## Definition as Approximation

Known unknowns and unknown unknowns!

Moderators: AMod, iMod

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Definition as Approximation

In regard to the nature of approximates Wittgenstein observed: “"Inexact" is really a reproach, and "exact" is praise. And that is to say that what is inexact attains its goal less perfectly than what is more exact. Thus the point here is what we call "the goal". The more narrowly we examine actual language, the sharper becomes the conflict between it and our requirement. (For the crystalline purity of logic was, of course, not a result of investigation: it was a requirement.) The conflict becomes intolerable; the requirement is now in danger of becoming empty. —We have got on to slippery ice where there is no friction and so in a certain sense the conditions are ideal, but also, just because of that, we are unable to walk. We want to walk: so we need friction. Back to the rough ground!” (Wittgenstein, Philosophical Investigations)

The nature of approximation enables a degree of stability in observation as a reflection of the cause through effect through linear logic. It is in this respect cause maintains a symmetry through effect, which effect being a symmetry of cause, further increasing the symmetry between cause an effect. The approximation of a cause, through effect, allows for various points to manifest enabling the "friction" Wittgenstein observes as inherently necessary. It is this manifestation of “points” that allows logic to maintain a stability through a propagation of further medians, through circularity and paradoxes, to explore. Further questions to observe would be:

- If the “requirements” for exactness cause the very inexactness we observe?
- If rigor is the continuous manifestation of symmetry as a form of symmetry in itself?
- If exactness and inexactness are observations of cause and effect (through linear logic) as non-approximate and approximate?

Londoner
Posts: 761
Joined: Sun Sep 11, 2016 8:47 am

### Re: Definition as Approximation

I would not read it in that way, as being about 'cause and effect' or approximation.

As I understand it, if we work from the idea that language creates a 'picture' of the world, then we require the logical relationships within language, the fundamental grammar, to exactly reproduce the relationships that hold in the world. When he writes of 'logic' he is describing those relationships. So (rather crudely), if our language works with subject-object, or subject-predicate, we assume the same is true in the world the language describes. That the logical relationships within language mirror the 'logic' of reality. And they do, but that is only because we will only accept a picture of the world that conforms to our requirements! But the problem is that if we try to clarify exactly what those relationships are, by making the logical relationships within language more exact, we find they slip away, as he expresses with the 'ice' metaphor.

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Definition as Approximation

Londoner wrote:
Sat Nov 04, 2017 1:12 pm
I would not read it in that way, as being about 'cause and effect' or approximation.

As I understand it, if we work from the idea that language creates a 'picture' of the world, then we require the logical relationships within language, the fundamental grammar, to exactly reproduce the relationships that hold in the world.

Thats the point, what we understand of reality is generally cause and effect. A leads to B. B leads to C. Etc. We see this observed in linear logic...a type of cause and effect progression where the effect is simply a "cause for another cause" and in this respect an approximate cause in itself.

What we understand of "B", through A and C, is strictly that "B" is an approximate of A and C. B is defined through approximation.

When he writes of 'logic' he is describing those relationships. So (rather crudely), if our language works with subject-object, or subject-predicate, we assume the same is true in the world the language describes. That the logical relationships within language mirror the 'logic' of reality. And they do, but that is only because we will only accept a picture of the world that conforms to our requirements!
But the problem is that if we try to clarify exactly what those relationships are, by making the logical relationships within language more exact, we find they slip away, as he expresses with the 'ice' metaphor.

Hence the result is "approximation".

Londoner
Posts: 761
Joined: Sun Sep 11, 2016 8:47 am

### Re: Definition as Approximation

Eodnhoj7 wrote:
Sat Nov 04, 2017 2:43 pm
Thats the point, what we understand of reality is generally cause and effect. A leads to B. B leads to C. Etc. We see this observed in linear logic...a type of cause and effect progression where the effect is simply a "cause for another cause" and in this respect an approximate cause in itself.

What we understand of "B", through A and C, is strictly that "B" is an approximate of A and C. B is defined through approximation.
There is a philosophical debate to be had about 'cause-and-effect' but I do not think it is what Wittgenstein was referring to.

