Deductive and Inductive Arguments



"Give instruction to a wise man, and he will be yet wiser.” Proverbs 9:9

Deductive and Inductive Arguments

“An argument whose conclusion is supposed, alleged, or claimed to be certain relative to its premisses is called deductive. Even if the argument has an error in it and does not do what it is supposed to do, we call it ‘deductive.’ Calling it ‘deductive’ does not make it good or bad. It just tells everyone what is to be expected of it.

An argument whose conclusion is supposed, alleged, or claimed to be more or less acceptable relative to its premisses is called inductive. Even if the argument has an error in it and does not do what it is supposed to do, we call it ‘inductive. Calling it ‘inductive’ does not make it good or bad. It just tell everyone what is to be expected of it.”

Alex C. Michalos. Improving Your Reasoning.

Valid Arguments and Argument Schemata

All cats are animals.

All tigers are cats.

So, all tigers are animals.

All humans are mortal.

All Greeks are humans.

So, all Greeks are mortals.

All______are _______.

All______are _______.

So, all . . . are . . . .

True All dogs are animals. Some polygons are triangles.

True All cats are animals. Some squares are polygons.

False Hence, all cats are dogs. Thus, some squares are triangles.

Unsound Arguments

1. Invalid Schema

2. False Premiss

3. Irrelevant or ‘Circular’ Premiss (The country needs a good five cent cigar)

The Catalogue of Valid Forms (The Fifteen ‘Cousins’)

Barbara Celarent Darii Ferio Cesare

All M is P. No M is P. All M is P. No M is P. No P is M.

All S is M. All S is M. Some S is M. Some S is M All S is M.

All S is P. No S is P. Some S is P. Some S is No S is P.

not P.

Camestres Festino Baroco Disamis Datisi

All P is M. No P is M. All P is M. Some M is P. All M is P.

No S is M. Some S is M. Some S is All M is S. Some M is S.

not M.

No S is P. Some S is Some S is Some S is P. Some S is P.

not P. not P.

Bocardo Ferison Camenes Dimaris Fresison

Some M is No M is P. All P is M. Some P is M. No P is M.

not P.

All M is S. Some M is S. No M is S. All M is S. Some M is S.

Some S is Some S is No S is P. Some S is P. Some S is not P.

not P. not P.

Quick Assignment: Using the fifteen cousins, test these syllogisms using one of the following sets:

M: rodents P: animals S: squirrels

M: Christians P: Americans S: Priests.

M: Students P: Humans S. Utahns

"Notional evidence is second-hand, academic, probable. Real evidence is first-hand, experiential, certain.

Reason argues from data that are certain to conclusions that are, in varying degrees, probable. Induction argues from consistent patterns to generalizations: every time I put out a pan of water when the temperature is below thirty-two degrees, the water goes stiff; every time I drink five martinis, I regret it; every time I've seen people treat sex like a game, it's lost its importance to them. Deduction applies generalizations to new cases: every time I drink five martinis, I regret it; but this is my fifth martini; therefore, Ooops! Analogy tries to explain realities we do not understand in terms of realities we do understand.

Expert testimony is trustworthy, provided the person is speaking in his or her field of expertise.

Eyewitness testimony is trustworthy, but only to a point.

First-hand experience is the best evidence there is (even though it, too, is limited). Seeing is not believing, seeing is knowing.

Common Sense is also close to certain.

William J. O'Malley, S.J. Becoming a Catechist: Ways to Outfox Teenage Skepticism

“For Aristotle and Plato, education is the search for the good life. Since we disagree on what the good life is, says Aristotle, then education has to teach us how to disagree politely as we continue the search. Socrates says of Homer and Solon that they should be called not wise men but lovers of wisdom. Wisdom is not something that can be possessed; in Thomas Aquinas’ words, it is available to us “as on loan.” Contrast that to Hegel’s project to transform philosophy from a search for wisdom to the possession of knowledge. This is truly an anti-Christian attitude, a collapsing of the restraint that the religious exercises on the quest for knowledge and power. In his illuminating study of the Bible, Northrop Frye notes, “It is curious but significant that ‘gnostic’ and ‘agnostic’ are both dirty words in the Christian tradition; wisdom is not identified with either knowledge or the denial of knowledge.”

Gabriel Moran. The Religious Element in Education

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