DOES MATH EXIST?
(Is math discovered or invented?)
These are actually an age-old philosophical questions. Recently, Plato’s Cave philosophy meetup member,
Pamala Clift, posted a video that does a great, entertaining job of addressing these questions. Below is a thread
from a post I made to my ‘WING CIRCLE’ math/philosophy facebook group.
So, check it out. Feel free to add comments to the facebook thread, +/or in this Plato’s Cave discussion post.
TIA.
ReallYours,
swami_mathtraveler
P.S. This thread includes LOTS of great discussion points and exchanges, plus a little humor along the way:)
There are also some nice links worth following. Of particular note is Alan Gaynor’s “On a Notation for
Dimensionally Qualified Predicate Calculus Quantification”, including his ‘dimensional cardinality
discontinuum’ (of abstract/concrete). He considers combinations from 3 space dimensions and one time
dimension. See the nice table in his paper. Also, I posted links to a past Wing Circle meeting addressing ‘HOW
BIG IS MATH?’ (overview/thread, recap).
Swami WorldtravelerWing Circle
DOES MATH EXIST?!...
http://youtu.be/TbNymweHW4E  WATCH THE VIDEO HERE.
Video: "Is Math a Feature of the Universe or a Feature of Human Creation?" (Idea
Channel, PBS)
- One of the most entertaining treatments of the philosophical question of whether
math is DISCOVERED OR CREATED.
- What say you?...
Video description: "Math is invisible. Unlike physics, chemistry, and biology we can't
see it, smell it, or even directly observe it in the universe. And so that has made a lot
of really smart people ask, does it actually even EXIST?!?! Similar to the tree falling in
the forest, there are people who believe that if no person existed to count, math
wouldn't be around . .at ALL!!!! But is this true? Do we live in a mathless universe? Or
if math is a real entity that exists, are there formulas and mathematical concepts out
there in the universe that are undiscovered? Or is it all fiction? Whew!! So many
questions, so many theories..."
LikeLike · · Stop Notifications · Share · Edit · Promote · July 26
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Steve Parady, Tim Osmar, Nathaniel Wilson and 4 others like this.
John Conolley It seems obvious to me that math is just a way of talking about the
world. It isn't an entity. It's entirely abstract.
July 26 at 11:31pm · Like · 1
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Mango Spy Of course it exist. Concepts exist too, without physical qualities. I believe
Kant called math a synthetic priori. Time and space are also priori concepts. Any
arguments against their existence can only exist because they exist. In other words: a
posteriori of empirical cognition can never cancel out the very priori concept it relies
upon.
If you start to question the existence of anything that can be thoughts of or named,
you're just categorically confused....so says the little mango.
July 27 at 12:17am · Like · 1
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Rami Kuttaineh As discovered by a six year old girl [essentially] "All is invention."
(insight relayed via Benjamin Zanders, conductor of the Boston Philharmonic)
Under this framework one only need ask who is doing the inventing. I look forward to
reading the essay. Thanks Swami!
July 27 at 5:12am · Edited · Like
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Rami Kuttaineh Response
here:https://plus.google.com/101288525163904.../posts/S3dvEx6qzFJ
The question heard behind what he was asking is, "Does the human brain
exist…
plus.google.com
The question heard behind what he was asking is, "Does the human brain exist
anywhere other than the universe?" Since what appears to be agreed upon, at… Rami Kuttaineh - Google+
July 27 at 5:57am · Like · Remove Preview
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John Conolley Mango, that sounds like some Kantian hand-waving dreamed up to
stop us questioning the existence of God. You can jabber about unicorns or Easter
bunnies all you want, but they don't exist. Neither does God, and abstractions exist
only abstractly. Don't mix up entities and our ways of thinking about entities. Math isn't
a thing, logic isn't a thing, prayers and dreams aren't things.
July 27 at 7:55am · Like
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Mango Spy Conolley, If we are to count only physical entities as existing, then the
above article is a joke altogether. We obviously all know math doesn't have legs, or a
surface we can touch. Silly!
