Chapter 3, Tutorial 1
"Ampliative" Reasoning
and
Inductive Argument Types
All the deductive logic, at least all that we'll see, is formal. If we understand the right pattern of reasoning, a valid deduction can be easy to make.
If A or B, but not-A, so B.
We don't even need to know what 'A' and 'B' are about.
But one of the lessons of the very first tutorial of chapter one was that sometimes reasoning goes beyond form. Let's remind ourselves:
Informal reasoning typically leads to a conclusion by means of some educated guess-work. Maybe we should call this something like detective work. It takes evidence and amplifies it. (Think CSI, if you watch TV.) Let's review what we know from chapters one and two.
Here's the chapter one formulation of the two kinds of reasoning:
Formal reasoning (of deductive logic) manipulates the statements of evidence and performs something of a calculation on them in virtue of their form or sentential structure.
(Think about the simple "process of elimination" argument for Chris's B grade: "Either A or B but not A, so B".)
Informal reasoning (of inductive logic) interprets the evidence to form a conclusion. This thinking amplifies the evidence -- often by generalizing, predicting, or uncovering the best account of this evidence.
(Think about figuring out that Chris is in love. This may be a "best guess" but it may be a reasonable one.)
Here's a review of our main deductive concepts relating to arguments:
Think about all the arguments we symbolize in SL as good examples of deductive arguments. Keep in mind, say, the arguments about Bush (e.g., If he's US president, then he is a US Citizen. He is US president, so...). Then:
- Deductive arguments attempt to provide grounds for making their conclusion inescapable.
- If they succeed in this attempt, the argument is valid.
- But, just as essential to a good deductive argument, the premises must be true. If the argument is both valid and has all true premises, then it is sound.
Another little diagram
to keep in mind, then, is this.
For a deductive argument:
Sound = Valid + No false premises.
Let's compare this to our inductive concepts:
Inductive arguments are just as common. Our reasoning to the conclusion that Chris has fallen in love is one example. It's an attempt to give the best account of the evidence...it could be wrong, maybe Chris is faking it. But we are trying to give the likely cause of his behavior here, not the only possible one.
That's the big difference between inductive and deductive. And we can picture it this way:
- Inductive arguments attempt to provide grounds for making the conclusion likely or probable.
- If an inductive argument succeed in this attempt, the argument is strong.
- But, just as essential to a good inductive argument, the premises must be true. If the argument is both strong and has all true premises, then it is cogent.
So, for an inductive argument:
Cogent = Strong + No false preemies.