Unit VI Logical Reasoning Crash Course – Quick Revision (Terms & Concepts) Based on New Paper 1 Syllabus for 2021

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Syllabus

  • Unit-VI Logical Reasoning Understanding the structure of arguments: argument forms, structure of categorical propositions, Mood and Figure, Formal and Informal fallacies, Uses of language, Connotations and denotations of terms, Classical Square of opposition. Evaluating and distinguishing deductive and inductive reasoning. Analogies.
  • Venn diagram: Simple and multiple use for establishing validity of arguments. Indian Logic: Means of knowledge.
  • Pramanas: Pratyaksha (Perception) , Anumāna (Inference) , Upamana (Comparison) , Shabda (Verbal testimony) , Arthapatti (Implication) and Anupalabddhi (Non-apprehension) . Structure and kinds of Anumāna (inference) , Vyapti (invariable relation) , Hetvabhasa (fallacies of inference) .
  • Square of Opposition
  • Syllogism
  • Euler Diagram
  • Logical Reasoning
  • Assumption
  • Argument
  • Conclusion
  • Inference
  • Theme Detection
  • Branches of Philosophy
  • Axiology: Axiology is the study of value.
  • Nature and status of value
  • Ethics
  • Aesthetics
  • Ontology – what is real
  • Epistemology – study of knowledge
Indian Schools
  • Astika – Orthodox

According to Nyaya, there are exactly four sources of knowledge (pramanas) :

  • Perception
  • Inference
  • Comparison
  • Testimony
  • Nyaya accepted four sources of valid knowledge, the Vaisesika accepted only two- perception and inference.

Purva Mimamsa School was to establish the authority of the Vedas

  • The Vedanta, or later (Uttara) Mimamsa School, concentrates on the philosophical teachings of the Upanishads rather than the ritualistic injunctions of the Brahmanas
    • Indian Scholar – Vivekananda, Chanakya

Vedas Knowledge

  • The four-fold values of life- dharma, Artha, Kama, and moksa constitute the essential message of the Vedas. The word Veda is derived from the root ‘vid’ , which means ‘to know’ . Thus, the word Veda means wisdom
    • Rigveda
    • Yajurveda
    • Samaveda
    • Atharvaveda

The Vedanga are six auxiliary disciplines in Vedic culture that developed in ancient times

  • Aprama – 5 theories of illusion or error:
  • Svatahpramanya (Self-Validity) - self-validity of knowledge or intrinsic validity of knowledge
  • Paratah-Pramanya (External-Validity) - criticized on the ground that a purely external correspondence of valid knowledge is meaningless as well as impossible
  • Pratyaksha - Types of Ordinary Perception: External & Internal
    • Extraordinary Perception (Alaukika)
    • Samanyalaksana (Perception of Classes)
    • Jnanalaksana (Super Normal Sense Contact)
    • Yogaja (Intuitive Perception)
    • Internal Perception
  • Mind (manas) is regarded as an internal sense organ in Nyaya. Internal perception is brought about by the mind՚s contact with physical objects. It produces knowledge of pleasure, pain, hatred, morality, immorality etc.
    • Manas Pratyaksha
    • Yogic Perception

External Perception

  • External perception involves the connection of objects with the five senses- visual, tactual, auditory, gustatory, and olfactory.
    • Visual Perception
    • Tactual Perception
    • Auditory Perception
    • Olfactory Perception
    • Gustatory Perception

Anumāna – Inference – (Smoke & Fire)

Paksha Hetu and Sadhya

Paksadharmata Vyapti

  • Inferential cognition (Anumiti) is a proposition that follows from the first two propositions and so corresponds to the conclusion of the syllogism
  • Vyapti expresses the relation of invariable concomitance of hetu (middle term) with the sadhya (major term) .
    • Sadhya
    • Paksha - Sapaksha: The place where the sadhya definitely is exists is Sapaksha (kitchen) & Vipaksha: The place where the sadhya is definitely absent is Vipaksha (lake)
    • Hetu
    • Linga
    • Drstanta (Example)
  • Paksadharmata (Special Feature of the Subject) - judgment of such a perception. E. g. , existence of smoke on mountain. Paksadharmata of the paksha is essential for proving sadhya (fire) on the paksha
  • Paramsa: The process of inference relates the sadhya or major term to the paksha or minor term. This is done through the relation of the hetu to both the paksha (by Paksadharmata) and the sadhya (by Vyapti) . Subsumptive reflection is the knowledge of reason (hetu) existing on the paksha together with the knowledge of invariable concomitance (Vyapti) between hetu and sadhya.

Types of Vyapti: Co-Presence, Co-Absence, and Co-Presence/Co-Absence of Hetu & Sadhya

  • Anvayavyapti (Co-Presence of Hetu and Sadhya)
  • Vyatirekavyapti (Co-Absence of Hetu and Sadhya)
  • Anvaya-Vyatirekavyapti (Positive-Negative Relation)

Types of Anumāna: Based on Vipaksha or Paksha

  • Kevalanvayi (Positive Inference)
  • Kevala Vyatireki (Negative Inference)
  • Anvaya Vyatireki (Positive & Negative Inference)
  • Visama-vyapti: A Vyapti between terms of unequal extension, such as smoke and fire, is called asamavyapti or Visama-vyapti
  • Sama Vyapti: A Vyapti between two terms of equal extension is called samavyapti or equipollent concomitance.

