I'm taking this out of context, for the sake of a comment. I'm a little rusty on natural deduction but I think reductio is usually like this: A (assum...
Yes that's probably necessary, but something I overlooked. Here's the sort of thing I was trying to remember. It's Gentzen's stuff. And similarly What...
Is this what you mean: 'Validity' is being defined as a concept that applies to arguments which have the form P_0 \land P_1 \land ... \land P_n \to C ...
You might want to double-check that. Actually, he isn't. The OP's question was not about ordinary English at all: I mainly use formal logic for analys...
"George is opening tomorrow, and we all know what that means." "George isn't opening tomorrow." The conditional here is actually true, because George ...
None, or . Just trying to think of real world examples of a formula like "A ? ~A", likely dressed up enough to be hard to spot. Excluding reductio, wh...
Feynman had a party trick he used to do, I think in grad school. He could tell whether any mathematical conjecture was true. What he would do is imagi...
@"Count Timothy von Icarus" Still hunting for a solid example, but in the meantime there's (1) You only won because you cheated. The sequence from her...
Yes, that was my meaning, as with the boat example. I think, though, we can allow a somewhat negative connotation because reliance in argumentation on...
Agreed, a natural reading, but my target was really someone who might present an argument in the OP's schema, as a perfectly respectable modus ponens....
I'll just say that no opprobrium was intended. I too have gained, I believe, from my study of logic and mathematics, and I have found formal methods i...
Quite. I worked through some of the usual metatheorems years ago when I was studying formal logic. If you're interested in the properties of these for...
1. Meaning what exactly? 2. Is the answer to (1) something I should care about? I don't really care. It's abusive. I'll come up with one. I think you ...
But (A->~A) & A is a contradiction. If you assert A->~A, and then go on to assert A, then you have contradicted yourself. The set {A->~A, A} is not a ...
I still think there's a divide here. If you look at formal approaches to language -- Frege, Tarski, Montague, that sort of thing -- language is a syst...
Yeah I think Sausaure's phrase is a little misleading. On the one hand, as I said, it refers to the conventional nature of the linkage between signifi...
Also, for what it's worth, Baggs used to speak, went through something like normal language acquisition, got all the way to college before they starte...
The obvious example was right in front of me: cartographic symbols. While there is obviously structure in the way these are placed on the map, that st...
Maybe my next reply covered that. Generally, although I think children need to learn to see pictures as pictures of things. It doesn't seem to be quit...
Further reply with example. Sometimes maps for children will have little pictures. At Paris, a little Eiffel Tower; at South Dakota, a little Mount Ru...
Whether the picture is being used as a picture or a sign. Writing, for example, seems to begin pictorially, but then become simplified, stylized, and ...
I mean, it depends, right? But I think Wittgenstein is right, that it doesn't just depend on the thinker's intention. There's some obvious wiggle room...
Or stipulated, scientific definitions. I agree, but I'm curious about some people's strong intuition to call this behavior linguistic. On the one hand...
I don't think that's it really. I think the disagreement is between (1) those of us who think language is primarily and originally for mediating the c...
What puzzles me is that you seem to be offering the second sentence as a reason supporting the first. My inclination is just to say that thought need ...
I lean toward "not" and honestly I'm not sure why the word "language" gets used here. Some of the places where there's a sort of extended use of the w...
At first I didn't like the way you were using the word "productive", but here's another way you might stick with that. Every moment you're making the ...
Common solutions: we introduce other toys so that everyone gets something (not an option in our example); no one gets it (not allowed in our example);...
In an artificially bounded task like this, with artificial bounds on the means by which we may complete it, there are no options. Life is not like tha...
I think what's strange about this problem is that the setup makes human beings helpless before the implacable necessity of mathematics, and that's the...
Doesn't this remind you of "Two Dogmas of Empiricism"? Quine's target was the atomic proposition, and he intended to show that there's no hope of teas...
I understand the point you're making, but I want to push back on this a little. The most interesting thing going on here is the creative leap of enlar...
Do we really expect explanations of anything to be relative to nothing , not even the whole universe? Ho ho, comes the answer, mathematics is eternal ...
Something's not right here, which is just sloppiness and rustiness on my part. In general, three non-colinear points in 3-space determine a unique pla...
Way back when we started, what interested me was decoupling the point with reference to which the circle is constructed from the plane within which it...
I think this is the simplest version of what I was thinking. Given a sphere centered about A, pick any three points in the sphere, those three points ...
As you like. It seems to me you think this is a question that can only ever be asked in one way and in one context, and therefore it only ever has one...
If I'm doing something dumb, it's okay to just say that. Yes exactly. Here again is how I got here. In school, we learn to think of circles this way: ...
There's nothing much to the geometry, but here's a picture to start with. https://i.postimg.cc/RF0rCQPD/diagram1.png (There's other ways to look at th...
I'm glad you came back to this, and I'm going to draw some pictures. I had decided last night there was nothing here and I don't know why I was going ...
I guess once you have the "axel" in mind, you could say that choosing the point where that line intersects the plane of the circle as the point that "...
I'll draw if I have to, but I think I can clarify it verbally. 1. Pick a point and a length. These together determine a bunch of circles in 3-space. 2...
Yeah I was only thinking about the point being away from the plane, no other fiddling. If I've ever considered that, it was so long ago I've forgotten...
Does that point need also to be coplanar? Is there a counterexample I'm missing? You realize that on the sphere it's just a straight line, I hope. ?? ...
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