Kaplan and two-dimensionalism

(The following is adapted from Laura Schroeter’s article “Two-Dimensional Semantics”)

"We can think of contexts as what David Chalmers calls ‘centered worlds.’ A centered world is a world, an agent within that world, and a time when the agent exists or utters something within that world <w, a, t>"

(The following matrices are adapted from Robert Stalnaker)

Trump’s use of ‘I’ in his inaugural address:
w1
w2
w3
⟨w1,DT,t0⟩
DT
DT
DT

The leftmost column represents context
The top row represents the world that takes us to an assessment of the utterance

Left is context of utterance
Top row is circumstance of evaluation

So, evaluating Trump’s use of ‘I’ in w1 requires that we keep the referent of ‘I’ fixed when we plug in w2 and w3.  So, ‘I’ is very much like a rigid designator.

In other words, possible worlds get appealed to twice—once at the level of character—and once again at the level of content.

Character: w1 in <w1, DT, t0> is the relevant context of use (in this case, the use of the expression ‘I’) and once this gets plugged in, the content of the expression can be determined from various circumstances of evaluation.

Content: the circumstances of evaluation (the top row) allow us to assess the content of the utterance from various vantage points—different possible worlds. As you can see, each circumstance of evaluation yields the same value—namely, DT. So, once the character is fixed by the context, the content of ‘I’ yields the same referent.

Kaplanian character of ‘I’:
w1
w2
w3
⟨w1,DT,t0⟩
DT
DT
DT
⟨w2,BS,t0⟩
BS
BS
BS
⟨w3,HRC,t0⟩
HRC
HRC
HRC

Left column: context of use (character is a function from context to content)
Top Row: circumstance of evaluation (Content is a function from possible world to truth value or semantic value more generally)


Kaplanian character of ‘the inaugural speaker in 2016’:
w1
w2
w3
⟨w1,DT,t0⟩
DT
BS
HRC
⟨w2,BS,t0⟩
DT
BS
HRC
⟨w3,HRC,t0⟩
DT
BS
HRC

Do you see how the character (and the content) of ‘the inaugural speaker in 2016’ differs from the character (and the content) of ‘I’? 

When the context is fixed (the left column), the content of the expression yields a different individual (the extension varies) depending on the circumstance of evaluation. Since in w2 Bernie Sanders is the inaugural speaker (see the context side), when the circumstance of evaluation is w2 (top row), Donald Trump’s use of the expression ‘the inaugural speaker’ in w1 picks out Bernie Sanders. 

When you and I discuss how it is possible that the inventor of bifocals was Thomas Jefferson, we are uttering the expression ‘the inventor of bifocals’ from our world (w1) and evaluating it (determining it’s content or extension) from w2. Since in w2 Thomas Jefferson invents the bifocal, w2 represents Jefferson as the value of the expression. 

Kaplanian character of ‘Donald Trump’:
w1
w2
w3
⟨w1,DT,t0⟩
DT
DT
DT
⟨w2,BS,t0⟩
DT
DT
DT
⟨w3,HRC,t0⟩
DT
DT
DT

This is as it should be since ‘Donald Trump’ is an RD.
No matter the context of use (left column) the content of the expression ‘Donald Trump’ yields the same semantic value, namely, Trump himself.

Assume Trump would attend the inaugural address of Sanders but not of Clinton, Sanders would avoid the inauguration of anyone who defeated him, and Clinton would attend Sander’s inauguration but not Trump’s.

Kaplanian character of ‘I am here’
w1
w2
w3
⟨w1,DT,t0⟩
T
T
F
⟨w2,BS,t0⟩
F
T
F
⟨w3,HRC,t0⟩
F
T
T

Look at the various ‘Fs’: They represent the fact that the utterance of ‘I am here’ is contingent. I did not have to be here right now. I could have been somewhere else, and thus ‘here’ would have picked out a different location. So, Trump’s utterance of ‘I am here’, where ‘here’ picks out the inaugural address turns out to be false in w3 since he would not have attended Clinton’s inaugural address. 

