CHSE Odisha Elective Logic common mistakes
CHSE Odisha Elective Logic · Understand the traps and how to avoid them.
When asked to identify the predicate term of a categorical proposition, the candidate names the grammatical object or the last word of the sentence rather than the term that is affirmed or denied of the subject; e.g., in 'All poets are dreamers' they call 'dreamers' the subject complement and refuse to label it the predicate term.
School grammar training makes candidates parse sentences grammatically (subject, verb, object/complement) instead of logically (quantifier, subject term, copula, predicate term). The word 'predicate' in grammar means the whole verb phrase, so candidates transfer that meaning and cannot isolate the single term.
What to do instead
Rewrite every statement into strict logical form: Quantifier + Subject term + copula + Predicate term ('All S are P', 'No S are P', 'Some S are P', 'Some S are not P'). Practise on ten ordinary sentences daily, underlining the two terms only, until the predicate term is identified as the class named after the copula, regardless of grammar.
The candidate labels a singular proposition such as 'Socrates is mortal' or a proposition with a proper name as an A proposition, then applies the full square of opposition to it and concludes that 'Socrates is not mortal' is its contradictory or that the two are contraries.
Textbook drills use only 'All S are P' forms, so candidates memorise the quantifier words and ignore that traditional square relations presuppose universal classes and existential import; singular statements have no quantity in the same sense and behave differently.
What to do instead
Before applying any square relation, check the statement's form: does it have an explicit quantifier and a general term as subject? If the subject is a proper name or a definite description, treat it as a singular proposition and note that the A/E/I/O machinery does not directly apply. Write a one-line justification with each answer naming the form you assigned.
When asked what follows from the falsity of an A proposition, the candidate answers 'the E proposition is true' by treating A and E as contradictories, instead of saying only that the O proposition is true and the E proposition is undetermined.
Candidates memorise the square as a picture of lines without distinguishing the two diagonal contradictories from the horizontal contraries and subcontraries; under exam pressure they pick the visually opposite corner rather than the logical opposite.
What to do instead
Rebuild the square from definitions each time: contradictories differ in both quantity and quality (A-O, E-I), contraries differ in quality only (A-E), subcontraries are the two particulars (I-O). Drill with a table of eight cells (each proposition true/false, list what follows) until the answers come from the definitions, not the picture.
The candidate tests a syllogism's validity by checking whether the conclusion sounds plausible or whether the terms are factually related, and declares a valid but false-premised syllogism invalid because the conclusion is untrue in the world.
Everyday reasoning rewards truth-tracking, and candidates have rarely been forced to separate validity (form) from truth (content). Textbooks often use true-premised examples, which reinforces the confusion.
What to do instead
Adopt a fixed procedure: identify the three terms and the middle term, write the mood and figure, then apply the rules mechanically (middle distributed at least once; no term distributed in the conclusion unless distributed in the premise; no two negative premises; negative premise requires negative conclusion and vice versa). Deliberately practise on syllogisms with absurd terms ('All unicorns are mammals') so that plausibility cannot influence the verdict.
When checking distribution, the candidate marks the predicate of an O proposition as distributed, or marks the predicate of an A proposition as distributed, because 'all' and 'not' feel like they cover the whole predicate.
Distribution is about whether a term refers to every member of its class, but candidates confuse it with the quantity word at the start of the sentence. The predicate's distribution depends on the quality of the proposition, not the quantifier.
What to do instead
Memorise the distribution table by derivation rather than rote: universal subjects are distributed, particular subjects are not; negative predicates are distributed, affirmative predicates are not. Then recite the four cases: A distributes subject only, E distributes both, I distributes neither, O distributes predicate only. Apply the table term by term before judging the syllogism.
The candidate names the figure of a syllogism by the order in which the terms appear in the conclusion, or counts the middle term's position from the wrong premise, so that a second-figure syllogism is reported as first figure and the mood is then written wrongly.
Figure is defined solely by the position of the middle term in the two premises, and candidates have no stable convention for labelling the major premise (the one containing the predicate of the conclusion) first.
What to do instead
Always identify the conclusion first, then label its subject as minor term and its predicate as major term, then find which premise contains the major term and place it first. Number the middle term's position: first figure subject-major/predicate-minor, second figure predicate in both, third figure subject in both, fourth figure predicate-major/subject-minor. Write the mood as three letters in the order major premise, minor premise, conclusion.
