What is mathematics?

Use this philosophy forum to discuss and debate general philosophy topics that don't fit into one of the other categories.

This forum is NOT for factual, informational or scientific questions about philosophy (e.g. "What year was Socrates born?"). Those kind of questions can be asked in the off-topic section.
Post Reply
Woodart
Posts: 290
Joined: March 3rd, 2017, 1:49 pm

Re: What is mathematics?

Post by Woodart »

Spectrum wrote: The further exploration can be done from Kant's philosophy. (I did 3 years full time on Kant, but at present is a bit rusty on it as I was focusing on Islam since the last 2+ years.)
Roughly,
  • 1. Kant asserted whatever is Mother Nature [all there is] as cognized is conditioned by humans.
    2. Thus Maths emerged after the human conditions a priori [categories, etc.] and a posteriori.
    3. Even the 'Sun' and 'Moon' emerged after the human conditions a priori and a posteriori.
    4. Point here is, 'before' and 'after' humans are time-based.
    5. Time and Space are sensible intuitions a priori which are conditioned by the mind.
    6. Thus whatever is 'Mother Nature' and the Universe is always conditioned by the mind. Thing-in-themselves [noumenon] do not exist independent of the human conditions.
    7. If we want to speculate more than the above, then we must understand and qualify they are mere speculations. As Wittgenstein had stated re thing-in-itself 'where we cannot speak of, we must remain silent.'
I don't want to go into a detail discussion of the above, I am merely giving a view on how far can the above ideas go as far as Kant is concern. Naturally there are counters [by realists] to the above views but having studied Kant in so much depth, I agree with his views [which are also aligned with Eastern philosophies] on the above.

I respect many of your ideas Spectrum, however many times I find it difficult to clearly understand what you are saying. If you have a point of contention – can you brake in down in simpler terms?

Consul wrote:
It depends on what you mean by "math(ematics)":
I mean just what I said several times - Math exists before humans exist – it is a fundamental part of the structure of the universe. Look at the nautilus shell – it presents one of the finest natural examples of a logarithmic spiral - Fibonacci spiral. It represents a mathematical concept. Is that not clear – if it is not – look at the Roger Penrose video again.
User avatar
Consul
Posts: 6036
Joined: February 21st, 2014, 6:32 am
Location: Germany

Re: What is mathematics?

Post by Consul »

Woodart wrote:I mean just what I said several times - Math exists before humans exist – it is a fundamental part of the structure of the universe. Look at the nautilus shell – it presents one of the finest natural examples of a logarithmic spiral - Fibonacci spiral. It represents a mathematical concept. Is that not clear – if it is not – look at the Roger Penrose video again.
Yes, of course, there are physical objects exhibiting geometric forms or structures; but it doesn't follow that nature contains platonistically abstract or "ideal", purely mathematical entities, or that there really are (perfectly) 0D, 1D, or 2D objects, i.e. mathematical points, lines, or surfaces, in physical reality.
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars
Woodart
Posts: 290
Joined: March 3rd, 2017, 1:49 pm

Re: What is mathematics?

Post by Woodart »

Consul wrote:
Woodart wrote:I mean just what I said several times - Math exists before humans exist – it is a fundamental part of the structure of the universe. Look at the nautilus shell – it presents one of the finest natural examples of a logarithmic spiral - Fibonacci spiral. It represents a mathematical concept. Is that not clear – if it is not – look at the Roger Penrose video again.
Yes, of course, there are physical objects exhibiting geometric forms or structures; but it doesn't follow that nature contains platonistically abstract or "ideal", purely mathematical entities, or that there really are (perfectly) 0D, 1D, or 2D objects, i.e. mathematical points, lines, or surfaces, in physical reality.

Your funny - if you define math in human terms - then yes before humans existed - there is no human math - profound conclusion!
User avatar
Consul
Posts: 6036
Joined: February 21st, 2014, 6:32 am
Location: Germany

Re: What is mathematics?

Post by Consul »

Woodart wrote:Your funny - if you define math in human terms - then yes before humans existed - there is no human math - profound conclusion!
What exactly do you mean by "math" in this statement of yours: "Math exists before humans exist – it is a fundamental part of the structure of the universe." (?)

