Philosophy cheat sheet

Arguments

An argument offers premises as reasons for a conclusion. Identify the reasoning before deciding whether you agree.

“Because” often introduces a premise, but wording alone does not establish the structure.

Knowledge questions

Epistemology examines knowledge, justification and belief. A confident belief and a well-supported belief are not equivalent.

Ask what would count as a reason to revise the claim.

Ethical reasoning

Ethical theories emphasise different considerations, such as consequences, duties, rights or character. Define the criterion before comparing decisions.

A useful result does not settle every question about how it was obtained.

Conceptual analysis

Clarify what a term means, consider examples and test boundary cases. A disagreement may concern a definition as well as a fact.

Distinguish what is legally permitted from what is ethically justified.

Deduction and induction

Deductive reasoning aims at a conclusion that must follow if its premises are true. Inductive reasoning supports a conclusion with evidence without guaranteeing it.

A generalisation from repeated observations may be well supported while remaining revisable.

Necessary and sufficient conditions

A necessary condition must hold for something to occur; a sufficient condition guarantees it in the stated model. A condition can be necessary without being sufficient.

Being a rectangle is necessary for being a square, but not sufficient.

Ethical frameworks

Consequentialist, duty-based and virtue approaches ask different questions about outcomes, obligations and character. Apply a framework consistently and examine conflicts and assumptions.

An ethical argument needs reasons for its principle, not only a statement that an outcome feels right.

Counterexamples

A counterexample tests a universal claim by providing a case that meets its conditions but fails its conclusion. A relevant exception can refute a universal statement.

One black swan refutes “all swans are white”; it does not show that no swans are white.

Worked example: valid structure

All mammals are animals. All whales are mammals. Therefore all whales are animals. The conclusion follows from the premises through class inclusion.

Validity concerns the connection; soundness additionally requires true premises.

Common mistake: disagreement proves relativism

The existence of disagreement does not by itself show that all views are equally justified or that truth is impossible. Examine the evidence and standards of justification.

Separate what people believe from an argument about what makes a belief justified.

Check your understanding

Can an argument be valid with false premises?

Yes. Validity concerns whether the conclusion follows; soundness requires validity and true premises.

Curriculum connections

Sources