The candidate classifies an argument as a fallacy of the consequent when the error is actually affirming the antecedent's converse, or labels any weak argument 'begging the question', without matching the concrete pattern to the named fallacy.
Fallacy names are learned as a vocabulary list with one example each; candidates match on surface similarity of topic rather than on the logical form or the specific move that makes the argument bad.
What to do instead
For each informal fallacy, write its pattern in one line (e.g., ad hominem: attacking the arguer's circumstances instead of the argument; begging the question: the conclusion, or a near-restatement of it, appears among the premises). When answering, quote the exact words in the passage that instantiate the pattern and state the pattern; if you cannot quote it, the label is probably wrong.
When constructing a truth table, the candidate fills in the reference columns in the order TTFF, TFTF for two variables but then, for three variables, uses TTTTFFFF/TTFFTTFF/TFTFTFTF inconsistently, producing wrong truth values in the main column and an incorrect classification of the formula.
The standard ordering is a convention (halving the block size at each column) that is easy to memorise for two variables and easy to corrupt for three; candidates also skip intermediate columns and compute the main connective from memory.
What to do instead
Use the halving rule: for n variables the first column has blocks of 2^(n-1), the second 2^(n-2), and so on down to alternating T/F. Always draw a separate column for every subformula, and compute the main column last from those columns only. Verify by counting rows: 2^n, and check that the final column has the expected number of T's for a tautology (all) or contradiction (none).
In a natural-deduction proof, the candidate applies modus tollens or hypothetical syllogism to a conditional whose antecedent is a conjunction, or discharges a conditional proof without cancelling the assumption, and then claims the derived line is a theorem.
The inference rules are learned as sentence patterns, and candidates match the pattern loosely, ignoring brackets and scope; the conditional-proof rule's dependency on an assumption is a bookkeeping step that is easily dropped under time pressure.
What to do instead
Before applying a rule, write the exact form it requires beside the line (modus ponens: p, p implies q, therefore q) and check that the antecedent is the whole formula, brackets included. In conditional proofs, indent every line that depends on the assumption and mark the assumption discharged only at the line where the conditional is introduced; never use an indented line after the indentation closes.
The candidate treats an argument from analogy or a causal generalisation as deductively valid, or rejects a strong inductive argument because its conclusion is not certain, and answers 'invalid' where the question asks about inductive strength.
The candidate has just spent most of the course on validity and carries the deductive standard into inductive questions; the distinction between truth-preserving form and probabilistic support is stated once in the textbook and rarely drilled.
What to do instead
Before evaluating, classify the argument type: does the conclusion claim more than the premises guarantee (inductive) or exactly what they entail (deductive)? For inductive arguments, assess strength by relevance and number of instances, and state the conclusion as probable, not certain. For causal claims, check whether the method used (agreement, difference, concomitant variation, residues) actually supports the causal link rather than mere correlation.
When asked to distinguish a hypothesis from a law or to state the role of verification, the candidate says a hypothesis is 'a guess' and that a single confirming observation proves it, ignoring the requirement of testability and the possibility of auxiliary assumptions failing.
The scientific-method chapter is read as a list of stages (observation, hypothesis, experiment, theory) and candidates reproduce the list without the logical point that universal hypotheses cannot be conclusively verified by finite instances.
What to do instead
Learn the structure, not the list: a hypothesis must be testable and falsifiable, predictions are deduced from it together with auxiliary assumptions, and a failed prediction may indict either. Practise writing, for a given hypothesis, one confirming prediction and one falsifying prediction, and state explicitly which observation would count against it.
The candidate uses the word 'valid' for a single proposition ('this statement is valid'), or calls an argument 'true', and mixes the object language with the metalanguage when symbolising, e.g., writing 'p is true' inside a formula as if 'true' were a connective.
Ordinary English uses 'valid' and 'true' interchangeably, and the textbook's metalanguage remarks about truth values are not practised as a separate skill; candidates therefore carry truth-talk into the object language.
What to do instead
Fix the vocabulary: propositions are true or false; arguments are valid or invalid (deductive) or strong or weak (inductive). When symbolising, translate only the connectives and the atomic propositions, and keep truth-value talk outside the formula. Do five symbolisation exercises per session and annotate each with 'this is a proposition' or 'this is an argument'.