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diff --git a/org/An Unpleasant Surprise/An Unpleasant Surprise.org b/org/An Unpleasant Surprise/An Unpleasant Surprise.org
index 37273fa..6a96ad9 100644
--- a/org/An Unpleasant Surprise/An Unpleasant Surprise.org
+++ b/org/An Unpleasant Surprise/An Unpleasant Surprise.org
@@ -1,5 +1,5 @@
 #+TITLE:An Unpleasant Surprise
-#+DATE: <2024-02-01 Thu 20:01>
+#+DATE: <2024-02-01 Thu 20:02>
 #+TAGS: Libertarianism, Philosophy, Philosophy of Mathematics
 #+HTML_MATHJAX: align:left indent:5em tagside:left
 
@@ -21,9 +21,9 @@ Indeed, first of all we do have to define our terms. If we are trying to refute
 
 Infinity, in foundations of mathematics, only applies to sets, or unordered collections. These are the only "things" which comprise the ontology of mathematics; the rest of the taxonomy of mathematical objects are built from or coaxed out of them. A refutation of the general metaphysical concept of infinity, as he has attempted to construct, therefore bears no necessary relation to the term-of-art "infinite" in the context of this ontology.
 
-Indeed, the mathematical definition is actually meaningfully different: they claim $$\exists X [\exists e (\forall z \lnot (z \in e) \land e \in X) \land \forall y(y \in X \to y \cup \{y\} \in X)]$$ (Zermelo-Fraenkel axiom of infinity, cf. Wikipedia). I.e., there exists a set containing the empty set and all sets buildable by "iterated nesting" starting with the empty set, i.e. there exists a set containing all von Neumann ordinal numbers.
+Indeed, the mathematical definition is actually meaningfully different: they claim ∃X[∃e(∀z¬(z∈e) ∧e∈ X)∧∀y(y∈X → y∪{y} ∈ X)] (Zermelo-Fraenkel axiom of infinity, cf. Wikipedia). I.e., there exists a set containing the empty set and all sets buildable by "iterated nesting" starting with the empty set, i.e. there exists a set containing all von Neumann ordinal numbers.
 
-The claim "$Y$ is infinite" means only that there exists a surjective map from $Y$ to $X$, i.e. one can formally define a correspondence between elements of $Y$ and elements of $X$ that doesn't "miss" any elements of $X$. There is no concept of "without end," "never-completed," or "without boundaries" here without adding more exogeneous structure that allows one to talk about "end," "completion," or "boundary."
+The claim "Y is infinite" means only that there exists a surjective map from Y to X, i.e. one can formally define a correspondence between elements of Y and elements of X that doesn't "miss" any elements of X. There is no concept of "without end," "never-completed," or "without boundaries" here without adding more exogeneous structure that allows one to talk about "end," "completion," or "boundary."
 
 #+begin_quote
 
@@ -124,7 +124,7 @@ This passage is where I stopped reading, as it became clear that he /has not eve
 
 First off, he's done the thing again where he's stated three inequivalent words as if they were synonyms in order to define a concept in a way that is entirely private so that he can delude himself into believing he's made an argument. An infinite set is not (strictly) bigger than itself. In the case of the integers, its /elements/ always have larger elements. These are completely different orders. These are different classes of objects. I can't possibly imagine how anyone could make this most basic of object-type errors and expect to be taken seriously in their opinions on philosophy of mathematics, much less found an /institute/ on the basis of said errors. An infinite set, indeed, is what it is. It simply /is not/ more than itself; no one since Cantor other than he has ever attempted to abuse concepts to assert so.
 
-Moreover, the final nail in the coffin, in order to assert that something is a contradiction, he must demonstrate that the premises entail both $A$ and $\lnot A$. He does not even attempt to give an argument why "is" and "more than" are such that "thing" and "more than thing" are necesarily different. He merely /asserts/ it. This is the opposite of an argument.
+Moreover, the final nail in the coffin, in order to assert that something is a contradiction, he must demonstrate that the premises entail both A and ¬A. He does not even attempt to give an argument why "is" and "more than" are such that "thing" and "more than thing" are necesarily different. He merely /asserts/ it. This is the opposite of an argument.
 
 The root of his misunderstanding appears to be the mistaken belief that the "things mathematics are about" are in some way procedural in nature, and that when a mathematician writes down something that would seem to encode a nonterminating process, his only option for reasoning about that object is to somehow complete the nonterminating process. In fact, he can just...use the properties that define the object he has notated, without ever actually completing a supertask. To prove that every natural number is either odd or even, I need not check every natural number. Nevertheless, my deductions will hold for all (infinitely many) natural numbers. Mathematics is not computation, and computation is not mathematics. Specifications and algorithms are distinct.