People may view this in different ways. But, for me, as far as the bare bones context of extensional set theoretic mathematics: Two different, but iso...
It's not a definition. What definiendum do you have in mind? It's for whomever wishes to read it. What definition? I didn't take issue with a definiti...
No, Godel proved a meta-theorem regarding formal systems of a certain kind, including PA. The proof of that metatheorem can be done in various formal ...
That seems right to me. Lois Lane doesn't know that they are the same, but that doesn't entail that they're not the same. What are not the same is Loi...
Unless I've overlooked something, it seems to me that it's easy to prove that it is not the case that any two strict linear orderings with the least u...
To each his own, but I don't feel a much difficulty in adjusting to contexts, so that in some contexts I pay attention to the formal implications of t...
The show I'm interested in seeing is a hoped for episode in which you account for all the configurations to determine which are a continuum and which ...
Your strawman arose because you don't take seriously (though you make it a point to say that you do) the posts to which you reply. You suggested that ...
If you wish to engage me with this, then know that first I need for you to determine what are all the possible configurations and then to say exactly ...
What is your trip, man? You said, "my only qualm with set theory is the philosophy underlying it (centered around actual infinities)". So that would b...
For reference, here are definitions of 'is a graph', 'is an undirected graph' and 'is a loopless graph': G is a graph <-> EVDf(G = <V D f> & V not= 0 ...
What logic do you use? Classical? Intuitionistic? Other? If you don't state your logic then I will take it to be classical. What set theory axioms do ...
I'm going to put 'k-' in front of words to be clear it's your terminology not to be conflated with the usual mathematical usage. So far, you haven't d...
I'm not a big fan of matter. How nice it would be to exist without being subject to the vicissitudes of objects - massive, medium size and subatomic -...
I am working on putting some of your illustrated explanations into actual mathematics. Might take me some time to assemble into a post, hopefully I wi...
You said you have no objection to set theory itself but that you object to misinterpretations of it. The first in your list there is just an observati...
Are you mixed up? You said ChatGPT struggled to make sense of my actual definition, not my parodic definition. When I put my actual definition to Chat...
Should be Wikipedia too.* * Actually, I don't favor censoring references to the output of AI bots or publicly edited encyclopedias. And Wikipedia is m...
What misinterpretations of the meanings of foundational mathematics? What writings by mathematicians or philosophers are you referring to? The mathema...
But wait, out of curiosity, I put my definition to ChatGPT verbatim, and ChatGPT replied: So, I don't know why ChatGPT "struggled to make sense of it"...
You've not defined 'a continuum' (a bunch of itself undefined verbiage is not a definition). So I don't know what you're talking about in mathematics ...
Not close enough. If I had, I'd have more bad things to say about them. Is your stuff supposed to be mathematics, or mathematics infused with philosop...
Again, best to keep things straight: (1) 'the continuum' is noun that names the set of real numbers. (2) 'is a continuum' is an adjective that we talk...
Here's a definition: A continuum is a decomposition of a hyperspace module with sidewise-partitionable step-wise radii decomposition: limitless regard...
Is what you wrote supposed to be informal unfinalized mathematics, or informal unfinalized mathematics infused with philosophy, or informal unfinalize...
https://thephilosophyforum.com/discussion/comment/934861 There has been unclarity in this discussion. Two concepts have not been held distinctly: (1) ...
As I understand from this conversation: Let: Q for the set of rationals Q_o for the set of open subsets of Q Q_i for the set of open intervals of Q R ...
I don't know what you mean by "isn't already contained in R". R is the complement of L in the rationals. No irrational number is in R...period. (By th...
Without comment on the rest of your post, the very first claim is incorrect : With your letters: The interval is just {r}. And L and R are sets of rat...
The blame falls on those who presume to explain it but don't know what they're talking about. It's not Godel's fault nor the fault of those who do und...
The argument that @"MoK" gave involved the real numbers and their ordering, and real intervals, and his own confused notion of infinitesimals. He gave...
There is no consistent formal theory that proves all the arithmetic truths. But it's not the case that there is an arithmetic truth such that there is...
I don't recall the notion of logical impossibility being mentioned (maybe it was?). However, of course, if from certain premises we derive that the co...
Define 'point based'. In greatest generality, a point is a member of a set. Df. the continuum = <R L> where R is the set of real numbers and L is the ...
In other posts, I emphasized definitions of 'the continuum' and 'continuous function'. But lately I overlooked that I also defined 'a continuum' as ab...
Mendelson is a great standard textbook. I have the fourth edition. I can try to answer any questions (though it's been a long time since I read in tha...
That makes no sense and is wrong: (1) By definition, a theorem is a statement that has a proof. (2) Incompleteness is not that there are statements th...
It often has good information. But it's not reliable, as well as even when articles have good information, they are often very poorly organized (thus ...
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