Possible Worlds

Think of possible worlds as various ways the world could have been.  You could be going to a different college.  There is a description of a world that has you going to a different college.  Someone else could be the president.  That is there is a coherent description of a world in which someone else is the president.  All the ways the world could have been are different possible worlds (and of course our world—the actual world—is a way the world could have been).  You can think of a possible world as a maximally consistent description of the way things could have been.  Our world is like that.
Possible worlds can be thought of as simply helpful tools for regimenting language and logic.  They help us get clear on the meaning and logical patterns associated with particular terms/concepts such as—would, could, should, must, might, can, cannot, necessarily, possibly, impossibly, etc. Possible worlds have been used to help clarify various issues in ethics, metaphysics, epistemology, philosophy of religion, philosophy of mind, philosophy of language, linguistics, computer science, and other areas.  
Below I use the term/concept ‘proposition’ to refer to the content of a declarative sentence or belief. So, a proposition is the bearer of a truth-value.  Take for example the sentence ‘The earth is round.’  That sentence (the inscription on this page) refers to something that is either true or false, can be expressed in different language, and can be believed by different people at different times.  That thing (the thing that is expressed by the sentence that can be either true or false, etc.) is the proposition that the sentence refers to. 
The information below is meant to help you see how possible worlds are used by philosophers and how they can help us think about various issues.
(NOTE: iff = if, and only if; just in case = iff)
Maximality: for every proposition p, either p or not-p at w
Maximality ensures that worlds will be complete.  It tells us that for every single proposition there is, either it is true or false at w.  We should add a consistency requirement as well, so that we don’t end up with impossible worlds, but we can leave that off for now.
W is a possible world just in case w is a complete description of the way a world is.
W is a complete description of the way a world is iff at w for all p, either p or not-p.
            This is just another way of stating Maximality
So W is distinct from W* iff there is at w, p and at w* not-p (for some p).
In other words, in order to get two different worlds there needs to be some difference between them.  Since worlds simply are complete and consistent sets of propositions, the only way to get a difference between two worlds is through a difference in the distribution of truth-values amongst the worlds’ propositions.  
Worlds differ from each other if different propositions are true at each of them.
Our world is a possible world (our world is a maximally complete description of the way a world is) and it is called the actual world.
A proposition p is true just in case p is true at the actual world.
            My Name is David E. Alexander.  
                        The above sentence expresses a true proposition. 
A proposition p is possibly true just in case there is a world w such that p is true at w
            My name is Jonathan Alexander
                        The above sentence expresses a possibly true proposition
A proposition p is necessarily true just in case for all w, p is true at w
            2+2=4
                        The above sentence expresses a necessarily true proposition
A proposition is contingently true just in case there is a world w such that p is true at w and a world w* such that p is not true at w*
            My name is David E. Alexander
                        The above sentence expresses a contingently true proposition

Exercise: what is the relationship between the various types of truths that propositions can have?
Example: if P is possibly true, what follows?  Is P true? Is P necessarily true?  Is P contingently true?

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