Anyone frequent any science or physics forums/groups

[I_Ryan]

@Clayton

However, I reject both of these views. I believe what we’re really saying is more like what Pinker is talking about in how we use language to slice up the physical world in very specific ways. What we’re really saying is something more like, “Hey, you know how you envision the essence of straightness in your mind? Well, any object you envision in your mind which you would think of as ‘straight’ cannot cross itself, right?” The rules of the mathematical formalisms that we find “envisionable” and which we, for that reason, find important are not selected arbitrarily, they are selected to conform to these definite ways in which we envision things in our minds.

First, think of a straight line.

Second, think of something that can’t cross itself.

But what’s the meaning of the proposition “a straight line can’t cross itself”?

Simple, it just means that there is a group of particulars that you call “straight lines”, that there is a group of particulars that you call “things which can’t cross themselves”, and that each of the particulars in the first group is the same as one of the particulars in the second group. It doesn’t mean anything but that the each of the particular things associated with the first string of words is the same as one of the particular things associated with the second string of words.

For example let’s say that the string of words “straight lines” refers to the particulars A, B, and Y and that the string of words “things which can’t cross themselves” refer to the particulars A, B, C, D, and E. So the proposition that “a straight line can’t cross itself” just points out every particular associated with the first string of words - A, B, and C - is included in the group of particulars associated with the second string of words - A, B, C, D, and E. And, in this example, of course that is true, because, out of the particulars in the first group - A, B, and C - all of them appear in the second group - A, B, C, D, and E. There are two extras in the second group not in the first group, but that doesn’t matter because the proposition just says that the first string of words is “contained in or the same as”, not that it’s necessarily “the same as”.

And, by the way, when I say “particulars”, I’m not just talking about things that appear in the outside world. I’m talking about anything that you can sense, conceive of, or whatever. If you can see it, hear it, or whatever, it’s a particular, whether it’s in your head or in the outside world. Particulars are just things that you can sense or conceive. And, actually, on that note, I should point out that I was asking whether “infinity” in conceivable, acting like it would be nonsense if it’s not. Well, I still have a similar position, but I can weaken it a bit. There’s no reason why I should say that I have to be able to conceive of it - which seems to mean think of it in my head. We could say that infinity is meaningful simply by showing something to our senses, such as moving our finger up and down with no end in sight, or whatever. It doesn’t have to be conceivable, it just has to be something that I could observe - whether in my head or in the outside world. But don’t let that be too misleading. At least in principle - whatever that means - we can conceive of anything that we sense in the outside world. The only problem is that often it’s a lot harder to conceive of something than to just put it in front of us. Let me give you an example. What’s pi? Zang explained it before as imagining something, but I found it pretty hard to imagine. But you could definitely animate it or do it with some plastic or something. Anyway, that’s a bit of a tangent.

[I_Ryan]

@Clayton

I understand the praxeological aspect of this, and assent to its importance, but I feel that it completely misses the point. We (humans) envision the world in certain, definite ways (see this lecture by Steven Pinker here). These abstract, immaterial ways of envisioning the real, physical world are, I believe, the ultimate foundation of most mathematical constructs. What do we mean when we say “a straight line cannot cross itself”? Do we really mean that a rigid piece of physical substance which is straight (whatever that means) cannot cross itself? Or do we mean something more ephemeral and metaphorical? I don’t think we’re making any kind of statement about the physical world outside of our brain. The formalists try to say we’re merely pushing symbols around, concomitant to certain rules (whatever a “rule” is) and “A straight line cannot cross itself” is simply a statement about the properties of any object which can properly be described by the symbol “straight.”

Earlier in this thread, you linked it this, but now you linked to this.

I haven’t watched either yet. Are they different? Or are they essentially the same talk?

[adam_knott]

ZB:

I created a new thread for the means/ends discussion:

Means / Ends

This is a new thread that continues a discussion from “Anyone frequent any science or physics forums/groups” Zangelbert Bingledack wrote: 'guess if you take the idea of a means to its logical end, it really could be the entire state of affairs (Mises) someone is faced with. an axe is my means to chop wood…but really so is gravity, friction, momentum, my arm, the fact that my arm is attached to my body, the fact that i am not in handcuffs, the fact that there is light for me to see by…these a…

AK

[ClaytonB]

Are they different? Or are they essentially the same talk?

