Summary Logic and Philosophy

Logic & Philosophy, Summary
Summary written by Saskia Kriege
Cognitive Science and Artificial Intelligence

, TFL

Needed for TFL:
- Atomic sentences
- Connectives
- Brackets


Term Meaning

Argument Any collection of premises together with
a conclusion

Validity An argument is valid if and only if it’s
impossible for all of its premises to be
true and the conclusion false

→ if a conclusion is true, always valid
(necessarily truth)

Soundness An argument is sound if and only if it is
both valid and all of its premises are true

→ can never have a false conclusion,
because it is valid and all premises are
true. So if the conclusion was false it
would be invalid

Jointly consistent Sentences are jointly consistent if and
only if it is possible for them all to be
true together

If in one line all main operators are the
same

Jointly inconsistent Sentences are jointly inconsistent if and
only if it is not possible for them all to be
true together

→ valid, because not all sentences can
be true together, so impossible for all
premises to be true together

If there is no line where all main logical
operators are true

Necessary truth A sentence is a necessary truth if and
only if it is true and it is not possible to
be false