[Vision2020] [Q2] Induction Part III

[Art Deco]

Well Michael, we progress handily towards a meaningful discussion of the problem of evil and related issues.  But before we examine your succinct description of the inductive process, we still have a few little things to agree upon.  I do not expect any disagreement to what follows.  But having come laboriously this far together, it is best to make sure.

 

 

C.    Brief but Important Remarks on Arguments, Truth, Part I

 

Some arguments which appear to be inductive are really deductive, especially when obviously missing premises (but necessarily not all) are added.

 

Example:  The frequently made argument:

 

If two regular coins are tossed, it is less likely than not that two heads will be the result.

 

can be reformulated in a more full-bodied valid deductive argument as follows:

 

[P1]        If a regular coin is tossed, the probability of a result of a head is 0.50.

[P2]        Since the results of two coin tosses of a regular coin are independent of each other, the probability of a result of two heads in two tosses is the product of the probabilities of the result for each toss.

 

              Therefore,

 

[C1, P3]  The probability of two heads resulting from two tosses of a regular coin is (0.50)(0.50) = 0.25.

[P4]        0.25 is less than 0.50.

 

Therefore,

 

[C2]        If two regular coins are tossed, it is less likely than not that two heads will be the result.

 

 

The example above also demonstrates two things:

 

[1]   Correct mathematical calculations are valid deductive arguments.

 

A further example (with some obvious premises elided) with the intended conclusion:  Matt's residential lot is larger than Mike's:

 

[P1]        The area of a lot is calculated by multiplying its width by its length.

[P2]        Matt's lot is 70' by 82'.

[P3]        Mike's lot is 69' by 81'.

 

[C1, P4]  The area of Matt's lot is 5,740 square feet.

[C2, P5]  The area of Mike's lot is 5,589 square feet.

 

[P6]        5,740 is greater than 5,589.

 

Therefore,

 

[C3]        Matt's residential lot is larger than Mike's.

 

 

[2]   There is a very significant difference between asserting that a sentence is true and asserting some probability of its truth.  It is important in attempting to characterize the inductive process to distinguish clearly between truth and the probability of the truth of sentences.

 

Example:  

 

John Kerry will be the next president of the United States.

 

The truth or falsity that sentence may be determined eventually.  However, at this time (11/28/05) there exist a large number of different estimates of the probability of the truth of that sentence based on different assumptions and/or different inductive arguments.

 

Further, there are billions of sentences whose truth cannot be determined and whose probability of truth would be very difficult to estimate accurately.

 

Example:

 

On November 30, 1309 at 12:30 in the afternoon there were exactly 35 deer on the Moscow Mountain land now owned by J. Douglas Kohl.

 

One point of the above examples is:  There are a lot of things that humankind does not know and most likely will never know with any degree of assurance.  This state of affairs is part of the meaning of the sentence:  We live in a contingent universe.

 

 

In particular, the truth or probability of the truth of a conditional sentence [If X, then Y.] is sometimes very difficult to determine.

 

The determination of truth or probability of the truth of:

 

If it rains really hard on Lower Hog Eye Road between 10:00am and 11:00am today, Lower Hog Eye Road will be wet today at 11:00am.

 

is not difficult.  However, the determination of truth or probability of the truth of:

 

If Preacher Wilson Jones wears his short red dress and matching red high-heeled shoes on July 4, 2006, the Chicago Cubs will win the World Series in 2009.

 

is more problematic because there is no apparent connection between the two events named in the conditional.

 

The problem of determining the truth or probability of the truth of conditional sentences is brought about because conditional sentences like "If X, then Y." assert a connection of some kind between X and Y whose truth or probability of truth must be determined in some manner.

 

 

Michael, I apologize for subjecting you to such trivia as above.  As an erudite scholar, you probably resent being put through such an elementary catechism, especially from an amateur.  However, we don't want to seriously discuss the problem of evil without a basic understanding and agreement of certain very elementary things.

 

Please let me know if you agree with the above or not.  Then we can see if we agree on the ways of determining the truth and/or the probability of truth of those sentences used as premises in arguments supporting knowledge claims.


Wayne A. Fox
1009 Karen Lane
PO Box 9421
Moscow, ID  83843

(208) 882-7975
waf at moscow.com

-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mailman.fsr.com/pipermail/vision2020/attachments/20051128/e0ed99ec/attachment-0001.htm