Introduction to Logic and Critical Thinking
Study guide – concise, organized, and easy to read
1. What Is Logic?
| Aspect |
Description |
| Definition |
The systematic study of valid reasoning and inference. |
| Goal |
Distinguish good arguments (those that guarantee their conclusions) from bad ones. |
| Scope |
Formal (symbolic) logic, informal logic, and applied reasoning in everyday contexts. |
| Key Terms |
Proposition, premise, conclusion, inference, validity, soundness. |
1.1 Types of Logic
| Type |
Main Features |
| Deductive |
Reasoning from general premises to a specific conclusion. Truth of premises guarantees truth of conclusion (if valid). |
| Inductive |
Reasoning from specific observations to a general claim. Conclusions are probable, not certain. |
| Abductive |
Inference to the best explanation. Chooses the most plausible hypothesis that accounts for the data. |
| Formal |
Uses symbolic notation and strict rules (e.g., propositional, predicate logic). |
| Informal |
Analyzes everyday language, arguments, and fallacies without symbols. |
2. Structure of an Argument
- Premises – Statements that provide support.
- Conclusion – The claim being supported.
Example
- Premise 1: All mammals are warm‑blooded.
- Premise 2: Whales are mammals.
- Conclusion: Therefore, whales are warm‑blooded.
2.1 Evaluating Arguments
| Criterion |
What to Check |
| Validity (deductive) |
Does the conclusion follow logically from the premises? |
| Soundness (deductive) |
Are the premises true and is the argument valid? |
| Strength (inductive) |
How probable is the conclusion given the premises? |
| Cogency (inductive) |
Are the premises credible and the argument strong? |
3. Common Logical Forms
| Form |
Symbolic Pattern |
Example (English) |
| Modus Ponens |
(P \rightarrow Q,; P ;∴; Q) |
If it rains, the ground gets wet. It is raining. → The ground is wet. |
| Modus Tollens |
(P \rightarrow Q,; \lnot Q ;∴; \lnot P) |
If the alarm is set, it will ring. It did not ring. → The alarm was not set. |
| Hypothetical Syllogism |
(P \rightarrow Q,; Q \rightarrow R ;∴; P \rightarrow R) |
If I study, I will pass. If I pass, I will graduate. → If I study, I will graduate. |
| Disjunctive Syllogism |
(P \lor Q,; \lnot P ;∴; Q) |
Either the light is on or the switch is broken. The light is not on. → The switch is broken. |
| Universal Instantiation |
(\forall x, P(x) ;∴; P(a)) |
All birds have feathers. → A sparrow has feathers. |
| Existential Generalization |
(P(a) ;∴; \exists x, P(x)) |
This apple is red. → Some fruit is red. |
4. Informal Logic &