COLOUR THEME
Start here. What logic studies, statements and arguments, how truth differs from validity and soundness, and deductive versus inductive reasoning.
5 sub-topics, in the order to study them. Tap one to jump to it.
Revision mode hides the full explanations and keeps each section's key terms, lists and tables. Use it from your second read onward.
In brief
Logic is the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning.
Logic is the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning. It does not study how people actually think (that is psychology). It studies the relationship between premises and conclusion.
In brief
A statement is a declarative sentence that is either true or false .
A statement is a declarative sentence that is either true or false. Commands ("Close the door"), questions, requests and exclamations are not statements, so they have no truth value and cannot be premises or conclusions. The truth or falsity of a statement is called its truth value.
In brief
An argument is a group of statements in which one (the conclusion ) is claimed to follow from the others (the premises ).
An argument is a group of statements in which one (the conclusion) is claimed to follow from the others (the premises). Every argument therefore has at least one premise and exactly one conclusion in the basic form.
Conclusion indicators: therefore, hence, thus, so, consequently, it follows that, accordingly, which shows that.
Premise indicators: because, since, for, as, given that, inasmuch as, the reason being.
Non-arguments: mere description, report, explanation, command, question, simple conditional statement. An explanation tells why something happened (the fact is already accepted), while an argument tries to prove that something is true.
In brief
These three words are the most tested distinction in the unit.
These three words are the most tested distinction in the unit.
| Term | Applies to | Meaning |
|---|---|---|
| Truth / Falsity | Statements (propositions) | Agreement or disagreement with fact |
| Validity / Invalidity | Deductive arguments | Conclusion follows necessarily from premises |
| Soundness | Deductive arguments | Valid and all premises true |
| Strength / Weakness | Inductive arguments | How probable the conclusion is, given the premises |
| Cogency | Inductive arguments | Strong and all premises true |
Key facts to memorise:
Validity depends only on form, not on the actual truth of the statements.
A valid argument can have a false conclusion, but only if at least one premise is false.
If the premises are true and the conclusion is false, the argument is definitely invalid.
A valid argument with a false premise is valid but unsound.
An invalid argument can have true premises and a true conclusion. Truth of the parts does not guarantee validity.
Propositions are true or false; arguments are valid or invalid. Never say "a true argument" or "a valid statement".
In brief
Feature Deduction Induction Direction (traditional) General to particular Particular to general Claim Conclusion follows necessarily Conclusion follows probably Conclusion…
| Feature | Deduction | Induction |
|---|---|---|
| Direction (traditional) | General to particular | Particular to general |
| Claim | Conclusion follows necessarily | Conclusion follows probably |
| Conclusion | Contained in the premises (no new information) | Goes beyond the premises (new information) |
| Evaluation | Valid / invalid | Strong / weak |
| Effect of added premises | Valid argument stays valid | Strength can increase or decrease |
| Example | All men are mortal; Socrates is a man; so Socrates is mortal | The sun has risen every day so far; so it will rise tomorrow |
Caution: the "general to particular" and "particular to general" rule is only a rough guide. Some deductive arguments move from general to general, and some inductive arguments move from particular to particular (analogy). The real test is whether the conclusion is claimed to follow necessarily or only probably.
Types of induction: perfect induction (complete enumeration of all cases, which is really deductive in force), imperfect induction (a sample is generalised, which is the usual inductive method), analogy, causal inference, statistical generalisation and hypothesis. Francis Bacon's Novum Organum championed the inductive method, and J. S. Mill systematised the canons of induction.
Practise with free MCQs and answer keys, then return here to fix what you got wrong.
↑ Module 1: Western Logic: Arguments and Categorical Reasoning · All 19 topics in Logical Reasoning · Unit overview and sample MCQs
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