I'm focusing on your claim that mathematicians assume but have not justified the methods of analytic geometry. I'm not a mathematician, but you're usi...
I directed the OP towards a (highly online) reference that explains how mathematicians disarmed his or her objections over a century ago. The date is ...
I'm saying that your objections are more than a century out of date. In order to understand why, you need to learn a bit of synthetic geometry and abs...
In order to understand the justification for analytic geometry, you need to study synthetic geometry. In particular, Hilbert's work on the foundations...
I agree with @"fdrake" and @"SophistiCat" that I was "confusing the map with the territory." I will try to separate the core of my argument from your ...
It's important to remember that conservatives aren't interested in meaningful debate. The so-called war on truth is not an epistemic war, but a series...
The position I want to defend goes something like this. Consider a counterfactual sentence like "If you had hit the baseball, the window would have br...
The concept of political correctness was invented as satire by the left, adopted by conservatives lacking the self-awareness to realize they were bein...
A theory that permits self-referential definitions is called an impredicative theory. An example of a theory that permits defining a proposition by qu...
The problem with the traditional terminology is that "one-to-one" is ambiguous between injection and bijection. If you think about the etymology of ea...
I think I disagree. The best analysis of modal language we possess is possible worlds semantics. By systematically translating modal talk into talk ab...
I think you're missing something about crackpots. For example, I struggled with the concept of compactness when learning topology. For some time, I th...
You can't do that. The subtraction operation on infinite cardinals is not well defined. For example, let 2\mathbb{N} denote the set of even numbers an...
The Cantor-Dedekind axiom is not an axiom in the usual sense. You can construct a complete ordered field over the Euclidean plane from the axioms of s...
There are resurgent white supremacist movements across North American and Europe; white supremacists hold positions of power and influence in governme...
By definition, \aleph_0 is the cardinality of the natural numbers. Your argument does not establish that the natural numbers have finite cardinality. ...
When you say "the set of natural numbers," you mean "the set of all objects that can be generated from zero and the successor function and which satis...
You are misinterpreting my response. I was responding to your argument by clarifying what people mean when they say things like "the series equals inf...
Hopefully this explains my comment. If f is a function from a set A to a set B, then f is injective iff f(x) = f(y) implies x = y for all x and y in A...
The correct terminology is that the series \sum_{i = 0}^\infty 1 diverges. In other words, the limit of the partial sums \sum_{i = 0}^n 1 does not con...
I don't understand why skepticism about the meaning of mathematical language is relevant to the discussion about potential and actual infinities. The ...
This is false. For example, \mathbb{N}^+ is a proper subset of \mathbb{N} and the function f(n) = n - 1 is a bijection from \mathbb{N}^+ to \mathbb{N}...
I haven't read Dreyfus, but I'm familiar with Heidegger. In response to your question, I would argue that for Davidson beliefs are behavioral disposit...
Davidson is arguing that members of actual linguistic communities have mostly true beliefs about the world. It is relevant to his argument that disagr...
I didn't see a new members thread, so I'd like to say hello! Here is a shoutout to all the names I recognize from the (now defunct) philosophyforums.c...
The principle of induction is intimately related to the recursion theorem. The principle of induction states that if \phi is a predicate such that \ph...
The simple answer is that "Mary might buy ice cream" is true iff there is an accessible world in which Mary buys ice cream. The heart of your question...
The problem with your argument is that the described function is not bijective. Instead, you have constructed an injection from the set of even number...
I have never seen necessitation presented as an axiom. Rather, it is usually presented as a deduction rule. It states that if \phi is a theorem of a m...
The problem with your algorithm is that the binary representation of a natural number is finite. Therefore, your algorithm picks out only those number...
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