Saying the Same Thing Concepts Counting by Sentence

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 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 the same sense, i. e. dictionary-meaning. They are synonymous. Counting by PROPOSITION is another way of counting the same things: 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. tom. AHto 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, 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 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! 18 ag l F 12

Example: A Question from an Old Quiz Somebody’s been eating my porridge Somebody’s been eating Mom’s porridge F__1 Papa and Mama are uttering the same token sentence. T__2 Papa and Mama are uttering the same type sentence. T__3 Papa and Mama are expressing the same proposition. F__4 Papa and Mama are making the same statement. F__5 Mama and Baby are expressing the same proposition. T__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 context-independent 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 - true English* 4 = ***** 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 English-Speaker English*-Speaker

True ** + ** = ***** False 2 + 2 = 4 - true 2 + 2 = 4 - false 2 + 2 = 5 - true English* 4 = ***** 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. Changing language doesn’t change the world!