# logical induction and deduction

## Deduction

I have a Case, and a Rule, and I infer a Result

Case: Socrates is human

Rule: All humans are mortal

Result: Therefore, Socrates is mortal

nibli, ja'o (too often the longer equivalent .iseni'ibo), Resurrected Gismu idni

• Whence these strange definitions? They don't work for a vast array of interesting cases:

This or that. Not this Therefore that.

Socrates is human, Socrates is a philosopher, Therefore, Some philosopher is human

#### Induction

I have a Case and a Result, and I infer a Rule

Case: Socrates is human

Result: Socrates is mortal

Rule: Therefore, All humans are mortal

sucta, su'a, Resurrected Gismu usna

Objection:

Case: Socrates is human

Result: Socrates was a philosopher

Rule: Therefore, All humans are philosophers

To do good induction you need a lot of case-result pairs.

• This is more plausible in a way, but deals with only one type of induction and it the least useful. Statistical induction and causal induction are more important and don't fit this pattern at all.

#### Abduction

I have a Result and a Rule, and I infer a Case

Rule: All humans are mortal

Result: Socrates is mortal

Case: Therefore, Socrates is human

tolsucta, su'anai

Objection:

Rule: All tree frogs are mortal

Reslt: Socrates is mortal

Case: Therefore, Socrates is a tree frog.

i.e. Abduction is logically and scientifically silly; but as a (fallible) inferential mechanism it actually underlies much of human assumptions about the world.

• Well, this pattern certainly is, but the usual abduction (in this sense of the word)is fairly sturdy: If H held, T would occur; If H does not hold, T is pretty unlikely to occur, T occurs, Therefore probably H holds.

What about all the rest of the inference types tht logic deals with? Interpretation, analogy, evaluative, not to mention again the ones under induction? They and abduction, too, often get buried away in "induction" but here there seems to be some sorting out.