#splitinfinities

[philosophytranslator]

I study mathematical logic, which is, of course, an outgrowth of philosophy, but we our perspective and language are somewhat different so I may be misunderstanding. In your post on logic, you state under completeness "Arguments that break this rule are fallacies". I believe that should be arguments which break soundness. Completeness says certain arguments must exist. The only way to break completeness, then, is if one of them doesn't. The system breaks completeness, arguments don't.

I goofed when writing that part of the post, and you’re actually right.

One of the weird things about soundness is that formal fallacies don’t really care about it: they’re only concerned about the structure. So, an argument can have true premises, true conclusion, yet be formally invalid; just as an argument can have a nonsense premises that leads to an equally nonsense conclusion, because validity refers to the structure of an argument.

“Rose is a cat, all cats are felines; therefore the sky is blue.” All of these assertions are true, as is the conclusion, but the conclusion does not follow from the first, and so the argument is invalid. This would be the fallacy of irrelevant conclusion. However, “All cats are dragons, Rose is a cat; therefore, Rose is a dragon,” is a valid argument because the conclusion follows from the premises. Confusing, isn’t it?

But yeah, good catch. Most philosophers deal with logical systems that are “complete” in some way: only the much loathed Analytics try to demonstrate the incompleteness of logical systems as a way to discredit them.philo

[philosophytranslator]

I've been Googling around and reading a bit about Val Plumwood (after reading your post on logic). I'm curious specifically about the notion of dualism in her work. Do you have any recommendations about work I should be looking at to understand and contextualize dualisms?

Your best starting point would be her essay Paths Beyond Human-centeredness, the book Feminism and the Mastery of Nature, and her essay Nature, Self, and Gender: Feminism, Environmental Philosophy, and the Critique of Rationalism. 

Okay, so, from Feminism and the Mastery of Nature, you get stuff like:

Dualism… imposes a conceptual framework which polarises and splits apart into two orders of being what can be conceptualised and treated in more integrated and unified ways. But dualism should not be seen as creating difference where none exists. Rather it tends to capitalise on existing patterns of difference, rendering these in ways which ground hierarchy.

Pretty much, what dualisms do is take existing differences and interprets them in ways that generate hierarchical relationships: so the subordination of women to men based on the differences therein doesn’t inject difference where none exists; it takes the difference and treats it as a sign of inferiority and subordination. It creates relationship structured around the features that I listed in the post and then uses that relationship to organize the world.

That should provide a pretty good starting point without actually writing an entire post on the thing. Also, try not to confuse dualisms with binaries. For Plumwood, binaries emerge as a function of dualisms, but are not reducible to them. So, a dualism that has all or some of Plumwood’s features usually produces a binary that carves up the world in ways that mirror the relationship established in the dualism.

It’s been a while since I read Plumwood’s book, so I’m not 100% that a binary shows up in every dualism, but I think it’s likely. Anyway, those three sources should help you.