground of inference. Parâmarsa is the psychological ground of inference. • Vyâpti is an invariable and unconditional relation between the middle term and the major term. There are different methods for the establishment of vyâpti. • Vyâpti may be of two types: samavyâpti and visamavyâpti. • Inference is a knowledge of the mark (middle term) as having the universal relation with the major term and as being present in the minor term.

Classification of Inference

• According to the first classification of inference, inference is of two kinds, svârtha and parârtha.

➢ If a person wants to infer something for himself, it is called svârthanumâna ➢ An inference is said to be parârthanumâna when an inference is done in order to convince others.

• According to another classification, an inference is divided into three kinds, pûrvavat, sesavat and sâmânyatoda.

➢ Pûrvavat inference: When we infer an unperceived effect from a perceived cause we have pûrvavat inference. g. we see the dark clouds in the sky in the morning and infer future rain from the dark clouds. ➢ Seavat inference: When we infer an unperceived cause from a perceived effect we have seavat inference, e. g. when we infer previous rain from the swift muddy current of the river. ➢ Sâmânyatodta inference: When an inference is based not on causation but on uniformity of co-existence,it is called sâmânyatodta,e.g. when we infer cloven hoofs of an animal by its horns.

• According to another classification of inference, inference is divided into three types. They are — kevalânvayi, kevalâvyatireki and anvayavyatireki inferences. It is based on the nature of vyâpti.

➢ When vyâpti between the middle and the major term is derived from uniform agreement in presence alone, it is called Kevalânvayi inference. ➢ When vyapti between middle and the major is derived from uniform agreement in absence alone, it is called kevalâvyatireki inference. ➢ When the middle term in an inference is both positively and negatively related to the major term, it is called anvaya

Fallacies of inference (Hetvâbhâsa)

• In Indian logic a fallacy is known as hetvâbhâsa. This fallacy means, the middle term appears to be a reason but is not a valid reason. • A fallacy relates to material condition of an inference. So, all fallacies are material fallacies. There are five characteristics of a valid term. When these characteristics are violated, fallacies arise. Five characteristics of a middle term are:

➢ It must be present in the minor term (pakadharmatâ). Example: smoke must be present in the hill. ➢ It must be present in positive instances in which the major term is present. Example: smoke must be present in the kitchen where fire exists (sapakasattva). ➢ It must be absent in all negative instances in which the major term is absent; smoke must be absent in the lake in which fire does not exist (vipakasattva). ➢ It must be non-incompatible with the major term. Example, it must not prove the coolness of fire (abâdhita). ➢ It must be qualified by the absence of counteracting reasons which lead to a contradictory conclusion. Example, the fact of being caused’ should not be used to prove the ‘eternality’ of sound. (aviruddha).

• Violation of the above characteristics leads to the following fallacies.

➢ Savyabhichâra or the fallacy of irregular middle: A middle term may be irregularly related to the major term. When the middle is not uniformly related to the major term then that is called savyabhicâra hetu.

Let us take the following example, All bipeds are rational. Swans are bipeds. Therefore, swans are rational.

Here, the middle term is ‘biped’. But it is not uniformly related to the major term ‘rational’. The middle term in this example may be related to both rational and non-rational creatures. Therefore, it is a defective hetu.

➢ Viruddha or the contradictory middle: The viruddha hetu or the contradictory middle is that hetu, which though offered to establish the existence of the sâdhya actually establishes the non-existence of the sâdhya. Example: ‘sound is eternal, because it is produced’- here, the middle term ‘produced’ does not prove the eternality of sound but proves its non-eternality. Here, the middle term itself disproves the original proposition and proves its contradictory.

➢ Satpratipaka or the inferentially contradicted middle: When a hetu which is advanced to establish a particular sâdhya in an inference is validly contradicted by an another hetu which proves the non-existence of the sâdhya of the first inference, the fallacy of satpratipaka arises. In this case the first hetu is called satpratipaka hetu.

For example, ‘sound is eternal, because it is audible’ is validly contradicted by another inference ‘sound is non-eternal, because it is produced like a pot.’ Here, the middle term of the first inference, ‘audible’ is contradicted by the middle term of the second inference ‘produced.’

➢ Asiddha or the unproved middle: The asiddha hetu is one which is not yet proved, but requires to be proved, like the sâdhya. This means that the asiddha hetu is not a proved or an established fact, but an asiddha or unproved assumption.

Example: Skylotus is fragrant, because it has lotusness in it like a natural lotus’. The middle term of the argument is yet to be proved, because we are yet to establish the existence of skylotus.

➢ Bâdhita hetu or the non-inferentially contradicted middle: The middle term of an inference may be contradicted by some other ‘stronger ‘means of knowing, such as perception, testimony etc. It cannot prove the major term which is disproved by another stronger source of valid knowledge. Example: Fire is cold, because it is a substance. Here the middle term ‘substance’ becomes contradicted because its major term ‘coldness’ is directly contradicted by perception.