think about sorites in relation to infinite idealizations

(most) Infinite idealizations do not have a clear transition point because they only display the limiting behavior at 0 or infinity.md

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+I want to liken [[Sorites Paradox]] to [[Infinite Idealizations]], but there’s a problem:
+
+Sorites paradoxes have a clear point in “the middle” where the “vagueness” “is”, e.g. while a 1m person is short and a 2m person is tall, and we cannot really say where this transition point is, it seems to be around 1.80m
+
+In contrast, infinite idealizations are a problem *because* they occur at a point/configuration that isn’t attainable, e.g. at $\infty$ or $0$.
+
+This leads to the problem
+
+>[!note]
+>
+>Infinite idealizations are a bit like Sorites, but they do not have a “crossing over” point like the Sorites paradox has. Without it, there isn’t really a paradox at all.
+
+
+# Trying to phrase the paradox
+
+Let’s try to construct a Sorites argument for phase transitions.
+## Induction [1]
+
+1. 1 molecule of water does not display phase transition behavior
+2. If N molecules of water do not display phase transition behavior, N+1 molecules of water also do not display phase transition behavior.
+  C. There does not exist a finite number N molecules of water that displays phase transition behavior. $\forall N\in\mathbb{N} \quad \neg PT(N)$
+
+PROBLEM! C is True! So a) we have no motivation to negate 2 and construct the line-drawing case, and b) even if we were to construct it, it would not contradict C.
+
+Let’s try
+## Line-drawing [2]
+1. 1 molecule of water does not display phase transition behavior
+2. It is not the case that for all N molecules of water N does not display phase transition behavior ← not true!
+  C. There is a point at which N molecules of water do not display phase transition behavior, but N + 1 molecules of water do.
+
+
+Here’s the problem: 2 is true, therefore the line-drawing argument is unsound.
+
+
+# HMMMM
+
+Something is off. While 1.C is technically true thermodynamically, in “reality” it’s false: we *do* see thermodynamic phase transitions in systems of finite size, because everything is of finite size/density (except maybe singularities in black holes).
+
+How do we square this??? What are our claims actually about?
+
+# Ballspace & Infinite idealizations
+
+![A picture of a sphere portruding out of a box. The diameter of the sphere is larger than the height of the box, so the north and south poles are portruding from the top and bottom of the box, while the middle is fully enclodes by it.](media/ballspace.png)
+
+I think ballspace is a better candidate for likening an infinite idealization to Sorites paradoxes, as it (arguably) displays the same phenomena as the inf id, but has the transition point exist not on the far end of the variation axis. [[Sorites paradox requires the predicate to have multiple false points and multiple true points along the axis of variation]]
+
+
+This is *also* not true in the ballspace example, let’s construct it:
+
+>[!Ballspace Induction]
+>
+> 1. At thickness 1km the space is simply connected
+ 2. If a system of thickness N does not display the thing, then the system of thickness N-1nm also does not display the thing
+    C. There does not exist a thickness N that is multiply connected
+
+
+## So all hope is lost?
+
+Not completely: there is still this “vague” region in the FQHE/ballspace example because QM! Maybe this is my saving grace.
+
+
+
+

Components/Infinite Sphere.md

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-# Infinite Sphere
 import {useState} from 'react';
 
 const [val, setVal] = useState(20)

Infinite Idealizations Resemble Sorites because Both Have Discontinuous Transitions.md

@@ -15,7 +15,7 @@ My thesis heavily centers around two topics: [[Infinite Idealizations]] and [[va
 # Similarity
  Infinite Idealizations are similar to Sorites paradoxes because both are mathematical/logical reasons for why common explanations of phenomena don't (immediately) work out
 
-Vagueness/Sorites paradox is having a continuous or discrete transition from one concept/object/... to another, where at the one end a predicate is true and at the other a predicate is false, and there being equally good reasons for believing that neither predicate actually can change.
+Vagueness/Sorites paradox is having a continuous or discrete transition from one concept/object/... to another, where at the one end a predicate is true and at the other a predicate is false and it’s not obvious where the transition point lies. This leads to a paradox where either there is and isn’t a transition point, or the predicate is and is not true at any point.
 
 Example:
 
@@ -38,8 +38,7 @@ Now for Inf Ids.
 2) If the configuration space is 3D at n thickness/magnetic field strength, then the configuration space is 3D at n/2 thickness/ 2n magnetic field strength.
 