They are different but I’d recommend the talk at the second link since I think it’s pretty much a superset of the talk he gives at the first link.

Clayton -

[ClaytonB]

For example let’s say that the string of words “straight lines” refers to the particulars A, B, and Y

Are these physically existing things?

Clayton -

[I_Ryan]

@Clayton

Are these physically existing things?

What’s a “physically existing thing”?

Assuming it’s something only in the outside world, not necessarily.

But, assuming it’s something anywhere, yes.

(Very rough: Look at your computer monitor, and then close your eyes and imagine a computer monitor. They’re both composed of spatial relationships and whatever; the only difference is that the first is much more “vivid” than the second. So, when I say “particular” when I’m talking about visual stuff, I just mean anything that you could see or imagine. Seriously just anything that you can see or imagine. And keep in mind that you can’t actually see your whole monitor in one frame; in only one frame, you can only see one angle of it. But you could see every angle of it through a sequence of frames, though you would be locked into a specific order of seeing those angles. What’s interesting about your idea of your monitor is that it’s not tied down to a specific order that you see the angles at. But wait. Really it is. It’s simply that you usually don’t care what order you see it in, so you just group all of those different sequences - plus a bunch of other stuff - into one phrase: your computer monitor. But each order of seeing it is it’s own particular. Not very remarkable, because we constantly group particulars into groups based on being indifferent toward them as means/ends.)

[Zangelbert_Bingledac]

@baxter

if we are looking from the individual perspective, we can know nothing of any objective notion of time in the natural universe.

…

Even growing up in a closet, you still have a chance of learning the objective ordering of events. For, your own body is a datum external to the human mind and it obeys physical processes.

i’m saying an individual, working under the constraint of methodological individualism, is noncognitive to things like “objective ordering of events”. but anyway that would get into the issue of what we are trying to get at when we say “reality” or “objective”. i would splinter the thread if that happened, because it would be a long discussion.

[Zangelbert_Bingledac]

@I. Ryan

If the ordering were native to the frame, that wouldn’t be a problem. But the ordering isn’t native to the frame.

i am not sure how to interpret this so that it makes sense. it seems to me that i can quite readily tell that the memory (movie) of the most recent time i locked my door was the movie of when i did it today, not yesterday, 3 years ago, or so on.

[Zangelbert_Bingledac]

@Clayton

To get back to your question, programming languages are like spoken language insofar as they are a machine specification. Think of engineering an automobile engine. Somehow, you have to describe all those curved surfaces, the join points, dimensions, functional behavior, and so on. A programming language implies an abstract machine which has a sort of “mental shape”** to it, and it is this “mental shape” that constricts or liberates the programmer by making some things easy and other things hard.

…

**The “mental shape” is the implied, abstract machine residing behind the semantics of the language. In C, for example there are these things called “pointers” but pointers assume a certain memory model that is not applicable in other kinds of languages. This gives C a unique “mental shape” from other languages which do not have pointers.

the key I think is this “mental shape” of the underlying machine you mention, which I am suspecting is analogous to humans’ underlying way of slicing up concept-space, such as that instilled in spoken language. as with spoken language, in a language designed from the ground-up for a certain epistemology and view of the world, many things that for instance Mises wanted to say might be much easier to express. it is not that we cannot express them at all in English, but that it is quite cumbersome, and sometimes outrageously cumbersome. perhaps this is how it is with programming languages as well? i am guessing it never gets to the point of outrageously cumbersome with programming languages, though, just because there isn’t the problem of making compromises to help out the listener. in programming languages the “listener” is a computer who will understand everything perfectly, so you can be as convoluted as you want as long as you’re sure you said it right. and also there is no vagueness or anything like that.

a choice of natural language, with its underlying slicing up of thing-space, “constricts or liberates the [speaker] by making some things easy and other things hard” [to express]. the common language of society or of the elite divides up the world in a way that makes it easier to cheer for government solutions. words pairs like public/private are handy, but they contain a government bias.¹ it’s easier to make a case for more government with the word pair public/private than with a different word pair an anarchist might create.