I wouldn't be so quick to flush math down the toilet along with God. They are two very
different things. Math will always exist as a priori as long as there is time and space,
whether someone is there to organize it into thoughts, methods or not. God is a
human construct and wouldn't exist independently from us; however, math is a
transcendental concept that cannot be canceled out by empirical means.
July 27 at 11:03am · Like
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Swami Worldtraveler .
Interestingly, it seems hard to keep "God" out of the philosophical discussion of
mathematics. Oh well, be it as it may
July 27 at 11:06am · Edited · Like
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Mango Spy He started it!
July 27 at 11:10am · Like
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Swami Worldtraveler .
Haha. Yeah, well, somebody's gotta start it
July 27 at 11:10am · Like
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Mango Spy Interestingly enough (just letting my mango brain surf freely here for a
moment,) at the root of each human concept we find physical Neurotransmitters at the
core.
July 27 at 11:13am · Like
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John Conolley I'm not the one who dragged Kant in here. Everything Kant did was to
keep God alive. I don't think there's anything transcendent about math (or anything
else). I think math is a thing we do, and we do it our way. That it doesn't leap directly
from something pre-existent in reality is shown by the constants we have to use to
make it correspond to reality, such as c (speed of light), h (Plank's constant), and G
(gravitational constant).
July 27 at 11:19am · Like
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Mango Spy tran·scen·den·tal (trnsn-dntl)
adj.
1. Philosophy
a. Concerned with the a priori or intuitive basis of knowledge as independent of
experience.
http://www.thefreedictionary.com/transcendental
transcendental
www.thefreedictionary.com
Definition of transcendental by The Free Dictionary
July 27 at 11:22am · Like · Remove Preview
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Mango Spy You can't say "Math doesn't exist", but you can claim it doesn't exist
according to certain conditions (i.e. empirical conditions). But by doing so you have
moved away from the priori, upon which the posteriori depends. It's quite the
paradoxical dilemma you have there.
July 27 at 11:26am · Like
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Kathleen Fenton If math doesn't really exist then what was I tortured with in school for
all those years?
July 27 at 9:37pm · Unlike · 1
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Swami Worldtraveler .
LOL, Kathleen! You missed your calling in comedy
July 27 at 9:39pm · Like
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John Conolley Other than the mathematical use of the word, "transcendental" is a
concept from mysticism. It's double talk. You don't need to refer me to a dictionary. My
vocabulary is fine.
You have to differentiate between things and processes. Math isn't a thing, it's a
process. Like aging. Or life. These things don't exist. They're processes we go
through.You wouldn't say baking a cake exists. Would you? It's merely the process a
baker goes through to get a cake. Process is a difficult concept for human beings to
deal with. A process doesn't have clear edges. It's not a neat clear entity. Yet, neat,
clear entities are what we understand best. That doesn't make it reasonable to reify
abstractions.
July 27 at 10:19pm · Like
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Mango Spy John, the application of "transcendental" in philosophy does not refer to
mysticism. You have to understand that a definition of a word can vary depending on
its application. You seem a bit stuck in singular word definitions, hence your confusion
in regards to the many applications of "existence".
July 27 at 10:40pm · Like
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John Conolley I am neither stuck nor confused. Look back at that dictionary entry you
wanted me to see. Every usage but the last one is mystical.
July 27 at 10:41pm · Like
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Mango Spy Here we go: John, I agree with you that math does not exist as an object.
July 27 at 11:08pm · Like
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Swami Worldtraveler .
http://en.wikipedia.org/wiki/Mathematical_object
"The ontological status of mathematical objects has been the subject of much
investigation and debate by philosophers of mathematics."
Mathematical object - Wikipedia, the free encyclopedia
en.wikipedia.org
Commonly encountered mathematical objects include numbers, permutations,
partitions, matrices, sets, functions, and relations. Geometry as a branch of
mathematics has such objects as hexagons, points, lines, triangles, circles, spheres,
polyhedra, topological spaces and manifolds. Another branch - A…
July 27 at 11:46pm · Edited · Like · 1 · Remove Preview
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Swami Worldtraveler .
http://plato.stanford.edu/entries/platonism-mathematics
More at http://plato.stanford.edu/search/searcher.py......
