Making Lemonade out of L.E.J. Brouwer

That actually makes perfect sense to me.

… Yet you immediately make a personal remark that is dismissive and rude – which is fine, you can’t help yourself – but that in this case also happens to be totally fucking inaccurate. I know for a fact that I’ve never published a word on this site about world affairs. JSH has no rational basis for his statement. He’s just gorging on his own bile again.

I don’t get it man. You really have a bug up your ass. I did think we were having a civil conversation but I see there is none to be had with you.

Ed3 I apologize, I really thought we were going to have an intelligent and productive conversation. I will not hijack it further by interacting with JSH any more. I thought it could work and for a moment it seemed to, but he has just got a bug up his ass about something or other – I can’t for the life of me figure out what – and I see that it’s a distraction to the forum and a total waste of my time and energy to interact with him under any circumstances whatsoever.

Rude is in the eye of the beholder.

If you were not intending to be rude and dismissive, then what specifically is the evidentiary basis of this characterization of the state of my knowledge of the world:

What causes you to have this particular belief about me? Please be as specific as possible. I am curious to know.

In any event I could certainly stipulate that the world is under the control of maniacs pushing an agenda and a worldview; without having the slightest understanding of how Martin-Löf type theory fits into the plan. You stated that as a thesis but provided neither argument nor evidence.

I merely meant, without insult or offense intended, that even though obviously very mathematically informed, you had not become deeply philosophically informed, a different mentality … for whatever irrelevant cause. Philosophy is very different than physics or mathematics.

There are things of which I know far too little to debate. Everyone has their limits. It is hardly and insult to imply that someone has spoken beyond their own true knowledge. I do not take such implications to be insults. I seriously do not think that others should either, but some people get insulted by even the slightest implication that they are not the supreme source of all wisdom. Personally, I don’t really care. Place yourself wherever you belong.

I repeat: What is the evidentiary basis of your claim?

Hi wtf,

Thanks for your response. I appreciated it very much and intend to look into your references.

I did not mean to equate the denial of LEM with Brouwer’s mysticism. I should have made it clear that the denial of LEM has become an independent issue since Brouwer’s time.

In fact Aristotle had struggled with this very issue prior to codifying LEM. (It was fun for a short while to speculate that I had some of the same concerns as Aristotle. Then my wife reminded me that I was thousands of years late to the party).

Your concluding remarks seem insightful.

Thanks again Ed

As long as we are considering only lemonade, a little sideline could be added here that Pierce sought to avoid ambivalence, rather then face intuitive implications.

I have heard a little about Charles Sanders Peirce, with that spelling, if that’s who you are thinking of.

From what I understand – and this is a very superficial understanding on my part – Peirce says that whatever the continuum is, it certainly can not be the real numbers. For whatever we mean by continuum, it must certainly be the case that:

  • Every part is identical to the whole.

I find this a perfectly reasonable statement. Yet it is totally at odds with modern mathematics. In particular, the continuum – whatever exactly we mean by that – can not possibly be the mathematical real numbers. Because the real numbers may be decomposed into points, none of which are anything like the real numbers.

In particular, we may express the real numbers – or any set for that matter – as the disjoint union of all of its singletons. Symbolically:

$$\mathbb R = \cup_{x \in \mathbb R} ~{x}$$

From Peirce’s point of view, to the extent that I understand it, the above statement can’t possibly be true about the continuum. It’s absurd to break a continuum into points. Set theory in its entirety is therefore the wrong tool for understanding the continuum.

[I really hope I haven’t mangled his ideas too badly. This is as much as I understand].

I would very much like to know more about this point of view. Peirce is one of these people that when you first hear his ideas you wonder, Why isn’t this guy more famous?

He was the originator of pragmatism, and the front runner in semiotics, which was praised by the later positivists, he was commended to be the greatest modern philosopher-mathematician of all times.

His idea on the continuum , as I understand it, was that there are two kinds of infinite sets, one a definite, and two an indefinite one, and the law of excluded middle could not apply certain kinds of propositions, as the bivalance could.