Types of Anumāna

Purvat, Sesavat and Samanyatodrsta

  • Purvat: It is the inference of unperceived effect from perceived cause.
  • Sesavat: ‘Sesa’ means ‘effect’ . Gautama states that in sesavat inference we infer the unperceived cause from a perceived effect. That is, we perceive the consequent and infer the antecedent. Contrary to purvat, here the cause (cloud) becomes the sadhya and the effect (rain) becomes the hetu or probans in the Vyapti
  • Samanyatodrsta: Samanyatodrsta means the inference of movement of an object, which is perceived at different locations.
  • Making Valid Argument
  • Pratijna (Proposition)
  • Hetu (Reason)
  • Drstanta or Udaharana (Example)
  • Upanaya (Comparison or Application)
  • Conclusion (Nigamana) or Justification (Sthapana)

Types of Hetwabhasa

Hetwabhasa
  • Savyabhicara is the hetu which is inconstant, i.e.. which is present sometimes with the sadhya and sometimes not.
  • Sadharana Savyabhicara (Common Strayer) : If the Hetu is available in such a place where sadhya is absent
  • Asadharana Savyabhicara (Uncommon or Peculiar) : If the hetu is absent both in Sapaksha and Vipaksha (and possibly present only in paksha)
  • Anupasamhari Savyabhicari Hetwabhasa (Non-Exclusive) : Hetu without positive example or negative example is Anupasamhari Savyabhicari
  • Satpratipaksha Hetwabhasa or Prakaranas Ama (Opposable Reason) - The pre-molar teeth are eternal as they are the parts of mouth. And “as they fall naturally, the pre-molar teeth are non-eternal”
  • Asiddha (Futile Reason) or Sadhya Sama (Non-Availability) – hetu whose subsistence in the paksha is as unsettled as that of sadhya. For example, “The sky lotus is fragrant, because it has lotuses in it like a natural lotus.” Here, the minor term, sky-lotus is “unreal”
  • Baadhita happens when middle term (hetu) is contradicted by another pramana other than inference – water is cold as it is like water - Baadhita directly prevents inference
  • Viruddha - A hetu may be contradictory if and only if it is in contradiction with something that the proponent has already accepted or is known to hold - air is empty

Upamana

  • Sanjna - name
  • Sanjni - object
  • Sadrsya - comparison
  • Recollection
  • Upamiti – comparative knowledge
  • Upamana – connection due to similarity
  • the identification of a previously unknown object due to its similarity with a known object as described by a reliable source - similarity

Sabda Pramana (Verbal Testimony)

  • Knowledge comes through words when these are communicated. It is also called ‘apta-vakyas’ (statement of a trustworthy person) and agama (authentic word) .
  • Word or pada
  • Sanketa or indication
  • Lakshna or implication
  • Samskara – cognize words to meaning
  • Sentence or Vakya
  • Theory of Individuals (Vyaktivada) :
  • Theory of Universal (Sati Vada) :

Characteristics of good sentence

  • Akanksha (Expectancy) :
  • Yogyata (Consistency) :
  • Asatti (Proximity) :
  • Tatparya (Purport) :
  • An apta is a person whose testimony can be trusted.
  • Testimony can be
  • Drstartha (Worldly) :
  • Adrstartha (Supersensible)
  • Laukika (Ordinary Words) : Laukika or ordinary words
  • Vedic (Scriptural) Words:

Arthapatti (Presupposition or Postulation)

  • When we see that a man is fat and yet does not eat in day time, our knowledge of his fatness conflicts with our knowledge of his not eating in day time.

Srutarthapatti (Postulation from At Hand)

Drstarthapatti (Postulation from Seen)

Anupalabdhi (Non-Apprehension)

  • Anupalabdhi means non-cognition. There are two aspects of non-cognition in Indian philosophy:
    • As an Ontological Reality
    • As a Way of Knowledge

Posterior Nonexistence (Pradhvamsabhava)

Absolute Nonexistence (Atyantabhava)

Fallacies

  • Formal - invalid deductive argument that resembles a valid deductive pattern so that persons can be misled into thinking it is valid.
  • Appeal to Probability:
    • Bad Reasons Fallacy or Argumentum ad Logicam
    • Masked Man Fallacy or Intentional Fallacy
    • Non Sequitur

Fallacies

  • Informal - incorrectness is not due to an invalid form, but is a consequence of the ambiguity of language or one that is ultimately irrelevant to the subject matter of the argument. They are in turn divided into fallacies of relevance, defective induction, presumption, and ambiguity.

Fallacies of Relevance

  • Fallacies of relevance are the most numerous and the most frequently encountered. In these fallacies, the premises of the argument are simply not relevant to the conclusion. However, because they are made to appear to be relevant, they may deceive. We will discuss the following types:
    • Appeal to The Populace- ad Populum
    • Appeal to Emotion
    • Red Herring
    • Straw Man
    • Attack & Argument against the Person or ad Hominem
    • Appeal to Force or ad Baculum
  • Missing the Point, Irrelevant Conclusion, or Ignoratio Elenchi:
    • Fallacies of Relevance
    • Fallacies of Relevance
    • Fallacies of Defective Induction
  • In fallacies of defective induction, which are also common, the mistake arises from the fact that the premises of the argument, although relevant to the conclusion are so weak and ineffective that relying on them is a blunder. We will discuss the following:
    • Argument from Ignorance or ad Ignorantiam
    • Appeal to Inappropriate Authority or ad Verecundiam
    • False Cause or Non-Causa Pro Causa
    • Fallacy of Slippery Slope
    • Hasty Generalization

Fallacies of Presumption

  • In fallacies of presumption, too much is assumed in the premises. The conclusion depends mistakenly on these unwarranted assumptions. We will discuss the following:
    • Accident
    • Complex Question or Plurium Interrogationnum
    • Begging the Question or Petitio Principi

Fallacies of Ambiguity

  • The fallacies of ambiguity arise from the equivocal use of words of phrases. Some word or phrase in one part of the argument has a meaning different from that same word or phrase in another part of the argument.
    • Equivocation
    • Amphiboly
    • Accent
    • Composition
    • Division

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