¹EXAMPLE: “you want private property, but we are for public property.” it makes you sound selfish right off the bat, while hiding all the negatives about the alternative. and also i realize that that is not the only thing wrong with the public/private word pair. there is probably a better example.

[Zangelbert_Bingledac]

[quote=“I. Ryan”"]
(Which would mean that your “state of affairs” - your means - would be just what’s in the outside world. If you look at everything - including what’s in your head - there doesn’t seem to be any “choice” left. I just find by the principle of association that my mind transitions from X to Y etc and that’s it. Perfect determinism)
[/quote]

if we are noncognitive to the notion of “free will”, mustn’t we also be noncognitive to the notion of “perfect determinism”? [insofar as determinism is meant to be a denial of free will.]

[Zangelbert_Bingledac]

@Clayton

The natural numbers can be defined by positing a “first number”, 1, and a successor function:

s(x) = x+1

s(1) = 2

s(2) = 3

etc.

To me, infinity is the inevitable result of the following question - is there a number large enough to break the successor function, i.e. is there a largest number, or a number which does not have a successor? I think the answer to this is clearly no.

this is just saying, for instance, whatever number of pennies i can imagine, i can always imagine one more penny being added to the pile.

@Clayton

The next question which naturally follows is, how many numbers are there?

as many as you want

@Clayton

The answer, in terms of numbers we have already defined, is “no number”. There is no number that says how many numbers there are. But when we list the numbers out: 1, 2, 3, 4, 5… they look perfectly countable. So why can’t we count the whole lot of them, just as if they were a really big barrel of apples?

erm, seems there are five numbers there! oh wait, does that ellipsis mean something? “keep going”? 'til when?

A. 'til i stop?

B. infinitely?

if A, the count will be finite. if B, we have already thereby smuggled in the concept of infinity.

@Clayton

I see no reason why we can’t define a symbol, say Aleph_0 and say, “The number of natural numbers is Aleph_0” especially since there’s lots of interesting things we can then do with this symbol.

well sure, but what i wrote in previous posts (as the infinity talk was winding down) applies to this.

[Zangelbert_Bingledac]

whoops, forgot this bit:

@Clayton

Of course, such a magnitude cannot be physically instantiated… yet neither can a geometric plane and nobody has a problem with that. A geometric plane exists only in our imaginations… it’s a shared illusion or shared mental abstraction. Same goes for infinity.

gee whiz, i thought a plane looked like this, except with only one ply:

[scineram]

Do you think there is a greatest natural number? If not why not? If you do which is it?

[Zangelbert_Bingledac]

@Clayton

I understand the praxeological aspect of this, and assent to its importance, but I feel that it completely misses the point. We (humans) envision the world in certain, definite ways (see this lecture by Steven Pinker here). These abstract, immaterial ways of envisioning the real, physical world are, I believe, the ultimate foundation of most mathematical constructs.

i think i agree.

@Clayton

What do we mean when we say “a straight line cannot cross itself”? Do we really mean that a rigid piece of physical substance which is straight (whatever that means) cannot cross itself? Or do we mean something more ephemeral and metaphorical? I don’t think we’re making any kind of statement about the physical world outside of our brain.

i think if i say something like “a straight line cannot cross itself” i am just trying to make sure the audience knows for sure what i mean by straight line. but i may as well show them a picture instead.

or a few pictures if needed.

@Clayton

I believe what we’re really saying is more like what Pinker is talking about in how we use language to slice up the physical world in very specific ways. What we’re really saying is something more like, “Hey, you know how you envision the essence of straightness in your mind? Well, any object you envision in your mind which you would think of as ‘straight’ cannot cross itself, right?”

yea that’s it.

