Complete exam-focused revision notes on arguments, categorical logic, mood and figure, fallacies, analogies, Venn validity and the Indian theory of knowledge.
Logical reasoning में उत्तर “सही लगता है” इसलिए सही नहीं होता—देखना यह है कि conclusion, premises से नियमपूर्वक निकलता है या नहीं।
Separate evidence from the claim it supports
An argument is a set of statements in which one or more premises are claimed to support a conclusion. It is not merely a quarrel.
Premise कारण/evidence देता है; conclusion वह दावा है जिसे साबित करना है।
A declarative sentence capable of being true or false. Questions, commands and exclamations normally do not count as propositions.
Premise: because, since, for, given that, as shown by.
Conclusion: therefore, hence, thus, so, it follows that, consequently.
Indicators help—but meaning and role decide.
“Riya is eligible because she is 18” assumes a rule such as “All 18-year-olds meeting the other conditions are eligible.” Hidden assumptions can make an argument weak.
Necessity, probability and best explanation are different standards
Premises claim to make the conclusion necessary. Judge by valid/invalid.
A valid argument with true premises is sound.
NECESSITYPremises make the conclusion probable. Judge by strong/weak.
A strong argument with true premises is cogent.
PROBABILITYMoves from an observation to the best available explanation. It proposes a hypothesis; later testing may confirm or reject it.
PLAUSIBILITYValidity asks: If the premises were true, could the conclusion still be false? A valid form may contain factually false premises.
Valid form, unsound argument.
To show a deductive form invalid, construct one case where all premises are true but the conclusion is false. One genuine counterexample is enough.
Translate content into symbols before judging the form
| Name | Form | Status |
|---|---|---|
| Modus Ponens | If P→Q; P; ∴Q | Valid |
| Modus Tollens | If P→Q; not-Q; ∴not-P | Valid |
| Hypothetical syllogism | P→Q; Q→R; ∴P→R | Valid |
| Disjunctive syllogism | P∨Q; not-P; ∴Q | Valid |
Invalid. Q may have another cause.
Rain→wet road; road wet; therefore rain. A sprinkler is a counterexample.
Invalid. Q may occur without P.
No rain does not imply no wet road.
P only if Q means P→Q. Q is a necessary condition for P.
P if Q means Q→P. Q is sufficient for P.
Words can inform, express, direct and perform
Conveys information that can be assessed as true or false: “Delhi is the capital of India.”
Expresses or evokes feelings: “What a magnificent performance!” Emotional wording may influence judgment.
Attempts to cause action: command, request, advice or question—“Please submit the form.”
The utterance itself performs an act in an appropriate context: “I promise,” “I apologize,” “I declare the meeting open.”
Denotation / extension = the class of objects to which a term applies. Connotation / intension = attributes, associated meaning or emotional colouring carried by the term.
| Word | Denotation | Possible connotation |
|---|---|---|
| Home | Place of residence | Warmth, belonging |
| Snake | A reptile | Danger, betrayal |
| Youthful | Having qualities of youth | Energy, freshness |
Denotation शब्द का सीधा referent/class है; connotation उससे जुड़ा भाव या अतिरिक्त अर्थ है।
Quantity × quality gives the four standard forms
| Code | Standard form | Quantity | Quality | Distributed terms |
|---|---|---|---|---|
| A | All S are P | Universal | Affirmative | S only |
| E | No S are P | Universal | Negative | S and P |
| I | Some S are P | Particular | Affirmative | Neither |
| O | Some S are not P | Particular | Negative | P only |
Example: Some / researchers / are / teachers.
A term is distributed when the proposition says something about every member of the class denoted by that term.
In “No cats are dogs,” the statement excludes the whole cat class from the whole dog class—both are distributed.
Transform one categorical proposition without changing its logical force
Interchange S and P.
Change quality and replace predicate with its complement. Valid for all A, E, I, O.
All S are P → No S are non-P.
Interchange subject and predicate, replacing both with complements.
All S are P → All non-P are non-S.
Traditional Aristotelian logic often assumes that universal propositions have existential import. Modern Boolean logic does not infer existence from “All S are P” or “No S are P.”
Mood reads proposition types; figure locates the middle term
Mood is the A/E/I/O sequence of major premise, minor premise and conclusion. Example: AAA.
Figure 1: Barbara AAA, Celarent EAE, Darii AII, Ferio EIO.
Names are memory aids; validity still depends on distribution and quantity rules.
Truth travels along fixed relations—under traditional existential assumptions
A ↔ O and E ↔ I. Exactly one must be true and the other false. They cannot both be true or both be false.
A–E: cannot both be true; may both be false.
I–O: cannot both be false; may both be true.
Truth descends: A→I and E→O. Falsity ascends: I false→A false; O false→E false.
Universal से particular में truth नीचे जाती है; particular की falsity ऊपर जाती है।
Without existential import, only the contradictory pairs are guaranteed. Contrary, subcontrary and subaltern relations belong to the traditional/classical square.