It is certainly true that physical objects with geometric forms (shapes) or structures existed long before humans and human mathematics existed.
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars
Woodart
Posts: 290
Joined: March 3rd, 2017, 1:49 pm

Re: What is mathematics?

Post by Woodart »

Consul wrote:
It is certainly true that physical objects with geometric forms (shapes) or structures existed long before humans and human mathematics existed.
Physical objects with mathematical properties.
User avatar
Sy Borg
Site Admin
Posts: 14992
Joined: December 16th, 2013, 9:05 pm

Re: What is mathematics?

Post by Sy Borg »

Are we referring to entities themselves or the model used to describe them?

Entities feature patterning in structure (spheres/pi, crystals, branching, Fibonacci sequence) and in time (natural rhythms, infolding, extrusion, time crystals) - and these structures and dynamics are modelled with mathematics. Mathematics came with humans and was logically preceded by the patterns that gave rise to it.
Woodart
Posts: 290
Joined: March 3rd, 2017, 1:49 pm

Re: What is mathematics?

Post by Woodart »

Greta wrote:Are we referring to entities themselves or the model used to describe them?

Entities feature patterning in structure (spheres/pi, crystals, branching, Fibonacci sequence) and in time (natural rhythms, infolding, extrusion, time crystals) - and these structures and dynamics are modelled with mathematics. Mathematics came with humans and was logically preceded by the patterns that gave rise to it.

I agree with Penrose that we discovered math in "things". We also developed our own math. I think the universe has more math for us to discover.
Spectrum
Posts: 5161
Joined: December 21st, 2010, 1:25 am
Favorite Philosopher: Eclectic -Various

Re: What is mathematics?

Post by Spectrum »

Woodart wrote:
Spectrum wrote: The further exploration can be done from Kant's philosophy. (I did 3 years full time on Kant, but at present is a bit rusty on it as I was focusing on Islam since the last 2+ years.)
Roughly,
  • 1. Kant asserted whatever is Mother Nature [all there is] as cognized is conditioned by humans.
    2. Thus Maths emerged after the human conditions a priori [categories, etc.] and a posteriori.
    3. Even the 'Sun' and 'Moon' emerged after the human conditions a priori and a posteriori.
    4. Point here is, 'before' and 'after' humans are time-based.
    5. Time and Space are sensible intuitions a priori which are conditioned by the mind.
    6. Thus whatever is 'Mother Nature' and the Universe is always conditioned by the mind. Thing-in-themselves [noumenon] do not exist independent of the human conditions.
    7. If we want to speculate more than the above, then we must understand and qualify they are mere speculations. As Wittgenstein had stated re thing-in-itself 'where we cannot speak of, we must remain silent.'
I don't want to go into a detail discussion of the above, I am merely giving a view on how far can the above ideas go as far as Kant is concern. Naturally there are counters [by realists] to the above views but having studied Kant in so much depth, I agree with his views [which are also aligned with Eastern philosophies] on the above.

I respect many of your ideas Spectrum, however many times I find it difficult to clearly understand what you are saying. If you have a point of contention – can you brake in down in simpler terms?
I was merely throwing in Kant's view re thing-in-itself and other points. If you are not on to it, never mind.

-- Updated Sat Jul 08, 2017 9:32 pm to add the following --
Greta wrote:Are we referring to entities themselves or the model used to describe them?
Entities feature patterning in structure (spheres/pi, crystals, branching, Fibonacci sequence) and in time (natural rhythms, infolding, extrusion, time crystals) - and these structures and dynamics are modelled with mathematics. Mathematics came with humans and was logically preceded by the patterns that gave rise to it.
"Patterns" ??
If we dig deeper philosophically there is no such thing as 'patterns-in-themselves' [Kant].

Look at the letter "M" on a piece of paper. It is a pattern to humans but if you expand it a hundred times it just a 'random' arrangement of pixels of black dots. Expand it further to thousands of million times "you' [any human] will note there is no real 'M' at all.

