Recent content by A Toy Windmill

There's another way to flip this around. Suppose you start at some conclusions and you want a computer to come up with premises from which to derive them. Mathematicians like to do this when they axiomatize a mathematical field down to simple principles. But scientists do it too. For instance...

You are wrong on the irrelevance of P3. The conclusion follows from P3, P4 and P5 and can be formalized: P3) JH != JC P4) PM = BJ || PM = JH P5) PM = JC C) PM = BJ From P4 and P5, we have (by substituting PM for JC in the left disjunct) C1) PM = BJ || JC = JH From P3, we rule out JC = JH...

You're just on ignore now. Bye.

Can you restate the reason for me?

It's a good question. But is the status of validity something which tells of the likelihood, or even the possibility, that something will be accepted as sound? It seems that it's often the opposite. I know that you can often take a crappy and invalid argument, where the premises aren't strong...

Blatant contradictions where one premise is just the denial of another? Perhaps there is no good reason. Perhaps all such arguments are stupid. Perhaps we should be so eager to discard them that we will declare them illegal from the outset. It wouldn't bring the house down to do so. I come at...

To repeat, I like everything you said about stipulative and lexical definitions. There are stipulative definitions, such as those in mathematics, which appropriate common terms. Mathematical logic is not peculiar in this appropriation of natural language. Physics has stipulative definitions of...

Ironically, mathematical logicians often use the terms "valid" and "sound" differently to philosophers. I suggest it's another hang-up from syllogistic logic, which was a classification system for 256 argument forms into the valid ones and the fallacious ones. Mathematical logics aren't...

The argument can be formalized: P1) JC != BJ P2) BJ != JH P3) JH != JC P4) PM = BJ || PM = JH P5) PM = JC From P4 and P5, we have C1) PM = BJ || JH = JC From P3 and P4, we then have C2) PM = BJ

There are four poll options, with votes split evenly on three. If you constructed the poll to give exclusive and exhaustive options, that means that two-thirds of people voted wrong whatever answer is right. I'm not going to nitpick this further. Your poll is scientifically as worthless as your...

To the extent that there is a single correct notion of validity, and the poll representative, the results show that two thirds of people are confused.

I suspect this post is another waste of time. Unlike Angra Mainyu, I don't think anyone is reading these posts other than thread participants. One of my first posts to Speakpigeon gave the definition of syllogism, and explained how, by definition, there are no syllogisms with contradictory...

Let's talk again when you've gone back to school and got your degree.

I enjoyed that post. I made a suggestion above. Mathematical logicians, being mathematicians, aimed to be systematic. And when you are systematic with a bunch of intuitive rules, you sometimes unearth pathologies. This phenomenon happens with other mathematical concepts, such as the...

I didn't. I said that some mathematicians argue that definitions are neither correct nor incorrect, only useful or adequate. I am not one of those. My broader point was that mathematicians rarely give a justification for any definitions. They may motivate a definition, but they mostly let the...