It would appear obtuse to the layman, and maybe it just is. — Leontiskos
laws of logic — Leontiskos
The closer you get to the foundation, the surer it becomes. For example, modus ponens is arguably the most basic inference or law of propositional logic, and I don't see that it fails. — Leontiskos
Those supposed foundations are addressed in the Russell article.What's the "foundation" mean here? — schopenhauer1
Earlier logicians had drawn up a number of rules of inference, rules for passing from one proposition to another. One of the best known was called modus ponens: ‘From ‘‘p’’ and ‘‘If p then q’’ infer ‘‘q’’ ’. In his system Frege claims to prove all the laws of logic using this as a single rule of inference. The other rules are either axioms of his system or theorems proved from them. — A New History of Western Philosophy, by Anthony Kenney, 155
Straight lines on spheres? That's interesting too. — creativesoul
I am not sure if you can have an "epistemic endeavour," that is unrelated to being though. What is our knowledge of in this case? Non-being? — Count Timothy von Icarus
Logic is the study of validity and validity is a property of arguments. For
my purposes here it will be sufficient to think of arguments as pairs of sets and
conclusions: the first members of the pair is the set of the argument’s premises
and the second member is its conclusion. An argument is valid just in case
it is truth-preserving, that is, if and only if, whenever all the members of the
premise-set are true, so the conclusion is true as well.
The domain of logic, then, might be thought of as a great collection of
arguments, divided into two exclusive and exhaustive subcollections, the valid
and the invalid, the good and the bad, and the task of the logician as that of
dividing one from t’other. — Gillian Russell
Suppose we had a formal system that answered all our questions about physics, or maybe some area of it like fluid dynamics. How could it have "no relation" to being? At the very least, it would have a relation to our experiences, which are surely part of being. — Count Timothy von Icarus
I want to do leap year physics. You get a nice three year break. — Count Timothy von Icarus
They are supposed to be objections to Aristotle, so yes, of course they do. You might as well have objected to Mr. Rogers by telling us that you prefer people who put on shoes. Mr. Rogers puts on shoes in every episode. — Leontiskos
There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form (note: M – Middle, S – subject, P – predicate.):
Major premise: All M are P.
Minor premise: All S are M.
Conclusion/Consequent: All S are P.
The premises and conclusion of a syllogism can be any of four types, which are labeled by letters[14] as follows. ... — wikipedia
As has been pointed out numerous times, this is just gibberish. What do you mean by (1)? — Leontiskos
I don't exactly object to classical logic, though -- I'm saying it has limitations, not that it's wrong in every case. — Moliere
I don't exactly object to classical logic, though -- I'm saying it has limitations, not that it's wrong in every case.
What you'll be paid for is tracking patterns which people like to track, which usually involves manipulating the world in some way which we perceive as regular.
I would need to sit down with some algebra to understand it properly though. — fdrake
Regarding the projection - there will be a lot of degrees of freedom if you get to choose an arbitrary projection onto the plane — fdrake
Just a helpful point of clarification, "classical logic," is confusingly the logic developed by Frege and co. relatively recently. There is no good catch-all term for logic before the late 19th century. People call it "Aristotlean," but then this tends to miss everything between Aristotle and 1850 or so. — Count Timothy von Icarus
And why do we perceive it as regular? — Count Timothy von Icarus
I'm also not sure what "being" is supposed to be if it isn't what is given to thought. — Count Timothy von Icarus
(There's a direction-of-fit thing here: in one case, the center determines the circle; in the other, the circle determines the center.) — Srap Tasmaner
The way you are all using it is basically "axiomatic". I take "axiomatic" to mean "don't ask me anything further, this is as far as I'm going", or simply "duh!". It really doesn't mean much except that we need to start "somewhere" and "this seems like a good place to start". — schopenhauer1
When I gave some arguments against square circles, I suggested that one could quibble with the arguments, but not oppose them in any way that goes beyond a quibble. I think that has turned out to be right. — Leontiskos
Pick up a length of pipe. Look at it from the side and it's rectangular. Look at it straight on, it's circular. Done. "But I didn't mean that." — Srap Tasmaner
Eh. If you take it to mean axiomatic, then it has nothing to do with a good place to start. If you take it to mean a good place to start, then it is not axiomatic. Axioms are not good places to start except in a purely formal or economical sense. This chimera is understandable, given that my use of "foundational" was nothing like "axiomatic." Quite the opposite.
Again, the PNC is a more universal foundation or first principle than modus ponens. It is a foundation in the same sense that the first few feet of the trunk of a Redwood is a foundation. It is stable in a way that the upper branches are not, and folks never directly contravene the PNC. They only do so indirectly when they have climbed out onto limbs and lost track of where they are. — Leontiskos
Pick up a length of pipe. Look at it from the side and it's rectangular. Look at it straight on, it's circular. Done.
And then a "strong monism," would presuppose a "one true formal system?" But that doesn't seem particularly plausible either. — Count Timothy von Icarus
As I was saying to Leon, the "foundation" to logic would be a meta-logical theory, not the axioms/logical systems themselves. — schopenhauer1
Sure, if you like. Whether the binding between reality and logic is metalogical is largely dependent on how you conceive of logic. — Leontiskos
On my view something with no relation to reality (and therefore knowledge) is not logic. Ergo: something without that binding is not logic. It is just the symbol manipulation that Banno mistakes for logic. More precisely, it is metamathematics. — Leontiskos
When you want to call the binding metalogical that makes me think that you take logic to be something that is not necessarily bound to reality in any way at all. What I would grant is that it is a somehow different part of logic, but I do not think that these parts are as easily distinguishable as the modern mind supposes. — Leontiskos
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