Even with crystals, there are no crystal-in-themselves. A virus will note cognize any "crystals" at all. To a virus there is no such thing as a crystal but merely bits and pieces of molecular things.

Note an ice cube. There is no real cube pattern as there are no absolute boundaries to denote a specific cube in term of the contents of the H20.
https://plato.stanford.edu/entries/boundary/
At room temperature the H20 molecules are evaporating from the ice cube. As such there is no way we can identify the real ice cube.
Image

Fibonacci sequence? The 'nautilus fibonacci sequence' is only observed by humans with human invented mathematical computations. At the molecular or atomic level, there is no specific 'nautilus fibonacci sequence.'

Here is an image re a color blind test;
Image

The majority will see a '6' in that image because they are normal human beings.
Those who are color blind will not see a '6' but merely a circular image with small dots and circles.
I contend those who are color blind who merely see small dots are seeing something more real [factual] because they were not conditioned [brainwashed] by normal human programming.

My point is there are no patterns-in-themselves existing out there. Whatever patterns we observed are due to normal human conditioning [brainwashed] via evolution.

According to Kant, there is no thing-in-itself, no patterns-in-themselves, no mathematics-in-itself. Whatever exist are things-by-human_self.

If you don't get my point, never mind. It [Kantian philosophy] is not an easy concept to grasp plus my English is not superb to make it [such complex ideas] easier.
Not-a-theist. Religion is a critical necessity for humanity now, but not the FUTURE.
User avatar
Burning ghost
Posts: 3065
Joined: February 27th, 2016, 3:10 am

Re: What is mathematics?

Post by Burning ghost »

Math didn't exist before humans in the same respect that the concept of trees didn't exist 6 million years ago.

Nature exists and a human view of said nature is part of nature.
AKA badgerjelly
Spectrum
Posts: 5161
Joined: December 21st, 2010, 1:25 am
Favorite Philosopher: Eclectic -Various

Re: What is mathematics?

Post by Spectrum »

Burning ghost wrote:Math didn't exist before humans in the same respect that the concept of trees didn't exist 6 million years ago.

Nature exists and a human view of said nature is part of nature.
It is not only human view of nature, but rather it is nature itself that conditioned by the human mind.
Here is something for reflection, Kant stated;
“we ourselves bring into the appearances that order and regularity that we call nature, and moreover we would not be able to find it there if we, or the nature of our mind, had not originally put it there. [...] The Understanding is thus not merely a faculty for making rules through the comparison of the appearances: it is itself the legislation for nature, i.e., without Understanding there would not be any nature at all” (A125–126).
https://plato.stanford.edu/entries/kant/#LawGivNat


The "Understanding" is faculty of the human mind.
Kant stated, without this faculty in our brain/mind called Understanding "there would not be any nature at all" for humans to give a view about nature.
The normal person will ask, how can that be when I am observing nature [birds, bees, tree, mountains, etc. doing their own thing] out there all the time?
This is quite a mind blowing view that require very deep reflection and familiarity with Kant's philosophy.

I don't want to go into a detail discussion on this but the point that it is quoted in the SEP is something credible and worthy to for one to understand this concept and then either to agree or disagree with it.

Understanding the above will give one an idea why Kant insist there is no 'mathematics-in-itself' floating freely and independently out there waiting for humans to discover.
Not-a-theist. Religion is a critical necessity for humanity now, but not the FUTURE.
User avatar
Burning ghost
Posts: 3065
Joined: February 27th, 2016, 3:10 am

Re: What is mathematics?

Post by Burning ghost »

Spectrum -

Trust me you don't need to quote Kant for my benefit. I was trying to put it in "simpler terms" for Woodart.

I prefer Nietzsche's question "why is belief in such judgements necessary", in reply to Kant's question posed about a priori judgements.
AKA badgerjelly
Woodart
Posts: 290
Joined: March 3rd, 2017, 1:49 pm

Re: What is mathematics?