Platonism in the Philosophy of Mathematics (Stanford Encyclopedia of
Philosophy)
plato.stanford.edu
Platonism about mathematics (or mathematical platonism) is the metaphysical
view that there are abstract mathematical objects whose existence is independent of
us and our language, thought, and practices. Just as electrons and planets exist
independently of us, so do numbers and sets. And just as st…
July 28 at 2:01am · Like · 1 · Remove Preview
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Swami Worldtraveler .
Concept:Concrete::Abstract:Real
Concept:Abstract::Concrete:Real
Real:Concrete::Abstract:Concept
July 28 at 2:07am · Edited · Like · 1
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Mango Spy Swami, you had to go make it worse, lol!
Here is how it goes guys: when you are communicating with someone, you're making
an effort at interpreting what they are telling you, so that you can reply accordingly and
so forth.
When John insists on interpreting my application of "transcendental" as mysticism
even after I've made it clear that I'm using it in its philosophical application....well, that
insane.
Swami, when I used the word "object" in my communication with John, I was applying
the definition he was communicating.
Now repeat after me: You cannot construct a counter argument based on alternative
word definitions.
Now, Swami - go sit in a corner!
July 28 at 8:29am · Like
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John Conolley Alternative? It was your dictionary. Read it for yourself.
July 28 at 9:50am · Like
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Swami Worldtraveler .
Mango: So, you object?
July 28 at 10:36am · Like · 1
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Swami Worldtraveler .
MATHEMATICAL PLATONISM "is the metaphysical view that there are abstract
mathematical objects whose existence is independent of us and our language,
thought, and practices."
COUNTER VIEW: "...philosophers have developed a variety of objections to
mathematical platonism. Thus, abstract mathematical objects are claimed to be
epistemologically inaccessible and metaphysically problematic."
(Ref. http://plato.stanford.edu/entries/platonism-mathematics.)
Platonism in the Philosophy of Mathematics (Stanford Encyclopedia of
Philosophy)
plato.stanford.edu
Platonism about mathematics (or mathematical platonism) is the metaphysical
view that there are abstract mathematical objects whose existence is independent of
us and our language, thought, and practices. Just as electrons and planets exist
independently of us, so do numbers and sets. And just as st…
July 28 at 10:53am · Like · Remove Preview
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Swami Worldtraveler .
Perhaps a view from (retired) university math professor, Michael Taylor, would add
interest and value to the discussion..
July 28 at 10:57am · Edited · Like
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Jack Fuller For a 'reality check', pun intended, check out Jim Baggott's, 'Farewell to
Reality, How modern physics has betrayed the search for scientific truth'.
July 29 at 10:14am · Unlike · 1
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Swami Worldtraveler .
- Amazon: https://www.amazon.com/Farewell-Reality.../dp/1605984728
- Review (short): https://www.kirkusreviews.com/.../jim.../farewell-to-reality
- Review (longer):http://www.math.columbia.edu/~woit/wordpress/?p=6002
- Review (broader; other related books, too):http://www.economist.com/.../21578366fundamental-physics...
July 29 at 10:23am · Edited · Like
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Rick Lane if NOT ! it will take MATH to prove it.
July 29 at 11:25am · Unlike · 2
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Swami Worldtraveler .
Rick: Haha, good one! You jest, but an attempt was famously made to prove math on
the foundation of logic in the late 1800's (Mathematica Principia), but failed!
July 29 at 12:56pm · Edited · Like
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Swami Worldtraveler .
See also "metamathematics" (math about math!).
July 29 at 12:56pm · Like
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Steve Parady Math shows repeatable patterns evident in the behaviors of physical
objects, so that makes it pretty real to me.