The logical architecture fails, regardless of the topic
| Rule | Fallacy when broken | Fast diagnostic |
|---|---|---|
| Exactly three terms | Four-term fallacy | A word shifts meaning between premises |
| Middle term distributed at least once | Undistributed middle | Premises never cover the whole M class |
| Any term distributed in conclusion was distributed in its premise | Illicit major / illicit minor | Conclusion says more about P or S than premises permit |
| Two negative premises yield no conclusion | Exclusive premises | No bridge between S and P |
| One negative premise requires a negative conclusion, and vice versa | Affirmative-from-negative / negative-from-affirmative | Quality mismatch |
| Two particular premises yield no valid categorical conclusion | Particular-premises fallacy | Insufficient distributed linkage |
| Do not infer existence from universals in Boolean logic | Existential fallacy | Universal premises, particular conclusion |
“Animals” is undistributed in both A premises. Sharing a class does not make the subclasses identical.
“Mammals” is distributed in the E conclusion but undistributed in the A premise.
Relevance, weak evidence, presumption and ambiguity
Ecological fallacy: infer individual properties directly from group-level data. Fallacy fallacy: conclude a claim is false merely because an argument offered for it is fallacious. A bad argument does not by itself settle the truth of its conclusion.
A:B :: C:D means relation(A,B) = relation(C,D)
Stronger when similarities are numerous, relevant and diverse; disanalogies are few; and the conclusion is modest.
Shade what is empty; place X where existence is asserted
Shade the part of S outside P: S ∩ non-P is empty.
Shade the overlap: S ∩ P is empty.
Place X in the overlap: at least one member is both S and P.
Place X in the S-only region.
Diagram the premises only; inspect whether the conclusion is already forced
Shading forces every S region outside P to be empty. The conclusion is already represented.
P and S may occupy different parts of M. Premises allow true premises with a false conclusion.
Shading never creates an object. A universal premise alone does not place an X in modern Boolean diagrams.
Pramāṇa is a valid means or source of knowledge
| Pramāṇa | Meaning | Signature example |
|---|---|---|
| Pratyakṣa | Perception / direct cognition | Seeing smoke on the hill |
| Anumāna | Inference from sign and universal relation | Inferring fire from smoke |
| Upamāna | Comparison / knowledge through similarity | Recognising gavaya from a prior comparison |
| Śabda | Reliable verbal testimony | Knowledge from a trustworthy speaker or text |
| Arthāpatti | Postulation / implication | Devadatta is stout but does not eat by day → he eats at night |
| Anupalabdhi | Non-apprehension as knowledge of absence | No pot is on the floor because it is not perceived under suitable conditions |
छहों Pramāṇa अलग-अलग तरीके से ज्ञान देते हैं: प्रत्यक्ष, अनुमान, तुलना, विश्वसनीय वचन, आवश्यक postulation और अनुपस्थिति का ज्ञान।
External perception uses the five senses; internal perception concerns mind and inner states.
Nirvikalpaka: indeterminate, pre-conceptual awareness. Savikalpaka: determinate recognition with name and qualities.
Laukika: ordinary. Alaukika: extraordinary—sāmānyalakṣaṇa, jñānalakṣaṇa, yogaja.
Indian philosophical schools do not uniformly accept all six Pramāṇas. Nyāya classically accepts four—perception, inference, comparison and testimony—while Mīmāṃsā and Advaita traditions accept additional means.
The smoke–fire model of inference, plus its failure modes
Pakṣa = subject/minor term (hill); Sādhya = probandum/major term (fire); Hetu = reason/middle term (smoke).
Vyāpti is the universal, exceptionless relation between Hetu and Sādhya: wherever smoke, there fire.
Anvaya: positive agreement—when H is present, S is present. Vyatireka: negative agreement—where S is absent, H is absent.
| Condition | Meaning |
|---|---|
| Pakṣadharmatā | Hetu is present in the subject under consideration. |
| Sapakṣasattva | Hetu occurs in positive similar instances where Sādhya exists. |
| Vipakṣāsattva | Hetu is absent in negative instances where Sādhya is absent. |
| Abādhita | The proposed conclusion is not contradicted by stronger knowledge. |
| Asatpratipakṣita | No equally strong counter-reason proves the opposite. |
| Hetvābhāsa | Core defect | Recall cue |
|---|---|---|
| Savyabhicāra / Anaikāntika | Irregular or inconclusive reason; no invariable relation. Types: sādhāraṇa, asādhāraṇa, anupasaṃhāri. | Wanders |
| Viruddha | Reason proves the contradictory of the intended conclusion. | Reverses |
| Satpratipakṣa | An opposing reason of equal force establishes the contrary. | Counterbalanced |
| Asiddha | Reason is unproved—āśrayāsiddha, svarūpāsiddha or vyāpyatvāsiddha. | Unestablished |
| Bādhita | Conclusion is contradicted by stronger knowledge, often perception. | Blocked |
Lock the distinctions before the exam
| Pair | First | Second |
|---|---|---|
| Validity / Soundness | Correct deductive form | Validity + true premises |
| Strength / Cogency | High inductive support | Strength + true premises |
| Formal / Informal fallacy | Defect in structure | Defect in relevance, evidence, presumption or language |
| Denotation / Connotation | Referents or extension | Associated/intensional meaning |
| Mood / Figure | A–E–I–O sequence | Position of middle term |
| Shade / X | Empty region | Existing member |
| Hetu / Sādhya | Reason or sign | What is to be proved |
| Vyāpti / Pakṣadharmatā | Hetu–Sādhya relation | Hetu present in Pakṣa |
These notes synthesize the supplied book pages with the complete UGC NET Paper 1 syllabus using original explanations, corrected distinctions, diagrams and practice interactions. In classical logic questions, always identify whether existential import is being assumed.
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