Notes—February 18, 2013

Ferdinand de Saussure
o Notion of a sign
o The signs ‘2’ and ‘II’ share the same referent, but not the same form.
Therefore, they are not the same sign.
o The English prefix “un—“ has two different meanings. Though the
form is the same, the meanings (the “signified”) are not. Therefore,
not the same sign.
o The things in the world that we refer to and the forms we use to refer
to them are separate.
Sign
Signified: what the
form refers to

Signifier: the form
used to refer to
something in the
world
Iconicity versus Arbitrariness
o Iconicity: the form attempts to resemble the meaning
 example: the symbol that means “stairs” shares some aspect of
a staircase (interesting, though, that it does not take the form
of a staircase as we actually see staircases)
o Arbitrariness (Also called “symbolic,” but that’s confusing and kind of
silly): the form does not attempt to resemble the meaning
 most words in language are arbitrary
 Personal soapbox: it is a misconception that signed languages
are entirely (or even mostly) iconic. Though they do employ
more iconicity than spoken languages, they are primarily
arbitrary. Signed languages are not universal languages. For
instance, British Sign Language is not mutually intelligible with
American Sign Language.

Token versus Type
o has to do with individuals versus sets
o “I own that book” can be taken in two ways:
 “That book, right there, is mine” (Token interpretation)
 or “I own a copy of that book” (Type interpretation)
o The above example also serves to demonstrate a distinction between
natural languages and formal languages—this type of ambiguity
would not occur in a formal language
Example from Homework: Beth Tableaux from problem 12, b
True
False
pq
q& r
q
r
p&q
~p
p
q
---------------------
One subtableaux closes, but one remains open. Therefore, the
statement is invalid. Counterexample: p=0, q=1, r=1.

Polish Notation
Symbol
Etymology
Meaning
C
A
K
E
N
Condition
Alternation
Conjunction
Equivalence
Negation
Conditional
Or
And
Biconditional
Not
Example of
Syntax
Cpq
Apq
Kpq
Epq
Np
Translation
pq
pvq
p&q
p  q
~p
*Interesting note: While our logic system seems to mirror the SVO (Subject Verb
Object) argument structure of English, the Polish notation more closely resembles a
verb-first language.

Note on Set Theory and language
o A proposition (e.g.“It is raining”) is the set of circumstances under
which the sentence is true.
o however, this does not distinguish between the real world and all
possible worlds—so, “gremlin” and “unicorn” would have essentially
the same referent, the empty set