July 29 at 1:34pm · Like · 1
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Michael Taylor Swami, you've heard me address this question before. So far as I'm
concerned, math exists. Two reasons: First, I work and live with
mathematics. The streets of topology and Hilbert spaces are familiar to
me. Second, this familiarity is not a purely personal dream. I know that
if I prove a mathematical result and someone else explores in that
direction, then he or she will find the same result. In other words, mathematics is a
shared reality.
The way the question is posed -- _Does math exist_? -- seems to imply
that the word "exist" has some sort of intrinsic meaning which is, or
ought to be, in this case, the common property of us all. I don't agree
with that.
If one asks, "Does Hillary Clinton exist?" or "Do unicorns exist?" then
there are commonly accepted means of settling those questions. These
questions lie within an arena in which "existence" has a commonly held
meaning. However it is not very hard to step outside that arena and ask questions
which -- because they have a similar form -- sound very
reasonable.
When I say, "Mathematics exists," what I'm doing is extending the
meaning of the word "exists." This is a personal choice taken for the
reasons indicated above. If someone says, "No! Math doesn't exist! It
has no weight! It has no location!" then they are taking the possession
of weight and location as criteria of "existence." This is another
personal choice, another way to extend the meaning of "exist."
_
Does math exist_? seems to me an unsatisfactory question. You can make
the answer come out any way you want depending on the manner in which
you stretch the meaning of "exist" beyond its ordinary usage.
Regards,
Mike
On 07/29/2014 01:34 PM, Steve Parady wrote:
July 29 at 3:56pm · Unlike · 3
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Rami Kuttaineh Unasked for, however I referenced the book you posted further up in
this thread back to Plato's
Cavehttp://www.meetup.com/.../thread/39404332/post/123369642/...
Rami Kuttaineh - Faith Philosophically As Inherently Irrational and Immoral Plato's Cave - The Orl
www.meetup.com
Welcome to Plato's Cave where, as prisoners of this realm, we seek
enlightenment through inquiry, reflection and cordial dialogue. If you are interested in
discussing philosophy, philosophers, and re
July 29 at 4:00pm · Like · Remove Preview
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Rami Kuttaineh And then mainly for the song at the
endhttp://mysticbourgeoisie.blogspot.com/.../finding-your...
mystic bourgeoisie: Finding Your Own Myth
mysticbourgeoisie.blogspot.com
this site is a labor of love. i.e., if you love me enough, I'll be able to complete it. send
proof of love via buttons above. please. if you can. thanks.
July 29 at 4:02pm · Like · Remove Preview
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Swami Worldtraveler .
Rami: The book I linked to was shared by Jack Fuller. I know next to nothing about it.
Would be interested in your thoughts. If too far off-topic, please start a separate
thread. Thx.
July 29 at 4:32pm · Like
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Jack Fuller I have read the book and believe much of it is, indeed, on-topic. It is a
thought provoking read. Much to comprehend and digest for a 318 page book. Could
not help but to hear Carl Sagan whispering, 'Extraordinary claims require....'.
July 29 at 5:13pm · Like · 1
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Swami Worldtraveler .
Care to summarize the thesis, and share any details, for the benefit of the thread
readers? TIA.
July 29 at 5:18pm · Like · 1
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Rami Kuttaineh Actually when you read Chris Locke's mysticbourgeoisie article you'll
find it does address just what is going on here (in a way).
July 29 at 5:34pm · Like
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Swami Worldtraveler .
Again, for the benefit of those on this thread, any summary +/or details would be
helpful. TIA.
July 29 at 6:01pm · Like
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Alan Gaynor I am currently in a cell phone-only location. As both Mike and Swami
Worldtraveler know, I have proposed an ontologically agnostic notation to address just
these sorts of questions in an objective way. I am very sympathetic to Mike's take on
the issues here and I have to say, this seems to me to be among the greatest
impediments to the reunification of science and philosophy!
Yesterday at 9:51am · Like
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Alan Gaynor When I am not net-handicapped, I will provide links to text and graphics.
