2/5/08
Reading
Hausman[2007] Logic and Philosophy Chapter 10
[The core of what follows is from Leblanc and Wisdom [1972] p.117 and f.]
Symbolization using the Universal Quantifier (of non relational English)
‘Everything is lovely’ we understand as meaning ‘Whatever thing you may choose, it is lovely’ and this becomes
(x)Lx
Similarly ‘Nothing is going right’ is read as ‘Whatever thing you may choose, it is not going right’ and this becomes
(x)~Rx
‘Violets are blue’ is read ‘Whatever x you may choose, if it is a violet, then it is blue’ which is
(x)(Vx⊃Bx)
Everything is either material or spiritual.
(x)(Mx∨Sx)
Nothing is both round and square.
(x)~(Rx&Sx)
All and only material objects obey physical laws.
(x)(Mx≡Px)
Everything fell off the shelf.
(x)(Ox⊃Fx)
All pacifists are Quakers.
Pacifists are all Quakers.
A pacifist is a Quaker.
To be a pacifist is to be a Quaker.
Every (any,each) pacifist is a Quaker.
If anyone’s (someone’s) a pacifist, he’s a Quaker. Only Quakers are pacifists.
None but Quakers are pacifists.(x)(Px⊃Qx)
No adults are trustworthy.
(x)(Ax⊃~Tx)
No babies are unattractive.
(x)(Bx⊃~Ux)
Old doctors are all conservative.
(x)((Dx&Ox)⊃Cx)
Doctors and lawyers are all conservative.
(x)((Dx∨Lx)⊃Cx) (*note the 'or' *)
People are intelligent if they are witty.
(x)(Px⊃(Wx⊃Ix))
No intelligent men are lonely if they are young and healthy.
(x)((Mx&Ix)⊃((Yx&Hx)⊃~Lx))
Symbolization using the Universal Quantifier (of English with relations)
Peter hates everything.
(x)Hpx
Everything is a delusion caused by God.
(x)(Dx&Cxg)
Raewyn gets everything she wants.
(x)(Wrx⊃Grx)
Nothing that Raewyn saw was new.
(x)(Srx⊃~Nx)
Symbolization using the Existential Quantifier (of non relational English)
‘Something fell off the shelf’ is understood as ‘There is at least one thing, x, such that x fell off the shelf’.
(∃x)Fx
‘Some teachers are infallible’ is understood as ‘There is at least one thing, x, such that x is a teacher and x is infallible’.
(∃x)(Tx&Ix)
Some teachers are not infallible.
(∃x)(Tx&~Ix)
Something is a centaur.
There are centaurs.
There is a centaur.
Centaurs exist.(∃x)Cx
Some tigers are mean if they are hungry.
(∃x)(Tx&(Hx⊃Mx))
Some young folk are neither rich nor unhappy.
(∃x)((Yx&Fx)&~(Rx∨~Hx))
Symbolization using the Existential Quantifier (of English with relations)
Peter doesn’t understand something.
(∃x)~Upx
Somebody lost something.
(∃x)(∃y)(Px&Lxy) or (∃x)(Px&(∃y)(Lxy))
Symbolization using both Quantifiers (of English with relations)
‘Everything has a cause’ becomes ‘Whatever thing you may choose, something (or other) is the cause of it’.
(x)(∃y)Cyx
‘Something is the cause of everything’ becomes ‘There is a something (the same thing) such that whatever thing you may choose, that something is the cause of it’.
(∃y)(x)Cyx
Everything is the cause of everything.
(y)(x)Cyx