[Vision2020] Induction

Sat Nov 12 09:54:54 PST 2005

Michael,

Please do not disgrace yourself by lying and imitating the rhetorical devices of your co-congregants straight out of The Art of Deception.  I mentioned before that Flew wrote cogently about the Euthyphro.  I did not claim he was an apologist for atheism nor did I even know at the time what his advocacy on the issue of theism/atheism is/was.  If you think I did, please direct V 2020ers and myself to that particular post -- I will apologize for my harsh words.  

I append below the line the contents of the email with the two questions previously posed.  These questions occur as the 6th and 5th paragraphs from the end.

Sorry to have to rebuke you.  I guess certain sub-cultural habits die hard even with the best of intentions.

Art Deco (Wayne A. Fox)
deco at moscow.com

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Michael,

As the next step in our discussion about the nature of the alleged god claimed by Christ Church, it is important to see whether we agree or not on the nature of the inductive process - empirical/quasi-empirical induction, not mathematical induction as defined by the Peano Postulates.

I beg for your patience in this matter for I am old and slow-witted.  This means that I must make sure that I have correctly and clearly understood what you have said and to try to make my replies to you as clear and precise as possible.  Being precise sometimes means using longer, more technical explanations so that ambiguity can be eliminated as far as possible or at least greatly reduced.  In my experience, a large part of being unable to resolve disagreements of any kind occurs because the parties are each using the same words to mean different things.  We need to avoid this pitfall, if we are to have a fruitful discussion.

My being old and slow-witted also means that I can only proceed by very small steps, since my capacity is severely limited.

Arguments, Part I

First of all, I think we are in almost complete agreement about the fundamental difference between a deductive argument and inductive argument.

So as we do not get sidetracked by irrelevant issues, I am intentionally restricting, I hope with your agreement, our discourse to the English language, and I am also assuming that the discussion will occur via email mainly by the exchange of sentences written in English (see the definitions below) accompanied by perhaps a diagram or two labeled and explained in English.

Let's start to find out the extent of our agreement by seeing whether you agree, for the purposes of our discussion, with the following slightly downsized, but not unelaborated, traditional characterizations of the nature of deductive and inductive arguments:

An argument can be described as a set of well formed English sentence(s) called the premises and another set of well formed English sentence(s) called the conclusion(s) related linguistically such that it is claimed that the truth of the premise(s) support in some way the truth of the conclusion(s).

Example:

[P1] Navonod Carbuncle is a slovenly know-it-all.

[P2] Guido does not like slovenly know-it-alls.

Therefore,

[C]  It is unlikely that Guido will be inviting Navonod Carbuncle to his next Tupperware/Lingerie party.

In the above argument {P1, P2} is the premises and {C} is the conclusion.

A valid deductive argument can be described as a set of well formed English sentence(s) called the premise(s) and another set of well formed English sentence(s) called the conclusion(s) related linguistically such that if the premise(s) are assumed to true, then by the very nature of the meaning of the words in the sentences, and by the structure of the argument itself as a whole, the conclusion(s) must be taken as true, provided that the meaning of all the words in all the sentences of the argument stay consistently and exactly the same throughout the entire argument.

Example:

[P1] Navonod Carbuncle has the gray pallor of death upon his visage.

[P2] All with the gray parlor of death upon their visage die with seven years from its first appearance.

Therefore,

[C]  Navonod Carbuncle will die within seven years.

In the above argument {P1, P2} is the premises and {C} is the conclusion.

Thus, in short, the distinguishing characteristic of a valid deductive argument is that in a valid deductive argument the truth of the conclusion follows necessarily from the assumption of the truth of the premises.  In other words, it would be impossible - a contradiction - for the premises to be true and also for the conclusion to be false.

An correct inductive argument can be described as a set of well formed English sentence(s) called the premise(s) and another set of well formed English sentence(s) called the conclusion(s) related linguistically such that if the premise(s) are assumed to true, then by the very nature of the meaning of the words in the sentences, and by the structure of the argument itself as a whole, the conclusion(s) has some probability, but not absolute necessity of being true, provided that the meaning of all the words in all the sentences stay consistently and exactly the same throughout the entire argument.

Example:

[P1] There are round animal tracks in Amsalu's drive which are about six inches in diameter with a claw mark at the end of each toe imprint.

[P2] Such tracks are usually made by Cougars.

Therefore,

[C]  The footprints in Amsalu's driveway were made by a cougar.

In the above argument {P1, P2} is the premises and {C} is the conclusion.

Thus, in short, the distinguishing characteristic of a correct inductive argument is that in a correct inductive argument, some probability of the truth of the conclusion is established from the assumption of the truth of the premises.

However, in a correct inductive argument, there is no claim that the truth of the premises absolutely necessitates the truth of the conclusion.  Further, other sentences whose truth is assumed may be added, such that the conclusion of the argument can be different.  That is, the additions of these new premises may change the probability of truth of the conclusion.

To forestall possible questions and problems, I have used above the term well-formed sentences to remove from use in our discussion of:

[1]   Syntactically malformed sentences such as "Red that car is."

[2]   Sentences which are self-referring or otherwise violate the Rule of Types such as "This sentence is false.", and

[3]   Syntactically correctly structured sentences for which, because of their very structure and the use of words therein, there are no apparent truth conditions, hence cannot be meaningfully said to be true or false.  An example would be "Barbequed integers forge Jesus."  Whether any particular sentence falls into this category is, of course, open to discussion and to investigation.

Please notice in the above, I have limited the discussion so far to characterizing deductive and inductive arguments.  There is no attempt in the above discussion to characterize deductive or inductive processes or any attempt to characterize induction in general.

To anticipate a question on your part:  I have used "set" terminology in the characterizations of the types of arguments because in certain anticipated parts of our discussion, using very elementary set notation will save hundreds of words, will make certain sentences much easier to understand, and will help us to be as clear and precise in our discussion as possible.

Questions to you:

[1]   Is the characterization for the purposes of our discussion of a valid deductive argument an accurate characterization?  If not, why not?

[2]   Is the characterization for the purposes of our discussion of a correct inductive argument an accurate characterization?  If not, why not?

It is important for us to agree on the definitions of deductive and inductive arguments before we proceed to a discussion of your characterization of induction, which for the sake of eliminating ambiguity, I will call the inductive process.  The discourse above is only a first step in coming to an agreement about the nature of deductive and inductive arguments and their use in validating or partially validating knowledge claims.

I am not sure that we have any real disagreement over what induction (the inductive process) as you have described it is or how it works to validate knowledge claims.  Using as clear and precise language as we progress can help us discover whether there is, in fact, a disagreement, and if so, how that disagreement might be satisfactorily resolved.

Thank you for your kindness and patience in dealing with a slow-witted, old man who can only digest and deal with esoteric subjects, if at all, a little bit at a time.  In fact, writing the above has so stretched and exhausted my meager and senile capabilities, that I must eat a whole huckleberry cream pie just to start the long process of rejuvenating myself.  I pray that some goodhearted Vision 2020 reader will give me one.

I look forward to your answers to the two questions above.

  ----- Original Message ----- 
  From: Michael 
  To: vision2020 at moscow.com 
  Sent: Saturday, November 12, 2005 8:42 AM
  Subject: [Vision2020] Induction

  Wayne:

  When you have time, I await your response to the two questions I asked in my last email on exploring the induction process. 

  Me:

  Did I miss two additional questions?  If so, give the date so that I can locate them.

  You had referenced Anthony Flew as an apologist for atheism, so I was just wondering if you had done any research on his recent conversion to theism.

  Thanks

  Michael Metzler

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