Yesterday at 9:53am · Like
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Robert Argento Of course it (they) exist. But that does not mean that it is a reality - in
the materialistic sense. We are speaking of models, especially when speaking of
math. A model does just that, it MODELS reality. And as a model always, by definition,
lacks at least one property of the thing of which it is a model. Otherwise it would be the
thing itself. I feel that In math we have a model, a very broad almost universal model
of a very prime property of reality. But it is, indeed, a model. And it does, indeed, exist.
Thus, the either/or question presented in the original question is merely a semantic
error based on different interpretations of what is meant here by the word "exist". I
know this is true because The Easter Bunny told me so.
Yesterday at 10:31am · Unlike · 4
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Alan Gaynor I hope you will take a look at these two artifacts. The PDF gives a
description in text of the dimensional qualification notation that I am proposing for the
predicate calculus. The attached image shows the Abstract-Concrete distinction as a
more articulate dimensional cardinality discontinuum. Don't let the words or the
symbolization scare you here. This is not really difficult and I think you will find it
conceptually useful in the context of this discussion.
Yesterday at 12:39pm · Unlike · 1
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Alan Gaynor Oops. Here is the link:http://files.meetup.com/.../On%20Dimensional...
and the image is below:
Yesterday at 12:40pm · Like · 1
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Alan Gaynor I have been working on and with this since at least 2011 so any
feedback, positive or negative would honor me.
Yesterday at 12:41pm · Like
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Alan Gaynor It is easy to see that the process of abstraction is a matter of subtracting
dimensions from the concrete. The dichotomy between abstract and concrete is not a
binary one. If this notation and conceptual framework has sense, there are 7
gradations of abstraction!
Yesterday at 12:44pm · Unlike · 1
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Alan Gaynor Numbers, of course, belong in the 0.0 category.
Yesterday at 12:45pm · Unlike · 1
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Alan Gaynor The question of the existence of numbers becomes a question of which
kind of existent they are. Materialists are free to assert that only things of
dimensionality 3.1 exist. The rest of us are free to allow the logical existence symbol
(the reversed E)--properly adorned with a dimensional cardinality qualifier--to bless the
variables we wish to use in our much more expressive and equally rigorous predicate
calculus expressions.
Yesterday at 12:53pm · Unlike · 1
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Mango Spy I think I see what you're saying Robert Argento. While you're using
different words. we're still down to the pure concept itself. I think some people are
having a problem defining the word "math" as well, and take it to only mean the
complete human construct.
Yesterday at 1:13pm · Like
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Swami Worldtraveler .
As this thread reveals, “exist” can take a range of meanings. Participants have clarified
their intended use via examples, comparisons, and other words. This is as it should
be; as it must be. Communication can be a process and an effort.
The meaning (or meanings) of “math” have not been discussed as much. One view
put forward is that it is a process. Indeed, it involves processes, but it is arguably more
than that. To get a sense of what math is, and its breadth/depth, check out a past
Wing Circle coverage of the topic…
THREAD: “HOW BIG IS MATH?!”
www.facebook.com/events/576228362402614
- MEETING RECAP
www.facebook.com/groups/300836690015888/321610207938536
Yesterday at 3:00pm · Like
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Robert Argento and therein lays the semantic paradox. One describes it as a noun,
"the complete human construct", albeit using a few descriptive adjectives. Thus, in one
sense, it "exists".
Alan's novel fantasized a language devised to bridge over these gaps and now he is
attempting to develop this into a reality. I must conquer my fear of the effort required
and study his suggestions a lot more closely .
Yesterday at 3:01pm · Like · 1
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Swami Worldtraveler .
Another aspect not really touched on is the possible difference(s) of the question,
“Does math exist?”, vs., “Is math discovered or invented?” For example, is math as an
abstract concept open to discovery by other beings? Is this different in nature in
comparison to other abstract concepts, like the tooth fairy? This admittedly ridiculous
example aims to get at thinking about the nature of the kind of abstract object math is.