 ...
-
-1) We never observe the FQHE
+3) We never observe the FQHE
 
 Or, other way around again
 
@@ -57,3 +56,9 @@ Or, other way around again
 So if the vagueness paradox is a problem for baldness than it is also a problem for this.
 
 Ah. But then I can't use this as a counter argument
+
+# Problems
+
+Two problems arise:
+1. [[(most) Infinite idealizations do not have a clear transition point because they only display the limiting behavior at 0 or infinity]]
+2. [[Physical systems modeled by infinite idealizations do display limiting behavior at non-infinitary points]]

Next stream.md

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+- [ ] Talk about vagueness
+- [ ] Go through Colyvan and maybe one other
+- [ ] Draw some parallells
+- [ ] Apply weirdness of vagueness to here to confuse everyone harharhar

Sorites paradox requires the predicate to have multiple false points and multiple true points along the axis of variation.md

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+The [[Sorites Paradox]] is about a vague transition point existing between two statements about something depending on a variation in *quantity*, e.g. when does a person start being tall between growing from 1m to 2m? If people were only tall at 2m, and could never get taller than that, we wouldn’t have the paradox because there is no dispute or conflicting intuitions about where the transition point is.
+
+Similarly, if there is a clear transition point, there is no paradox. This can happen either because the property is formulated separately from us forming intuitions about it, such as a tornado being category F5 on the Fujita scale if winds of > 419km/h are observed, or because there is a natural cutoff point, such as a person being *too tall* to be able to pass through a door without crouching. In both these cases there is a continuum, there are multiple points where the predicate is false and multiple points where the predicate is true, but there *is* a line to draw, such that the second premise of the inductive Sorites ($\neg \exists N\in\mathbb{N} \quad \neg P(N) \wedge P(N+1)$) is not true. Thus, no paradox.
+

Streams/04-10-2022.md

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+
+# TODO
+- Go over the arguments for why multiply connectedness leads to anyons leads to FQHE
+-
+
+# General notes
+- The FQHE is, in a way, way “simpler” to analyze than the thermodynamic limit, because in the thermodynamic limit you deal with 2 parameters that are connected in a complicated way: the temperature & the density of particles. You do not vary the density of particles when doing an experiment, you vary the temperature. But, the temperature is not the parameter you would vary in a sorites thingy, plus phase transitions don’t really happen *at* a temperature, they happen *over* it.
+- The only way for the FQHE/ballspace example to look like a sorites paradox is to either
+	- Make some brigde between theory and observation, because there *is* a nonzero length at which FQHE happens
+	- OR QM weirdness at the boundary point, which could count as vagueness.

Streams/23-09-2022.md

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+Link: https://youtu.be/NH4Afk1-PGo
+
+This stream we discussed:
+- What I’ve been doing with my website
+- What the heck are idealizations
+- Shech’s paper + briefly QHE
+
+Useful points to work out later
+- I can liken ballspace to the “Heap” paradox/vagueness
+	- Normally inf ids are hard to liken because there’s no clear boundary point you cross, you normally only “reach” it.
+	- With ballspace there is a space in 3d where there *is* multipliconnectedness and you can manipulate the space (add grains) to get to the problem region.
+	- I can also VERY EASILY DO THIS with freakin phase transitions!!! There is a clear point where you transition, you were just so hyperfocused on the number of particles that you did not take the temperature into account.
+	- COUNTERPOINT: Contra to the heap, we can define a specific (critical) point: our problem is not with understanding 2Dness or phase as it is with the heap.
+	- COUNTERCOUNTERPOINT: maybe we don’t understand phase or dimensionality as well as we think! Just like in the heap we understand grains, we just don’t understand their behavior, here we understand temperature/height, we just don’t understand phase/whatever.
+	- My thesis could just make the point: hey, these are similar, how interesting, someone should look into this more lmao
+	- PROBLEMO: the transition point is not vague, we have theory to tell us where it is.
+- Schech’s point about philsci needing to track scientists conceptions of explanation isn’t that strong because scientists are stupid sometimes, e.g. interpretations of quantum mechanics.
+	- Additionally, Philosophy of science is not anthropology
+- I should maybe redo my website as a completely SSRd thing
+- I could explain multiply connectedness with a cowboy lassoing something (could be better but its something!)
+- Maybe get a Wacom?
+-