I am not clear what you understand by 'linear logic', but I'm doubtful that we ever observe it. I would say we have problems just saying what 'reality' is, let alone how it operates. How do you know the cause-and-effect is a property of reality, rather than of the mind of the observer?
Hence the result is "approximation".
You can only know something is an 'approximation' if you have something to compare it to, i.e. if you had a language that could refer to 'reality' in an exact way, then you could say that ordinary language was only an approximation. But we don't.

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Definition as Approximation

Londoner wrote:
Sat Nov 04, 2017 4:03 pm
Eodnhoj7 wrote:
Sat Nov 04, 2017 2:43 pm
Thats the point, what we understand of reality is generally cause and effect. A leads to B. B leads to C. Etc. We see this observed in linear logic...a type of cause and effect progression where the effect is simply a "cause for another cause" and in this respect an approximate cause in itself.

What we understand of "B", through A and C, is strictly that "B" is an approximate of A and C. B is defined through approximation.
There is a philosophical debate to be had about 'cause-and-effect' but I do not think it is what Wittgenstein was referring to.

I do not believe it is what he intended to refer to, and in that respect I agree 100 percent with you. However what we understand of reality as "structural" is striclty a reflection of points as cause and effect.

I am not clear what you understand by 'linear logic', but I'm doubtful that we ever observe it.

"A leads B leads to C" is the general form. It is a deficient form of logic, but logic non the less.

I would say we have problems just saying what 'reality' is, let alone how it operates. How do you know the cause-and-effect is a property of reality, rather than of the mind of the observer?

All reality, both subjective and objective is composed of points. The point is a causal element in that is "causes" itself. IN causing itself, through reflecting inwards, it manifests a further point(s) as structural extensions of itself. These "point(s)" are the "effect" as "cause" strictly reflecting upon itself.

Let's look at it from a practical perspective. When we observe cause and effect in reality what we are do is observing a point in time and seeing it lead to a further point in time as effect. In this respect to observe cause and effect is to observe a "structure" in time.

Hence the result is "approximation".
You can only know something is an 'approximation' if you have something to compare it to, i.e. if you had a language that could refer to 'reality' in an exact way, then you could say that ordinary language was only an approximation.

Yes, and considering all language is strictly concepts compared to other concepts (the dictionary is a perfect example) language is an approximation of concepts. This nature of "approximation" is strictly equivalent to "effect" or "a cause reflecting another cause".

In this respect to observe definition as "approximate" is to observe it as both "causal" and "deficient in cause" (or "randomness" through effect).

What we observe as "effect" is strictly an approximation of cause as effect, with this approximation being a deficiency in cause equivalent to "randomness".

In these respect what we understand of definition as approximation is the observation of "causality" and "randomness" which results in the process of reflection.

But we don't.
Yes we do.

Londoner
Posts: 761
Joined: Sun Sep 11, 2016 8:47 am

### Re: Definition as Approximation

Eodnhoj7 wrote:
Sat Nov 04, 2017 4:20 pm

Yes we do.
So far, I think it is just you! Perhaps one day you will expand on that claim.

Anyway, I think you differ from Wittgenstein in thinking that, which was the point I was making.

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Definition as Approximation

Londoner wrote:
Sat Nov 04, 2017 5:10 pm
Eodnhoj7 wrote:
Sat Nov 04, 2017 4:20 pm

Yes we do.
So far, I think it is just you! Perhaps one day you will expand on that claim.

Anyway, I think you differ from Wittgenstein in thinking that, which was the point I was making.
I agree with your perception of Wittgenstein in that matter, however I don't believe what I am saying specifically contradicts his works but "works" with them.

On a seperate note he later argued against logical atomism in favor of logical holism. I believe he was right about the atomism and holism at the same time in different respects. I believe he was incorrect about being incorrect.

bahman
Posts: 874
Joined: Fri Aug 05, 2016 3:52 pm

### Re: Definition as Approximation

I think that language which is finite set of sentences which can be comprehended by an agent and it is structured by a finite set of forms, words (information). Any sentence or set of sentences in this regards is an approximation of reality since the reality as a whole is interconnected and contains infinite forms, unless one claims opposite--that the set of forms is finite--then language can be exact.

### Who is online

Users browsing this forum: Bing [Bot] and 3 guests