Alright, discuss:)…
Yesterday at 3:11pm · Like
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Robert Argento math was not invented. It has been developed, and that over
thousands of years by an uncountable number of thinkers. Shall we complicate the
issue by asking if there has been "fashion" in the culture of Mathematics over the
centuries?
Yesterday at 3:24pm · Like
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Swami Worldtraveler .
Doesn't a thing have to be invented (or discovered) before it can be developed?
Yesterday at 3:29pm · Like
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Robert Argento To that degree I would suggest that the question of its "discovery" is
trivial. Yes, someone did once "discover" that the sun always rose in the east. Was
this a "discovery" or was it an observation? Was it invention or was it insight? This isn't
the issue originally implied. The main issue, in my interpretation, concerned if
Mathematics was an artificial intellectual construction which may or may not have
anything to do with "reality". No, I think i would rather stick with the word "insight"
rather than "discovery" or "invention".
Yesterday at 3:54pm · Like
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Swami Worldtraveler .
So, might "other" beings have the same insight of math, thus perhaps indicating that it
is independent of human thought?
Yesterday at 3:58pm · Like · 1
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Robert Argento well, let us ask about things other than math in relation to other
beings. I easily can point to several things, phenomena or whatever we wish to call
them, where other earth-bound beings seem to have or can develop 2insight" into
relationships (cause and effect), perhaps not as abstract at math, but still. So, i can
imagine an alien finding itself on earth making the same sort of observation and
conclusion. Leaving Earth, we as humans are still making observations, collecting
information and drawing conclusions from these. So I see no difference in "another
being" doing the same. Thus, i conclude that other beings could have the same insight
of the abstract concept of math, based, of course, on their level of intellectual
development.
Now, if that "other being" was a sub-soil Martian bacteria, I tend to think that its
concept of math would be....well... limited.
Yesterday at 4:17pm · Like
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Swami Worldtraveler .
Well, bacteria do math all the time... they MULTIPLY!
21 hours ago · Edited · Like · 1
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Swami Worldtraveler .
They even follow a curve!...
21 hours ago · Like
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Swami Worldtraveler .
So, math "exists" as an abstract concept, at least, and possibly independent of the
human mind. As such, it is discovered. Of course, there are other views:)
21 hours ago · Like
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Swami Worldtraveler .
And, of course, Alan's approach is more formal and rigorous, but is not for the
intellectually disadvantaged.
21 hours ago · Edited · Like · 1
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Swami Worldtraveler .
Alan: I have read in the past your "On a Notation for Dimensionally Qualified Predicate
Calculus Quantification", and reread it just now. It is indeed perfectly suited to
addressing the nature of the existence of math.
*I suggest all interested parties give it a serious look...
21 hours ago · Like
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Swami Worldtraveler .
Alan: As you may recall, from a previous discussion on the notation, I suggested that
space, and time be allowed to span from zero and to all the integers. In fact, "multipletime" models of physics have been explored. And, to "complicate" matters (or make
more full?), complex, or even hyper-complex numbers (e.g. quaternions) could be
included.
20 hours ago · Like · 1
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Swami Worldtraveler .
Alan: I also like your "discontinuum" scale of abstraction.
20 hours ago · Like · 1
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Robert Argento Swami wrote; "So, math "exists" as an abstract concept, at least, and
possibly independent of the human mind. As such, it is discovered" - I will have to
disagree. One could easily exchange the word MATH for PHYSICS and suddenly
conclusion no longer works. Who DISCOVERED physics? No one, of course. We
gained insight into physical phenomena and simply call that insight "physics". Such is
also the case with mathematics. The mathematical relationship of things to one
another was there all of the time. This is not a case of "if a tree fell in the forest and no
one was there to hear it" . But then, yes, in a different sense of the word, different
principles of mathematics were "discovered" incrementally and there still is probably
more to "discover", i.e. understand. For it is more understanding than discovering.
18 hours ago · Like
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Swami Worldtraveler .
I reiterate: "Of course, there are other views:)"
18 hours ago · Like
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Swami Worldtraveler .
But, to continue the "debate"...
