we use Greek letters as schematic variables α, β, γ, etc.
These allow us to talk about all propositions of our formal language
for now we only need schematic variables for propositions
(we don’t need schematic variables for individual words)
Atomic proposition:
we use single letters as atomic propositions: P, Q, R, etc.
They are the most basic propositions (do not contain any connectives)
they correspond to simple sentences such as “it’s raining”
They are used as the building blocks to construct larger, more complex propositions.
exercise session
No philosopher is illogical. Jones keeps making argumentative mistakes. No logical person keeps making argumentative mistakes. All existentialists are philosophers. So, Jones is not an existentialist.
- No philosopher is illogical
- Jones keeps making argumentative mistakes
- No logical person keeps making argumentative mistakes
- All existentialists are philosophers
- All philosophers are logical (from 1)
- All existentialists are logical (from 4, 5)
7. Jones is an existentialist (supp.)
8. Jones is illogical (from 2, 3)
9. Contradiction (from 6, 7, 8)
No experienced person is incompetent. Jenkins is always blundering. No competent person is always blundering. So, Jenkins is inexperienced.
- No experienced person is incompetent
- Jenkins is always blundering
- No competent person is always blundering
- Jenkins is incompetent (from 2, 3)
5. Jenkins is experienced (supp.)
6. Contradiction (from 4, 5, 1)
Either the butler or the cook committed the murder. The victim died from poison if the cook was the murderer. The butler carried out the murder only if the victim was stabbed. The victim didn’t die from poison. So, the victim was stabbed.
- B or C
- if C, P
- only B, if S
- not P
not a valid argument
If the Cook is the killer, the victim would have died from poison
The Butler can be the killer only if the victim was stabbed.
The victim didn’t die from poison.
ONLY IF IS SUCH A STUPID FUCKING PIECE OF SHIT GOD FUCKING DAMN IT NEED TO REMBER FOR EXAM