Saying the Same Thing
Concepts
• Counting by
– Sentence token
– Sentence type
– Proposition
– Statement
• Synonomy
• Ambiguity
• Context Dependence
• Sense
• Reference
• Indexical
What we’re doing here
• Arguing that there are necessary truths
• Explaining how sentences have meaning in virtue of
the “families” to which they belong
• Noting that the meaning of a sentence depends on
the language in which it figures and, sometimes, its
context of utterance.
Different Ways of Counting
8 individual objects
Different Ways of Counting
3 colors
Different Ways of Counting
2 shapes
Are they the same?
Same shape,
Different color
Different shape,
Same color
The Moral: we can count things in different
ways, and come up with different correct
answers when counting the same objects.
There are 4 individual objects, 3 colors and 2
shapes represented in this picture.
Count the letters . . .
BANANA
Counting by TYPE
BANANA
There are 3 letters of the alphabet in “banana”
Counting by TOKEN
BANANA
There are 6 individual letters in “banana”
Type/Token Ambiguity
• “My husband and I drive the same car.”
• “Tweedledee and Tweedledum are identical twins.”
2 sentence tokens - 1 sentence type
1.
John is Paul’s brother
2.
John is Paul’s brother
TYPE and TOKEN aren’t
different kinds of things like
apples and oranges--they’re
just two different ways of
counting the same things.
We can count sentences by
token or by type.
1 proposition
1.
John is Paul’s brother
2.
John is Paul’s brother
3.
John is the male sibling of Paul
1, 2 and 3 express the same proposition
because they have they have the same sense,
i.e. dictionary-meaning. They are synonymous.
Counting by PROPOSITION
is another way of counting
sentences
What are propositions really???
• Equivalence classes
– example: denominations of bills
• Equivalence relation
– reflexive
– symmetric
– transitive
Equivalence Relation
• In mathematics, an equivalence relation is the relation that
holds between two elements if and only if they are members of
the same cell within a set that has been partitioned into cells
such that every element of the set is a member of one and only
one cell of the partition.
– These cells are formally called equivalence classes.
– The intersection of any two different cells is empty
– the union of all the cells equals the original set.
•
Examples
– Being the same shape
– Being the same color
– Being the same (monetary) denomination
Equivalence Class
• 14 bills – 4 denominations
• More about equivalence classes here
Synonomy
You should eschew obfuscation.
tomAHto
You should avoid obscurity.
Snow is white.
tomato
Owsnay isay itewhay.
Sentences are synonymous
when they express the same
proposition.
Ambiguity
I’m high!
Flying planes can be dangerous.
A sentence is ambiguous when it can be
used to express different propositions.
Context Dependence
A sentence is context dependent when what it
says depends upon the context of utterance, that
is where, when, by whom and in what
circumstances it is said.
Examples of context dependent sentences
• I am a philosopher
• Los Angeles is to the north of here
• It’s 10 am now.
• This dang thing is heavy!
Plato and Aristotle saying that they’re philosophers
I’m a
philosopher
Plato is a
philosopher
I’m a
philosopher
Aristotle is a
philosopher
Indexicals
• Words whose reference changes systematically
depending on where, when, by whom and in what
circumstances they are uttered.
• Examples: I, you, he, today, yesterday, tomorrow,
here, there, this, that, now…
Sense/Reference
Distinction
• “meaning” is ambiguous!
– “bachelor” means “unmarried male who never
has been married.
– I mean him!
• Frege “Auf Sinn und Bedeuting”
• Sense: dictionary-meaning
• Reference: “aboutness”, picking out
Sense and Reference
sense
square
square
reference
Same Statement
•
Sentences make the same statement when they
say the same thing about the same thing.
•
Example
1. 50 is even.
2. The number of states in the US is even.
• 1 is always true but
2 was not true in 1812!