@Clayton

The rules of the mathematical formalisms that we find “envisionable” and which we, for that reason, find important are not selected arbitrarily, they are selected to conform to these definite ways in which we envision things in our minds.

definitely, but this is only the case for relatively basic maths like numbers, arithmetic, and so on. most importantly, i think this is really the ONLY basis for proof. but that is just a tautology, in a way: to prove something you have to think it, but to think it you have to envision¹ it. a proof is just written evidence of this process. it is no wonder some mathematicians who work with visual proof methods claim

there is no principled distinction between inference formalisms that use text and those that use diagrams. One can have rigorous, logically sound (and complete) formal systems based on diagrams. (Barwise & Etchemendy, Diagrammatic Reasoning: Cognitive and Computational Perspectives, p. 214.)

¹envision to include not just vision, but any perceptive faculty such as feeling or hearing

[Zangelbert_Bingledac]

@scineram

Do you think there is a greatest natural number? If not why not? If you do which is it?

to me this is asking, “do you think there is a number of pennies you could imagine, where you would not be able to imagine a new penny added to the pile?” i would guess no. (why “guess”? because it is a question about my ability to actually imagine something. it is at least conceivable that my imagination could object at some point in the process.)

[baxter]

Do you think there is a greatest natural number?

Of course not, you can always produce a larger one by adding 1.

Even in the branch known as nonstandard analysis, where there is an integer N larger than any real number, there is still N+1, 2N, etc.

FYI people who actually use math don’t care about the pedantic handwringing over infinity here: “two distinguished physicists, A. Slavnov and F. Yndurain, gave seminars in Barcelona, about different subjects. It was remarkable that, in both presentations, at some point the speaker addressed the audience with these words: ‘As everybody knows, 1 + 1 + 1 + · · · = −¹⁄₂’. Implying maybe: If you do not know this, it is no use to continue listening” http://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E2%80%A6

[Zangelbert_Bingledac]

@Adam Knott

I created a new thread for the means/ends discussion:

https://forum.freecapitalists.org/t/means-ends/16983

link doesn’t work.

EDIT: nevermind, found it.

[Zangelbert_Bingledac]

by the by, if anyone was shocked by the things i wrote here and would like some more clarification without having to post here, feel free to private message me.

[I_Ryan]

@Zangelbert

i am not sure how to interpret this so that it makes sense. it seems to me that i can quite readily tell that the memory (movie) of the most recent time i locked my door was the movie of when i did it today, not yesterday, 3 years ago, or so on.

Very rough:

I’m starting to think that there are two parts:

We have “video bits” where the ordering is native to the sequence (in the sense that you don’t need to “think about it” to figure out the order; but the rest is what I was talking about before.

Like, right now I remember opening my refrigerator and seeing a bunch of swiss chard stacked on the middle shelf, and I also remember getting home and noticing some sun damage on my inner right forearm; but I can’t figure out how to relate those two “sensory fragments” to each other in terms of their order in time. Both of them come to me in a whole, but I can’t put them together into a bigger whole.

But I can relate each of them to other ones, and you’ll see how. I can say that the first one (the one about the swiss chard) happened sometime in the summer, because I remember carrying the swiss chard to my car in the blazing heat; and I’m able to tell you that the second (the one about the sun damage) also happened sometime in the summer, because I noticed it while standing out in the blazing heat.

So, for the first, I can tell you when it occurred, because my only sensory bit including having that much swiss chard happened while walking in the blazing heat; and, for the second, I’m able to say when it occurred, because the memory itself includes me standing in the blazing heat. But, based on that, I can’t tell you which summer it happened in and so on: For that, I would need to search for even more sensory bits to relate to it.

[Zangelbert_Bingledac]

i think i get it. seems you’re saying that the only way we order things in time is by, well, ordering them in time…that is, by finding other memories that give hints about the proper ordering. hence the structure of past time is built out of little fragments, some of which DO have hints about the time, such as the summer heat. the fragments of memory from which hints about the time of occurence CAN be deduced help to order those fragments of memory from which the time cannot be deduced from that fragment alone. right?