Maharashtra HSC Logic common mistakes
Maharashtra HSC Logic · Understand the traps and how to avoid them.
When converting a categorical proposition to its converse, candidates swap subject and term without changing the proposition's quantity or quality, so 'All S are P' is written as 'All P are S' and treated as equivalent.
The conversion rule is memorised as 'swap the terms', and the restriction that A and O propositions cannot be converted simply (only by limitation or not at all) is forgotten, because the textbook table of conversion is studied as a list rather than as a consequence of distribution of terms.
What to do instead
Before writing any converse, list which terms are distributed in the original (A: subject only; E: both; I: neither; O: predicate only). A term that is undistributed in the original may not become distributed in the converse. Drill the four rows explicitly, and for A-propositions always write the per accidens form 'Some P are S' with the existential assumption stated.
Candidates test a syllogism's validity by asking whether the conclusion is factually true, so a valid form with a false premise is marked invalid and an invalid form with a true conclusion is marked valid.
Everyday reasoning conflates truth with validity, and the exam's examples often use familiar empirical content (e.g. about students or animals) that invites agreement or disagreement with the conclusion rather than inspection of form.
What to do instead
Rewrite every argument in mood-and-figure notation (e.g. AAA-1, EIO-2) before judging it, and apply the five rules of syllogism (distribution of middle term, illicit major/minor, two negative premises, negative premise with affirmative conclusion, two particular premises). State the verdict on form first, then comment on truth separately.
In truth tables, candidates fill in the reference columns for compound components inconsistently, or evaluate a conditional as false only when both antecedent and consequent are false.
The material conditional's truth conditions are counter-intuitive, and students try to import everyday 'if...then' causality into the table; also, long tables are completed row by row without fixing the atomic proposition columns first.
What to do instead
Always build the table in strict stages: atomic columns first (2^n rows in a fixed order such as TTTTFFFF), then each subformula column, then the main operator. Memorise the conditional as false in exactly one row (T antecedent, F consequent). Verify by counting: a conditional with two atoms must have three T rows.
When constructing a formal proof, candidates apply a rule of inference to a part of a line rather than to a whole line, or use a rule of replacement as if it required whole-line substitution, producing invalid steps.
The distinction between rules of inference (which apply to whole statements) and rules of replacement (which apply to any part of a statement) is stated once in the chapter and then blurred, and students imitate worked examples without checking which kind of rule each step uses.
What to do instead
Annotate every derived line with the rule name and the exact line numbers used. Before writing a step, ask: is this rule in the inference list (MP, MT, DS, HS, Simp, Conj, Add, CD) or the replacement list (DeM, Comm, Assoc, Dist, DN, Trans, Impl, Equiv, Exp, Taut)? Inference rules must cite whole lines; replacement rules may be applied inside a subformula.
Candidates define logic as 'the science of correct thinking' and stop there, then lose marks on questions asking for the distinction between logic and psychology or between normative and descriptive study.
The opening definition is memorised verbatim from the first page and treated as a complete answer, so the scope questions that require contrast (logic studies form, psychology studies actual thought processes; logic is normative, psychology descriptive) are left unanswered.
What to do instead
Prepare a short structured answer for scope questions: definition, subject matter (propositions and arguments, form not matter), normative character, relation to psychology, relation to grammar and mathematics, and the traditional/modern distinction. Answer with at least three of these points whenever 'nature and scope' is asked.
Candidates classify terms as concrete/abstract, positive/negative, or distributive/collective by the word's sound rather than by its function in the proposition, so 'blindness' is called concrete and 'non-violence' is called negative without checking privation.
The classifications overlap and depend on use in context; students learn examples rather than criteria, and a word like 'humanity' or 'darkness' fits more than one heading depending on how it is predicated.
What to do instead
For each classification, apply the defining test explicitly. Concrete vs abstract: can it be the subject of a predicate of which it is itself an attribute? Positive vs negative: does it assert presence or absence of a quality (and is it privative, i.e. absence of a quality the subject could have)? Distributive vs collective: does the predicate apply to each member separately or to the group as a unit?
In fallacy questions, candidates label any weak or emotive argument 'begging the question' or 'ad hominem' without identifying the specific structural defect, and miss the distinction between formal and informal fallacies.
Fallacy names are learned as a vocabulary list with one example each, so under exam pressure the most familiar label is attached to any bad argument; also, several fallacies (circular reasoning vs complex question, equivocation vs amphiboly) look similar on the surface.
What to do instead
Use a two-step diagnostic. First ask whether the defect lies in the form (undistributed middle, illicit process, affirming the consequent) or in the content/language (ambiguity, relevance, presumption). Then match to the subfamily: relevance (ad hominem, ad populum, ad verecundiam, ad ignorantiam, ad misericordiam, straw man), ambiguity (equivocation, amphiboly, accent, composition, division), presumption (begging the question, complex question, false cause, accident, hasty generalisation). Name the subfamily in your answer.
Candidates treat inductive generalisation and the methods of experimental inquiry as a single topic, so they answer a question about Mill's method of difference with a description of agreement, or claim that induction yields certainty.
The five Mill's methods and the idea of inductive probability are taught together in one chapter, and the differences (presence vs absence, single vs joint variation, concomitant variation) are not separated into distinct criteria.
What to do instead
Learn each method by its question: Agreement - what is common to cases where the effect occurs? Difference - what is present when the effect occurs and absent when it does not? Joint method - both. Concomitant variation - do two factors vary together in degree? Residues - what remains after known causes are subtracted? Also state clearly that induction gives probable, not certain, conclusions, and that a hypothesis must be testable and falsifiable.
When symbolising ordinary-language sentences, candidates ignore the scope of negation and the difference between 'and' and 'but', or translate 'unless' as a conjunction rather than as a disjunction or conditional.
Symbolisation is treated as word-for-word substitution, and the textbook's list of equivalent English expressions for each connective is not practised on realistic sentences with multiple connectives.
What to do instead
Symbolise from the inside out: identify the main connective last. Fix a small translation dictionary for the sentence, then apply standard equivalences: 'unless' = 'if not...then' = 'or'; 'but'/'although' = 'and'; 'neither...nor' = 'not (A or B)'; 'only if' introduces the consequent, not the antecedent. Check the result by reading it back in plain English.
Candidates write categorical propositions in standard form carelessly, leaving out the copula or the quantifier, or misidentifying the subject term when the sentence begins with 'Only' or 'All...except'.
The four standard forms (A, E, I, O) are learned with simple examples, and non-standard English sentences are paraphrased loosely without restoring the explicit 'All S are P' pattern and without identifying the distributed terms.
What to do instead
Always reduce to one of the four patterns with an explicit quantifier, subject, copula and predicate. Treat 'Only S are P' as 'All P are S'; 'All S except M are P' as two propositions; 'No S are P' as E. Then state the quantity, quality and distribution before doing any inference on the proposition.