class 6 Flashcards
Non-quantified sentences are made of
‘names’ (singular terms) and
predicates in various combinations
* Mary [name – singular term] is blonde [predicate]
Singular term + predicate = sentence (state of affairs)
Basic transition: Mary is blonde or red
Bm v Rm
Basic transition: This chair is red and made of wood
Rc ^ Wc
Saturation of a predicate
Adding a subject so that they form true, false or senseless sentences:
* Biden is the President of the US →true
Gilles loves Mary
Lgm
Mary is John’s sister
Smj
Mary loves herself
Lmm
Loving someone
Lxy
Loving oneself
Lxx
Gilles loves Mary and Sophie, and Mary loves Brown
Lgm ^ Lgs ^ Lmb
Gilles loves Mary iff Mary does not love Robert
Lgm <–> –|Lmr
If Robert loves Mary then Gilles and Brown are sad
Lrm → (Sg ^ Sb)
All
∀ (universal quantifier)
Some
∃ (existential quantifier)
Everyone runs
∀xRx
For any value/substitution of x, x runs
Someone runs
∃xRx
For some values of x, x runs
There is at least one x which runs
All philosophers are wise
∀x(Px → Wx)
For any x, if x is a philosopher, then x is wise
Some philosophers drink beer
∃(Px ^ Dx)
There is at least one x, who is a philosopher, and drinks
beer
No philosopher is wise
∀x(Px → –|Wx)
For all x, if x is a philosopher, then x is not wise
or
–|∃x (Px –| Wx)
There is no x who is P and W
Some philosopher is not wise
∃x(Px ^ –|Wx)
There is some (at least one) x who is a philosopher and is not wise
Nobody cries
–|∃ xCx there is no x who cries
∀x–| Cx for any x, x does not cry
Contrariety
(A-E on top of the square: every – none / all – no)
- Mutually exclusive but not jointly exhaustive sentences
- Exclude each other, but there might be other possibilities
- Cannot be both true but can be both false
Contradiction
Contradiction (diagonal: A-O, E-I)
- Mutually exclusive and jointly exhaustive sentences
= exclude each other - cannot be both true - jointly exhaustive = there cannot be any other possibility - cannot be both false
Sub contrariety
- I-type and O-type propositions (particulars, not universal)
-can be both true but not both false
use –> for universal statements,
^ for particular ones
ok