Post by Woodart »

Spectrum wrote:
The "Understanding" is faculty of the human mind.
Kant stated, without this faculty in our brain/mind called Understanding "there would not be any nature at all" for humans to give a view about nature. The normal person will ask, how can that be when I am observing nature [birds, bees, tree, mountains, etc. doing their own thing] out there all the time? This is quite a mind blowing view that require very deep reflection and familiarity with Kant's philosophy.

I don't want to go into a detail discussion on this but the point that it is quoted in the SEP is something credible and worthy to for one to understand this concept and then either to agree or disagree with it.

Understanding the above will give one an idea why Kant insist there is no 'mathematics-in-itself' floating freely and independently out there waiting for humans to discover.
I hear what you are saying and I think it is a defensible thesis. However, it is not the only thesis. My particular bias is more of a mix of phenomenology and existentialism. These ontological debates are never settled – and – I don’t think they need to be. The richness of perspective is what makes it all interesting. If you would like to examine more on this – I would be happy too – you have a fine mind and profound understanding of things. Please do not apologize for your English – I find it very good – too good many times for me. Best regards.
User avatar
Consul
Posts: 6036
Joined: February 21st, 2014, 6:32 am
Location: Germany

Re: What is mathematics?

Post by Consul »

Woodart wrote:Physical objects with mathematical properties.
What exactly is a mathematical property, and what mathematical properties do you think are had by physical objects?

If a mathematical property of a physical object is simply a mathematically (numerically) representable (expressible) and measurable physical property or quantity, then physical objects do have mathematical properties. However, mathematical properties thus defined aren't purely mathematical ones, since e.g. when we ascribe a mass of 10kg to a material thing, we don't just ascribe a number to it but a number plus a physical unit ("kg").
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars
Woodart
Posts: 290
Joined: March 3rd, 2017, 1:49 pm

Re: What is mathematics?

Post by Woodart »

Consul wrote:
Woodart wrote:Physical objects with mathematical properties.
What exactly is a mathematical property, and what mathematical properties do you think are had by physical objects?

If a mathematical property of a physical object is simply a mathematically (numerically) representable (expressible) and measurable physical property or quantity, then physical objects do have mathematical properties. However, mathematical properties thus defined aren't purely mathematical ones, since e.g. when we ascribe a mass of 10kg to a material thing, we don't just ascribe a number to it but a number plus a physical unit ("kg").
[rule-breaking commentary on another's posting style removed]

1- nautilus shell – it presents one of the finest natural examples of a logarithmic spiral - Fibonacci spiral
2- Human DNA represents the Golden Ratio – PHI
3- Flowers – fish – pine cones – leaves – all demonstrate PHI

The Fibonacci spiral and Golden Ratio – PHI - are complex mathematical principles embedded in living objects. Watch the youtube videos I put in this thread. You are not advancing this thread – quite the contrary.
Steve3007
Posts: 10339
Joined: June 15th, 2011, 5:53 pm

Re: What is mathematics?

Post by Steve3007 »

Burning ghost:
Math didn't exist before humans in the same respect that the concept of trees didn't exist 6 million years ago.

Nature exists and a human view of said nature is part of nature.
This is a perfectly valid comment, but I think the thing that's different about mathematics is that, as I said earlier, although its origins are rooted in descriptions of the regularities in the physical world (like languages which include the word "tree") it has broken free of those origins and floats freely. This is the reason why earlier posters on this thread have been able to truthfully state that mathematical proofs are not dependent on empirical observations but stand on their own in an entirely abstract world.

If, following Plato, we decided that something similar was true of languages other than mathematics and that all real-life trees are imperfect reflections of a perfect, abstract "form of the tree" then maybe we could widen the idea?
Post Reply

Return to “General Philosophy”

2023/2024 Philosophy Books of the Month

Entanglement - Quantum and Otherwise

Entanglement - Quantum and Otherwise
by John K Danenbarger
January 2023

Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul

Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul
by Mitzi Perdue
February 2023

Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness

Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness
by Chet Shupe
March 2023