Example: A Question from an Old Quiz
Somebody’s
been eating
my porridge
Somebody’s
been eating
my porridge
Somebody’s
been eating
Mom’s porridge
__1 Papa and Mama are uttering the same token sentence.
__2 Papa and Mama are uttering the same type sentence.
__3 Papa and Mama are expressing the same proposition.
__4 Papa and Mama re making the same statement.
__5 Mama and Baby are expressing the same proposition.
__6 Mama and Baby are making the same statement.
Which sentences say the
same thing?
1.
[stated Sep 10, 2015] Today is Thursday.
2.
[stated Sep 11, 2015] Today is Thursday.
3.
[stated Sep 11, 2015] Yesterday was Thursday.
It depends on how you count!
Same proposition/different statements
1.
[stated Sep 10, 2015] Today is Thursday.
2.
[stated Sep 11, 2015] Today is Thursday.
3.
[stated Sep 11, 2015] Yesterday was Thursday.
1 and 2 have the same sense-same dictionary-meaning
Same statement/different propositions
1.
[stated Sep 10, 2015] Today is Thursday.
2.
[stated Sep 11, 2015] Today is Thursday.
3.
[stated Sep 11, 2015] Yesterday was Thursday.
1 and 3 don’t have the
same dictionary-meaning
but they pick out the
same day.
They say the same thing
about the same thing.
Translating into timeless sentences
1.
[stated Sep 10, 2015] Today is Thursday.
2.
[stated Sep 11, 2015] Today is Thursday.
3.
[stated Sep 11, 2015] Yesterday was Thursday.
1’ Sep 10, 2015 is a Thursday.
2’ Sep 11, 2015 is a Thursday.
contextdependent
1.
[stated Sep 10, 2015] Today is Tuesday.
2.
[stated Sep 11, 2015] Today is Tuesday.
3.
[stated Sep 11, 2015] Yesterday was Tuesday.
1’ Sep 10, 2015 is a Tuesday.
2’ Sep 11, 2015 is a Tuesday.
not contextdependent
We can translate context-dependent sentences into
sentences that are not context-dependent
Summing up so far…
• We distinguished different ways of counting
sentences
– by sentence token
– by sentence type
– by proposition
– by statement
• We noted that some sentences were contextdependent because they included indexicals but
• that they could be translated into contextindependent sentences.
The Moral of the Story
When we ask whether two sentences (or speakers) are
“saying the same thing” we need to be clear about what
we’re asking.
• Expressing the same proposition?
• Making the same statement?
• Uttering the same noises (or making the same marks)?
A Puzzle About Necessary Truths
How We Argue in Philosophy
• When we want to argue for a thesis we
need to respond to objections
• So sometimes we consider an
argument for something we want to
show is false
• In order to refute it
• We will consider a bad argument that
is supposed to show there are no
necessary truths
• And refute it
Bad argument
(supposed to show there are no necessary truths)
2 + 2 = 4 - true
2 + 2 = 4 - false
2 + 2 = 5 - false
2 + 2 = 5 - true
English
English*
4 = ****
4 = *****
5 = *****
5 = ****
Actual World
W*
This argument can be generalized!
• It is contingent that any given word has the sense it
does: we can change language!
• So it seems there can be no necessary truths!
• But this is crazy: changing language doesn’t change
the world! So we have to respond to this threat!
They’re making the different noises…
but expressing the same mathematical truth!
** + ** = ****
** + ** = ****
2+2=4
2+2=5
English-Speaker
English*-Speaker
Now they’re making the same noises…
but expressing the different mathematical propositions!
** + ** = *****
** + ** = ****
2+2=4
2+2=4
English-Speaker
English*-Speaker
True
** + ** = ****
** + ** = *****
False
2 + 2 = 4 - true
2 + 2 = 4 - false
2 + 2 = 5 - false
2 + 2 = 5 - true
English
English*
4 = ****
4 = *****
5 = *****
5 = ****
Actual World
W*
Changing language doesn’t change the world!
Lincoln’s Riddle
If you call a tail a leg, then how many legs
does a dog have?
Four.
Calling a tail a
leg doesn’t make
it one.
The End
Changing language doesn’t change the world!