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What holds things together?

Psyduck

Psyduck

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What holds things together?

Is "that-which-holds-things-together" ontologically "different" from things? If not, we get into a regressus. E.g. if between X and Y is some-thing (call it Z) which holds together X and Y, then what does hold together, or relationally connect, Z with X or Y then? If we call "all that is" Being, then Being must still be "more" than the arithematical sum of all individual beings/entities.

One can make the analogy with a straight line and the points it contains. A line is not the "discrete sum" of its points, what glues together all the point to make up the continuity?
 
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well I mean ontology is the study of how to categorize the fundamental forms of beings. If you wanna use the word "is" to make a being that actually holds the other beings together, than go ahead. All you are doing though is predicating the existence of that being.

The question of "Is "that-which-holds-things-together" ontologically "different" from things?" is very interesting though. There is going to be an ontological difference in the beings from your wording though. Once you start saying "is" and start predicating things then your basically engaging in ontology.
 
alasdairm said:
why not?

alasdair
Click to expand...

It will be on a piece of paper, but more strictly (by definition...) a point is infinitely small and has no extension (=shape/size/figure) whereas a line has extension.

In practice this is of course "possibile," cf. a laser-jet printer which can print billions of dots... but after reflection, we must say that it cannot print a line... and moreover, it's because our eyes are not sharp enough that we assume it's a real line (but in reality, it is only a discrete sum of extended dots).

* Add: printers cannot even print a mathematical point (without size/shape) only a physical point (having really really small shape/size).
 
in which sense should all points collapse?

the argument goes
0° x is a certain fixed number, e.g. x=1;
1° take some point you don't know anything about it yet
2° now, if the following condition holds: "for every epsilon>0 ||x-y||<epsilon
3° then x=y or y=1


you seem to confuse variables/numbers.
0° x=1;
1° next, one can say there are a bunch of points a1,a2,a3 which are arbitrarily close to x=1

[here you made the wrong presuppositions that they are already different, you don't know that yet; they are variables that will later be instantiated]
[the only thing you do is put some conditions on the variables in 2°]
[x is a number, a1,a2,a2 are variables]

2° for every epsilon>0 we have |x-a_1|<epsilon, |x-a_2|<epsilon, etc.
3° from which we deduce: a1=a2=a3=...=1
 
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Are we talking about resolution, Psyduck?

14761.jpeg


If a camera takes a picture at a certain resolution, what was the resolution of the original before it was copied?

da06.png


The answer involes the sampling rate of the measuring instrument. The more information the higher the resolution. It's just calculus.
 
chinup said:
and consider the interval [x, y], so we do know someting about y and certainly y !=x. i do indeed presuppose that the numbers i am considering in this interval are different, and that we also know this in advance as a basic fact about real numbers.
Click to expand...

I don't understand your confusion yet. Why do you assume that all points collapse to a point Z?

Take some random open neighborhood arround Z, say of radius delta>0; then we have the interval

I = ]Z-delta, Z+delta[

Take some distinct x,y € I, which are distinct which means that we have some epsilon>0 such that |x-y|>epsilon with epsilon<2delta

Proposition.
You assume that all points in some random open interval arround Z collapse into Z?

Above, we toke some random interval (with diameter delta), we also toke two points x,y in this interval.

Saying that they converge/collapse into Z means that

for every omega_1 > 0 that |Z-x|<omega_1
for every omega_2 >0 that |Z-y|<omega_2

take omega_1=omega_2=epsilon/2
(we can take the omega's whatever we like)

Now use the triangle equality, which yields

|x-y| <= |Z-x| + |Z-y| = epsilon/2 + epsilon/2 = epsilon

("<=" means 'smaller/equal than')

So, |x-y| <= epsilon

whereas we assumed earlier that |x-y|>epsilon

Q.E.D. (proof by contradiction)
 
It's interest that holds an appealing sequence together.

You choose all your variables. Drawing a line is misleading. A line is a boundary condition imposed by the variables of interest that was chosen by appeal. It means that a certain y is more favorable for a certain x, so you model the relationship by a line. That's all a line is. A model of interest. A linear regression of thought flow. You could put all your thoughts in the sequence they came and make a continuous line out of them. You had these thoughts as a linear regression of the previous thoughts you invested interest in. Math isn't tangible, so neither is the glue that holds a sequence together.

If we look deep enough we can notice that a square table isn't actually a 100% closed shape. It has gaps between the atoms. For our own sake we go ahead and give all the tiny points a series and call them lines. We can trust that it form's a line because we can take a random sample of the population of atoms and observe their behavior such that position is our random variable of interest. I guess interest is kind of like gravity. We can notice an object falls toward the earth but it doesn't normally leave a distinguished line or path. We just imagine that in our heads. There's a boundary condition on its weight and density that forces it towards the earth.
 
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