Physical relationships exist independent of humans, and so do mathematical
relationships. Both are discovered.
18 hours ago · Like
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Robert Argento ok. that will do. Same ides, different words. Now if we had taken that
in German, we could have been more precise. Of course we could have taken it in
Italian but then we would have been more confused.
18 hours ago · Unlike · 2
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Swami Worldtraveler .
An interesting difference between physics and mathematics. Physics is empirical, but
math need not be (e.g. prime numbers).
18 hours ago · Like
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Robert Argento If you had said imaginary numbers I would have agreed immediately
- but please explain about primes? I believe I, as many others, have written computer
programs to generate primes.
18 hours ago · Like
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Swami Worldtraveler .
Writing a program and a thing being empirical or not are unrelated.
18 hours ago · Like
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Swami Worldtraveler .
As for "imaginary" numbers, substitute "other kind of number". They are no more or
less "real" than real numbers. Negative numbers, and zero were problematic at one
time, too. Plus, there are "hyper-complex numbers", plus quite a few others.
P.S. Of course, use "imaginary number" in the reasoning, if you like
18 hours ago · Edited · Like
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Robert Argento please explain what you mean by empirical. I used the example of
programming in that it implies one understands the character of such numbers and
can thus generate a list of them. I am unclear as to "empirical" in this case.
18 hours ago · Like
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Swami Worldtraveler .
This one will do:
"Based on, concerned with, or verifiable by observation or experience rather than
theory or pure logic" Oxford Dictionary
(Similar ones at www.onelook.com/?w=empirical&ls=a.)
Definitions of empirical - OneLook Dictionary Search
www.onelook.com
18 hours ago · Like · Remove Preview
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Robert Argento so, an understanding of the generation of a list of primes, is that not
verifiable by observation? In suppose one COULD say that due to the massive amount
of calculation needed when into the higher primes, one cannot verify except using the
same princi...See More
17 hours ago · Like
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Swami Worldtraveler .
Empirical in the scientific sense of measurable.
17 hours ago · Like
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Swami Worldtraveler .
http://en.wikipedia.org/wiki/Empirical_evidence
Empirical evidence - Wikipedia, the free encyclopedia
en.wikipedia.org
Empirical evidence (also empirical data, sense experience, empirical knowledge, or
the a posteriori) is a source of knowledge acquired by means of observation or
experimentation.[1] The term comes from the Greek word for experience, Εμπειρία
(empeiría).
17 hours ago · Like · Remove Preview
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Robert Argento and primes having no dimension nor mass cannot be measured. ...
Hmmmm. Have we "discovered" the limitation of the concept "empirical"? We DO
measure TIME but often in relation to physical phenomena but then even time is
relative.
17 hours ago · Like
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Swami Worldtraveler .
Consider, "independent of experience", as in "a priori".
17 hours ago · Like
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Swami Worldtraveler .
Primes are a property of some integers, but not arrived at from measurement, i.e. not
empirical.
17 hours ago · Edited · Like · 1
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Alan Gaynor This is really a fascinating conversation. What I like about it is that it is
our participation in a conversation that is ages long. My conceit is that we may actually
be making progress that others could benefit from. This is my "progressive discourse"
rant. Let's try to summarize the essential questions and any proofs we believe we
have uncovered, shall we?
16 hours ago · Like · 1
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Robert Argento My summary is that there is no real right and wrong here.(Not that I
would expect any). We are experiencing the limits of language seeing even where
THIS model, language, has its limitations in describing things conceptual. It finally
brought us around to the idea of "empirical" which, to me, equated with the
materialistic as we had previously discussed the reality of non-materialistic "things".
Which, once again, brings me around to Alan´s work.
16 hours ago · Unlike · 1
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Mango Spy But (there's always a but, right?) Any intelligent entities birthed by our
universe would share certain universal concepts with humans, no matter how they
communicate those ideas I believe, and they could not communicate any ideas about
the volume[s] around them, or the changes and phenomena experienced without
applying the basic idea of what we consider math.
9 hours ago · Unlike · 1