Quick review All knowledge is conditional on evidence, which eventually leads back to our intuitions. The steps in an argument that make it valid are also assumed to be true. Probability and statistics are ultimately about making arguments to support certain propositions or statements.

Logic and arguments Probability is a matter of logic, so we review some simple logical arguments of the “All men are mortal” kind. We move from arguments that produce conclusions that are true to arguments that produce conclusions that might be true.

Arguments begin with a list of premises that are true, or are assumed to be true. A conclusion, which is related to these premises, is said to be “conditional on” or “given” or “based on this evidence” of the premises.

The simplest probabilistic argument is this: Premises “A die will be rolled; it has just six sides, only one of which will show, and only one of which is labeled ‘6’.” The Conclusion of interest: “A ‘6’ will show” has, conditional on, or given, or based on this evidence, the probability of 1/6 of being true.

Next time Other schools of probability and why I think they are insufficient or misleading. What “randomness” means.

These notes are not meant to be complete. See the class notes to the left (“Breaking the Law”), or search this site for “Chapter”, where you can find an early (somewhat crude) version.

Isn’t there a bit missing from the die example? There are six faces and they’re equally likely or the die is a fair die? And if you do include those don’t you have a tautology?

It’s been argued that all syllogisms are tautologies because the conclusion is actually “contained” in the premisses but that arguing in a circle is OK if your circle is big enough.

Also – sorry if this sounds like I’m complaining but I’m not really – isn’t “intuition” the whole point? Isn’t logic actually how our brains work which is why we find things like the Law of Identity obvious?

Random thoughts, sort of.

A
Briggs

October 16, 2009,

Rich,

Excellent question! I meant to put in that the answer to your question is, most emphatically, nowe do not need to add information about the faces being equally likely. I’ll explore this next week when we talk about “randomness.”

I can certainly see the tautology, self-referencing syllogism argument. Believing that doesn’t change what we know about non-deductive arguments, nor, more importantly, inductive ones.

Isn’t there a bit missing from the die example? There are six faces

and they’re equally likelyorthe die is a fair die? And if you do include those don’t you have a tautology?It’s been argued that all syllogisms are tautologies because the conclusion is actually “contained” in the premisses but that arguing in a circle is OK if your circle is big enough.

Also – sorry if this sounds like I’m complaining but I’m not really – isn’t “intuition” the whole point? Isn’t logic actually how our brains work which is why we find things like the Law of Identity obvious?

Random thoughts, sort of.

Rich,

Excellent question! I meant to put in that the answer to your question is, most emphatically,

nowe do not need to add information about the faces being equally likely. I’ll explore this next week when we talk about “randomness.”I can certainly see the tautology, self-referencing syllogism argument. Believing that doesn’t change what we know about non-deductive arguments, nor, more importantly, inductive ones.