Friday, May 29, 2015

17.1 Clarification, term, Inductive Logic

Clarification of the term Inductive Logic.
With all these white swans, you can't possibly deny that all swans are white, now could you?
None of the cool kids do! You want to be in the cool kids group, now don't you?

White swans, white schmanns.  A swan is a swan is a swan.

I don't see any black swans here.  There must not be any!!

Just to be sure I was using the term 'inductive logic' in a generally acceptable way, as equivalent to my intended "preponderance of evidence," I checked wikipedia--which serves as a good arbiter of generally accepted knowledge of its readers.

I was (using the term rightly).  I stand with my assertion that it would be formally (deductively) in error to deny the existence of God, Santa Claus, the Flying Spaghetti Monster or the Invisible Pink Unicorn.  I believe there is a formal proof of the existence of God, but I'm treating it as an interesting exercise rather than anything more, because, like the argument in Plato's Republic I-III, it may be correct but unpersuasive.

And, again, My Project here is to introduce a preponderance of evidence that God exists. All argument has its existential limits, but following Augustine, I'm committed to faith being reasonable.

Another aside.  I am of the opinion that all the interesting questions of life and art are inductive, i.e., follow from a preponderance of evidence rather than from deductive certainty from known premises.

Here are the relevant paragraphs.

Inductive vs. deductive reasoning[edit]

Unlike deductive arguments, inductive reasoning allows for the possibility that the conclusion is false, even if all of the premises are true.[4]Instead of being valid or invalid, inductive arguments are either strong or weak, which describes how probable it is that the conclusion is true.[5]
A classical example of an incorrect inductive argument was presented by John Vickers:
All of the swans we have seen are white.
Therefore, all swans are white.
Note that this definition of inductive reasoning excludes mathematical induction, which is a form of deductive reasoning.

And from the pages of the online text used in University of Massachusetts' Logic courses.  Here is the link by Hardigree.  I'm sure there's one by Copi somewhere, if we want to search.

Chapter 1: Basic Concepts 5
Let us go back to the two arguments from the previous section.
  1. (a1)  there is smoke; therefore, there is fire.
  2. (a2)  there were 20 people originally; there are 19 persons currently; therefore, someone is missing.
There is an important difference between these two inferences, which corresponds to a division of logic into two branches.
On the one hand, we know that the existence of smoke does not guarantee (ensure) the existence of fire; it only makes the existence of fire likely or probable. Thus, although inferring fire on the basis of smoke is reasonable, it is nevertheless fallible. Insofar as it is possible for there to be smoke without there being fire, we may be wrong in asserting that there is a fire.
The investigation of inferences of this sort is traditionally called inductive logic. Inductive logic investigates the process of drawing probable (likely, plausi- ble) though fallible conclusions from premises. Another way of stating this: induc- tive logic investigates arguments in which the truth of the premises makes likely the truth of the conclusion.
Inductive logic is a very difficult and intricate subject, partly because the practitioners (experts) of this discipline are not in complete agreement concerning what constitutes correct inductive reasoning.
Inductive logic is not the subject of this book. If you want to learn about inductive logic, it is probably best to take a course on probability and statistics. Inductive reasoning is often called statistical (or probabilistic) reasoning, and forms the basis of experimental science.
Inductive reasoning is important to science, but so is deductive reasoning, which is the subject of this book.
Consider argument (a2) above. In this argument, if the premises are in fact true, then the conclusion is certainly also true; or, to state things in the subjunctive mood, if the premises were true, then the conclusion would certainly also be true. Still another way of stating things: the truth of the premises necessitates the truth of the conclusion.
The investigation of these sorts of arguments is called deductive logic.
The following should be noted. suppose that you have an argument and sup- pose that the truth of the premises necessitates (guarantees) the truth of the conclu- sion. Then it follows (logically!) that the truth of the premises makes likely the truth of the conclusion. In other words, if an argument is judged to be deductively cor- rect, then it is also judged to be inductively correct as well. The converse is not true: not every inductively correct argument is also deductively correct; the smoke- fire argument is an example of an inductively correct argument that is not deduc-
6 Hardegree, Symbolic Logic tively correct. For whereas the existence of smoke makes likely the existence of fire
it does not guarantee the existence of fire.
In deductive logic, the task is to distinguish deductively correct arguments from deductively incorrect arguments. Nevertheless, we should keep in mind that, although an argument may be judged to be deductively incorrect, it may still be reasonable, that is, it may still be inductively correct.
Some arguments are not inductively correct, and therefore are not deductively correct either; they are just plain unreasonable. Suppose you flunk intro logic, and suppose that on the basis of this you conclude that it will be a breeze to get into law school. Under these circumstances, it seems that your reasoning is faulty. 

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