General propositions of the kind, where truth and falsity of that proposition are of the sort , where if p~X, for instance, where the ~ sign is of the form - X follows p; then the law of contradiction will result in the necessary negation of that conclusion.

In ambivalence, there exists definite, rather then indefinite propositions, whereby, only the possibility exists what he calls by implication, rather then that necessity.

My daughter pressed me to go to Starbucks with her, so if I may continue , in terms more the philosophy of language effecting a different(ial) logic. , in a few hours.

I think it was pointed out rightly that the effect of language on logic is at play, and not the other way around.

The continuum problem in terms of this dichotomy between definite and indefinite sets flows out of this difference, in my opinion, and this is why the 'vague-math he coins between his shift from intuitive to to ‘definite’ values.

But as his Kantianism seeks to connect the dots,or the ’ points’ you so rightly being up, one can’t fail to implicate a hidden integration among possible propositions.

I’m that regard he has not advanced over the unsolved and perhaps unsolvable issues with intuitionism, as regards open and closed sets.

Hi Memo,

Thanks for your post.
I am intrigued by Pierce. Could you elaborate a little more, and, if my question is answerable, could you point the way to a foundation of mathematics that I think Pierce may have offered.

Thanks Ed

Peirce. Note the spelling.

Read anything by Fernando Zalamea, the most original philosopher of math in decades.

amazon.com/Peirces-Logic-Co … 0983700494

amazon.com/Synthetic-Philos … 0956775012

If you Google around you can find pdf’s of Zalamea’s papers and articles on Peirce’s continuum. Zalamea is an extremely lucid and interesting writer. The only continental philosopher who actually understands modern math. The only philosopher of math of any type who has moved the philosophy of math from the turn of the 20th century Frege/Russell/Gödel to the modern world of Grothendieck and category theory.

Here’s a good starting point.

uberty.org/wp-content/uploads/20 … tinuum.pdf

Ed & WTF , : Charles Sanders is a very well written comprehensive reference, and I have one at home which I shall forward as well, with a logically based analysis for the layman as well.

:Robert Lane, ‘Physical Companion to C. Peirce’,

Hi wtf & Meno_

From your posts, I am very interested in discovering Peirce.

Thanks for your references.

Ed

Im lurking here, and learning.

One note so far:
Apparently, and reasonably, Peirce held the progression of real numbers as a peudo-continuum.

And indeed it appears that numerical division absolutely precludes continuum.

Distinction of one existent from another itself is a refutation of continuum. Thus, one might say that logic itself precludes continuum.

Logic requires division of empirical reality into ultimately arbitrary abstractions, which lose part of their arbitrariness by being coherent with each other - but this does not make them pertinent beyond the method they allow for.

Thus “A” only equals “A” if we already agree that reality is divided into blocks that can be compared and identified in terms of each other by equation and contradiction.

Hence “A”><“A” is more accurate, in that “A” is greater than “nothing” by the same measure that “A” is greater than “nothing”: neither “A” actually has a direct equal though.

Thats how logic comes to the (unwelcome) aid of mathematics.

Universite´ de Montre´al, C.P. 6128, succursale Centre-ille, Montre´al, Que´bec H3C 3J7, Canada
Neuropsychological research on the neural basis of behaviour generally posits that brain mechanisms
will ultimately suffice to explain all psychologically described phenomena. This assumption stems
from the idea that the brain is made up entirely of material particles and fields, and that all causal
mechanisms relevant to neuroscience can therefore be formulated solely in terms of properties of
these elements. Thus, terms having intrinsic mentalistic and/or experiential content (e.g. ‘feeling’,
‘knowing’ and ‘effort’) are not included as primary causal factors. This theoretical restriction is
motivated primarily by ideas about the natural world that have been known to be fundamentally
incorrect for more than three-quarters of a century. Contemporary basic physical theory differs
profoundly from classic physics on the important matter of how the consciousness of human agents
enters into the structure of empirical phenomena. The new principles contradict the older idea that
local mechanical processes alone can account for the structure of all observed empirical data.
Contemporary physical theory brings directly and irreducibly into the overall causal structure certain
psychologically described choices made by human agents about how they will act. This key
development in basic physical theory is applicable to neuroscience, and it provides neuroscientists
and psychologists with an alternative conceptual framework for describing neural processes. Indeed,
owing to certain structural features of ion channels critical to synaptic function, contemporary
physical theory must in principle be used when analysing human brain dynamics. The new
framework, unlike its classic-physics-based predecessor, is erected directly upon, and is compatible
with, the prevailing principles of physics. It is able to represent more adequately than classic concepts
the neuroplastic mechanisms relevant to the growing number of empirical studies of the capacity of
directed attention and mental effort to systematically alter brain function.