The content of the expression ‘I am here’ given the context <w1, DT, t0> is that Trump is in DC on Jan 21, 2016. Since he is not in DC on Jan 21 in w3, the expression is false. 

In other words, we want our semantics to conform to the fact that it is possible that I (the speaker) am not here (this particular location). It better not turn out that our semantics entails that ‘I am here’ is a necessary truth. If it did, then the speaker would be a necessary being and the location would be a necessary place. But that is either (a) not true at all, or (b) if it is true, it should not be entailed by the semantics but rather by lots of argument.

Look at the diagonal: ‘I am here’ is true whenever it is uttered.  For every possible context, the sentence will be true at the world of that context.  When we focus on the context—the world where DT, BS, or HRC is speaking—the utterance always comes out true according to that world.  So, where BS is the speaker and the world is one where he is at the inauguration, the utterance is true.  

This is supposed to be an instance of an apriori contingent truth. It is controversial, but the cool thing here is that 2D semantics seems to get the semantics of it right, even if the epistemology and metaphysics is controversial. So, 2D semantics allows us to do what it seems we should be able to do at least partially, namely, provide a semantics for a language that is as epistemically and metaphysically neutral as possible.

Of course, it is not completely neutral. All sorts of assumptions are at work, but the hope is that these assumptions are the most minimal and innocent—every plausible semantics will have to have them.

Comments

Post a Comment

Popular posts from this blog

Kaplan and Lewis

Let's see if we can make sense of the differences between Kaplan and Lewis.  Here is one way to see what Lewis is up to: Kaplan-to-Lewis Translation Method S is true relative to context C iff the character of S determines in C some content CON and CON is true relative to C It is important to see that what the above says is that Kaplan’s two levels of meaning are reducible to one level of meaning (remember my remark that Lewis is the arch-reductionist). The left side (the stuff before the ‘iff’) is equivalent to the right side (the stuff after the ‘iff’). So, if the above is correct, Kaplan’s two levels of meaning can be reduced to one level of meaning. It is not as though character and content are gone. They are just combined in one stage. The context C gets all of the stuff relevant to the character stage AND all of the stuff relevant to the content stage. So, C gets bloated in order to handle everything that is relevant for determining a truth-value of S. We just...
Read more

Grice's First Try

1 st Try : “x meantNN that p” iff x was intended by S to induce a belief in H First, let’s get clear on what this 1 st Try is saying: ‘x’ refers to an utterance of some sort, where even gestures and various other kinds of conventional signals count as utterances (e.g. three rings of the bell…). ‘MeantNN’ stands for ‘conventionally means’ or ‘has a meaning that is not determined by some natural law or whatever.’ ‘p’ refers to the proposition that the utterance expresses. For example, the proposition that my utterance of “Snow is white” and your utterance of “La nieve es blanca” both express the same exact proposition.  So, on the left side we have: an utterance of x conventionally means that p The right side should be fairly clear. It is saying that the utterance is intended to bring about a belief in someone. Putting this all together we get: an utterance of x conventionally means that p iff the utterance of x is intended by S (the utterer) to bring about a belief in someo...
Read more

Donnellan on Russell

Attributive “A speaker who uses a definite description attributively in an assertion states something about whoever or whatever is the so-and-so”  Referential “A speaker who uses a definite description referentially in an assertion ... uses the description to enable his audience to pick out whom or what he is talking about and states something about that person or thing” “Smith’s murderer is insane.”  Russell : definite descriptions only apply to attributive uses (if it applies to anything) Donnellan : it is possible for someone to say something true even though nothing satisfies the description ‘the F’ in ‘the F is G.’ Semantics or Pragmatics              “Smith’s murderer is insane.”              Does the meaning of this sentence change on different occasions of use?          ...
Read more