11/30/06
[The core of this 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