Understanding the Structure of Arguments
- Argument forms: a set of premises offered in support of a conclusion.
- Categorical propositions come in four standard forms:
| Form | Statement | Example |
|---|---|---|
| A | Universal Affirmative — All S are P | All librarians are professionals |
| E | Universal Negative — No S is P | No librarian is untrained |
| I | Particular Affirmative — Some S are P | Some librarians are researchers |
| O | Particular Negative — Some S are not P | Some librarians are not administrators |
Mood and figure
In a categorical syllogism, mood is the combination of A/E/I/O propositions used, and figure is the position of the middle term across the two premises — together they determine whether a syllogism is logically valid.
Formal and informal fallacies
Formal fallacies are errors in the logical structure itself (e.g., affirming the consequent). Informal fallacies are errors in reasoning that arise from content or language — e.g., ad hominem (attacking the person, not the argument), hasty generalisation, and circular reasoning.
Connotation and denotation
Denotation is the literal, dictionary meaning of a term; connotation is the associated or implied meaning it carries beyond its literal sense.
Classical square of opposition
A diagram showing logical relations — contrary, sub-contrary, contradictory, and sub-alternation — among the four categorical forms (A, E, I, O).
Deductive vs. Inductive Reasoning
| Deductive | Inductive |
|---|---|
| General premises → specific, certain conclusion | Specific observations → general, probable conclusion |
| Validity is about structure; a valid argument with true premises gives a certainly true conclusion | Conclusion is never absolutely certain, only more or less probable |
| Example: All mammals breathe air; a whale is a mammal; therefore a whale breathes air | Example: Every observed swan is white; therefore all swans are white (may later be falsified) |
Analogies
Analogy questions test the ability to identify the relationship between a given pair of words/concepts and apply the same relationship to a new pair (e.g., Book : Library :: Painting : Museum, where the relationship is “is housed/preserved in”).
Venn Diagrams: Simple and Multiple
Venn diagrams represent categorical statements as overlapping circles, used to test the validity of syllogistic arguments visually — if a conclusion is not necessarily true in every possible diagram consistent with the premises, the argument is invalid.
Indian Logic: Means of Knowledge (Pramanas)
Classical Indian epistemology recognises several valid means of acquiring knowledge (Pramanas):
| Pramana | Meaning |
|---|---|
| Pratyaksha | Perception — direct knowledge through the senses |
| Anumana | Inference — knowledge derived by reasoning from observed signs |
| Upamana | Comparison — knowledge gained by analogy/similarity |
| Shabda | Verbal testimony — knowledge from a reliable authority’s word |
| Arthapatti | Implication — postulating an unstated fact to reconcile two known facts |
| Anupalabddhi | Non-apprehension — knowledge of the absence of something from its non-perception |
Structure and Kinds of Anumana
Anumana (inference) rests on Vyapti, the invariable/universal relation between two things (e.g., wherever there is smoke, there is fire), which licenses inferring one from the observation of the other.
There is fire on the hill (conclusion), because there is smoke (reason), and wherever there is smoke there is fire, as in a kitchen (example) — the hill is such a case (application), therefore there is fire on the hill (conclusion).
Hetvabhasas are fallacies of inference — errors where the reason given does not actually establish the invariable relation needed for valid inference.