SSR Lec4 Cr-Th CH3

If we wish to find out if a certain proposition is true, should we reconstruct the argument in the least convincing (bad reconstruction), or the most convincing way (good reconstruction) possible

With a bad reconstruction, you cannot find out if the premise is true. BUT your also cannot find out if the premise is FALSE.

You should reconstruct the argument in the best way possible. (Principle of charity)

Principle of charity

Requires you to interpret a speaker or writers argument in the strongest, most rational form possible

What is the truth-­ value of a proposition?

Whether or not that proposition is true or falsity

What is logical validity?

IF the premises were true, the conclusion MUST be true as well (cannot be false).

What does validity pertain to?

Whole arguments, or better said, inferences. (one argument can contain multiple inferences that are either valid or not).

Contraposition (of statements)

saying ‘If not-­ Q then not-­ P’ is equivalent to saying ‘If P then Q’.

or in the inclusive versus exclusive sense?

Inclusive: P is true or Q is true or BOTH are true

Exclusive: Either P is true OR Q is true. But never both

Deductive soundness

To say that an argument is deductively sound is to say: the argument is valid, and all its premises are (actually) true.

What follows if you know the conclusion of an argument is false (argument deductively unsound)?

Either one or more premises are false, or the argument is invalid, or both.

Modus ponens

P1) If P then Q

P2) P

C) Q

Modus Tollens

P1) If P, then Q

P2) Not-Q

C) Not-P

Disjunctive syllogism

P1) P or Q

P2) Not-P

C) Q

(or vice versa)

Argument by cases

P1) P or Q

P2) If P then R

P3) If Q then R

C) R

Chain (aka hypothetical syllogism)

P1) If P then Q

P2) If Q then R

P3) If R then S

C) If P then S

A, E, I, O-forms in venn diagrams

A: All S are P.

E: No S are P.

I: Some S are P.

O: Some S are not-­ P.

When are two (Venn diagram) forms logically contradictory?

When e.g. A-proposition is true, then the corresponding O-proposition must be false. And vice versa. Same for E and I.

Categorical syllogism

is any argument which is composed of two premises in the form of categorical propositions and a conclusion which is also a categorical proposition, AND the three propositions have collectively exactly three terms as in the example.