Philosophy 105
Fall 2005
Lecture Notes - Past to Future Arguments

Before turning to standard statistical arguments, it will be helpful to consider another kind of argument. Suppose I argue as follows

At least 50 inches of snow has fallen in Rochester every winter up till now. So, at least 50 inches of snow will fall in Rochester next winter.

The most straightforward reconstruction:

1. At least 50 inches of snow has fallen in Rochester every winter up till now.
2. At least 50 inches of snow will fall in Rochester next winter.

You could reword so that it follows an “All As are Bs” form. Try it.

1. All Rochester winters are times when at least 50 inches of snow fall.
2. This coming Rochester winter is a time when at least 50 inches of snow falls.

We could symbolize and better display the form:

W: A winter in Rochester
S: A time and place where more than 50 inches of snow fall.
t: The Rochester winter of 2005/6

The intended conclusion is: t is an S.

1. All Ws are Ss.
2. t is a W.
3. t is an S.

Valid. But (1) is the wrong premise. The premise was about the past. Be sure that you understand this point.

Suppose we try:

1. All past Ws are Ss.
2. t is a W.
3. t is an S.

Ill-formed. If you changed (2) to: t is a past W, the argument would be valid, but the revised (2) is false.

You could use cheap validity: If (1) then (3).

What you need is some version of a principle saying that the future will be like the past. It’s very hard to formulate that in any generally acceptable way. The future will be like the past in some ways, but not others: imagine predicting that next month will not be November 2005 because every previous month has not been that month. So maybe the best you can do is tailor a principle to the case under consideration and see how reasonable it is. For the present case, it would be something like:

1. Having more than 50 inches of snow in Rochester is a weather pattern that has held for all previous years. (All past Ws have been Ss.)
2. In most cases, weather patterns that have held for all previous years continue to hold for the next year.
3. Having more than 50 inches of snow in Rochester will hold for next year. (i.e., t is an S).

This is somewhat awkward, and saying exactly what the pattern is would be tricky. The key point is that in reconstructing arguments from how things have been in the past to how they will be in the future, the seemingly obvious reconstructions don't work. You need to make use of a fairly complicated principle linking past cases to future cases.

You can see the IBE idea underlying this: the best explanation of the past regularity is that there is a general pattern that it falls under. This is part of the reason we accept (2) in the final version of the argument.

Lesson to be drawn from these examples: you have to be very careful about the use of generalizations. Make sure that the argument is formulated so that the generalization is plausible and that the premises other than the generalization specify all the factors that you need to apply the generalization to the thing the argument is about.

Read section I of Chapter 9. Ask questions next time if you have them. This will not otherwise be covered in class. I’ve done it a little differently here than I did in the book. Exercises about this material are likely to be on the next quiz. Try out the exercises at the end of the section.