what von Neumann calls his ‘abstract ego’.

Review

Quantum physics in neuroscience and psychology:

a neurophysical model of mind–brain interaction

Friday, December 28, 2012
what von Neumann calls his ‘abstract ego’.
what von Neumann calls his ‘abstract ego’.

www-physics.lbl.gov/~stapp/PTRS.pdf

Review

Quantum physics in neuroscience and psychology:

a neurophysical model of mind–brain interaction

Jeffrey M. Schwartz

1, Henry P. Stapp2 and Mario Beauregard3,4,5,*

1

UCLA Neuropsychiatric Institute, 760 Westwood Plaza, NPI Los Angeles, CA 90024-1759, USA

2

Theoretical Physics Mailstop 5104/50A Lawrence Berkeley National Laboratory, University of California,

Berkeley, CA 94720-8162, USA

3

De´partement de Psychologie, Centre de Recherche en Neuropsychologie Expe´rimentale et Cognition

(CERNEC),

4De´partement de Radiologie, and 5Centre de Recherche en Sciences Neurologiques (CRSN),

Universite´ de Montre´al, C.P. 6128, succursale Centre-ille, Montre´al, Que´bec H3C 3J7, Canada

Neuropsychological research on the neural basis of behaviour generally posits that brain mechanisms

will ultimately suffice to explain all psychologically described phenomena. This assumption stems

from the idea that the brain is made up entirely of material particles and fields, and that all causal

mechanisms relevant to neuroscience can therefore be formulated solely in terms of properties of

these elements. Thus, terms having intrinsic mentalistic and/or experiential content (e.g. ‘feeling’,

‘knowing’ and ‘effort’) are not included as primary causal factors. This theoretical restriction is

motivated primarily by ideas about the natural world that have been known to be fundamentally

incorrect for more than three-quarters of a century. Contemporary basic physical theory differs

profoundly from classic physics on the important matter of how the consciousness of human agents

enters into the structure of empirical phenomena. The new principles contradict the older idea that

local mechanical processes alone can account for the structure of all observed empirical data.

Contemporary physical theory brings directly and irreducibly into the overall causal structure certain

psychologically described choices made by human agents about how they will act. This key

development in basic physical theory is applicable to neuroscience, and it provides neuroscientists

and psychologists with an alternative conceptual framework for describing neural processes. Indeed,

owing to certain structural features of ion channels critical to synaptic function, contemporary

physical theory must in principle be used when analysing human brain dynamics. The new

framework, unlike its classic-physics-based predecessor, is erected directly upon, and is compatible

with, the prevailing principles of physics. It is able to represent more adequately than classic concepts

the neuroplastic mechanisms relevant to the growing number of empirical studies of the capacity of

directed attention and mental effort to systematically alter brain function.

The rest pd the article can be downloaded here:

phymath999.blogspot.com/2012/12/ … o.html?m=1

And finally,

Neumann and Breuwer

math.ucr.edu/home/baez/games/games_20.html

pin.it/x3k5ohv2wazjmk

In the works, ongoing …

Thanks for bumping this thread. Once in a while a fella needs to be reminded of how dumb he is, and threads like this do the trick for me. Takes me back to those days when I chose to huff butane with ty and matt down by the creek rather than go to math class. And I’m glad I did, because if I knew all this shit, I couldn’t experience the joy of being humbled.

I’m gonna agree with wtf… I think.