The Unfakeable Code®

The Unfakeable Code®
by Tony Jeton Selimi
April 2023

The Book: On the Taboo Against Knowing Who You Are

The Book: On the Taboo Against Knowing Who You Are
by Alan Watts
May 2023

Killing Abel

Killing Abel
by Michael Tieman
June 2023

Reconfigurement: Reconfiguring Your Life at Any Stage and Planning Ahead

Reconfigurement: Reconfiguring Your Life at Any Stage and Planning Ahead
by E. Alan Fleischauer
July 2023

First Survivor: The Impossible Childhood Cancer Breakthrough

First Survivor: The Impossible Childhood Cancer Breakthrough
by Mark Unger
August 2023

Predictably Irrational

Predictably Irrational
by Dan Ariely
September 2023

Artwords

Artwords
by Beatriz M. Robles
November 2023

Fireproof Happiness: Extinguishing Anxiety & Igniting Hope

Fireproof Happiness: Extinguishing Anxiety & Igniting Hope
by Dr. Randy Ross
December 2023

Beyond the Golden Door: Seeing the American Dream Through an Immigrant's Eyes

Beyond the Golden Door: Seeing the American Dream Through an Immigrant's Eyes
by Ali Master
February 2024

2022 Philosophy Books of the Month

Emotional Intelligence At Work

Emotional Intelligence At Work
by Richard M Contino & Penelope J Holt
January 2022

Free Will, Do You Have It?

Free Will, Do You Have It?
by Albertus Kral
February 2022

My Enemy in Vietnam

My Enemy in Vietnam
by Billy Springer
March 2022

2X2 on the Ark

2X2 on the Ark
by Mary J Giuffra, PhD
April 2022

The Maestro Monologue

The Maestro Monologue
by Rob White
May 2022

What Makes America Great

What Makes America Great
by Bob Dowell
June 2022

The Truth Is Beyond Belief!

The Truth Is Beyond Belief!
by Jerry Durr
July 2022

Living in Color

Living in Color
by Mike Murphy
August 2022 (tentative)

The Not So Great American Novel

The Not So Great American Novel
by James E Doucette
September 2022

Mary Jane Whiteley Coggeshall, Hicksite Quaker, Iowa/National Suffragette And Her Speeches

Mary Jane Whiteley Coggeshall, Hicksite Quaker, Iowa/National Suffragette And Her Speeches
by John N. (Jake) Ferris
October 2022

In It Together: The Beautiful Struggle Uniting Us All

In It Together: The Beautiful Struggle Uniting Us All
by Eckhart Aurelius Hughes
November 2022

The Smartest Person in the Room: The Root Cause and New Solution for Cybersecurity

The Smartest Person in the Room
by Christian Espinosa
December 2022

2021 Philosophy Books of the Month

The Biblical Clock: The Untold Secrets Linking the Universe and Humanity with God's Plan

The Biblical Clock
by Daniel Friedmann
March 2021

Wilderness Cry: A Scientific and Philosophical Approach to Understanding God and the Universe

Wilderness Cry
by Dr. Hilary L Hunt M.D.
April 2021

Fear Not, Dream Big, & Execute: Tools To Spark Your Dream And Ignite Your Follow-Through

Fear Not, Dream Big, & Execute
by Jeff Meyer
May 2021

Surviving the Business of Healthcare: Knowledge is Power

Surviving the Business of Healthcare
by Barbara Galutia Regis M.S. PA-C
June 2021

Winning the War on Cancer: The Epic Journey Towards a Natural Cure

Winning the War on Cancer
by Sylvie Beljanski
July 2021

Defining Moments of a Free Man from a Black Stream

Defining Moments of a Free Man from a Black Stream
by Dr Frank L Douglas
August 2021

If Life Stinks, Get Your Head Outta Your Buts

If Life Stinks, Get Your Head Outta Your Buts
by Mark L. Wdowiak
September 2021

The Preppers Medical Handbook

The Preppers Medical Handbook
by Dr. William W Forgey M.D.
October 2021

Natural Relief for Anxiety and Stress: A Practical Guide

Natural Relief for Anxiety and Stress
by Dr. Gustavo Kinrys, MD
November 2021

Dream For Peace: An Ambassador Memoir

Dream For Peace
by Dr. Ghoulem Berrah
December 2021