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Mathematical physics, natural science, and philosophy of science

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#1 Otto Piechowski

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Posted 10 January 2020 - 04:09 PM

Please share your thoughts about any part (or all) of the following:

 

“Art, chance, and violence differ from nature and so aid in its definition, but a perhaps more significant opposite of the natural or the physical in our day is the mathematical.  This opposition becomes important when differentiating natural science from mathematical knowledge as this is applied to nature.  In mathematical physics, for example, the object of consideration is not the natural as such but rather the sensible or physical as compounded with the quantified or mathematical.  It is for this reason that mathematical physics is called a mixed science.  The middle terms or explanatory factors it employs are physico-mathematical, but the formality under which it demonstrates is mathematical and its conclusions are only terminatively physical.  The mathematical physicist must measure motion or time in order to treat it; the philosopher of nature has the problem of defining motion or time regardless of how it is measured.  Again, the results attained by the mathematical physicist require interpretation if one is to give a physical reason or explanation for the facts he knows in only their mathematical reasons.  Such interpretation, it can be argued, is itself external to mathematical physics; it is properly the function of the science of nature, where the physical causes of natural things are sought.  The mathematical physicist may himself take on this function, but it is noteworthy that difficult problems of interpretation are increasingly becoming the domain of the philosopher of science.”  (The Elements of Philosophy, William A. Wallace; PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §17.  NATURE  //  [paragraph] 7  //   [page] 48).

 

With gratitude,

 

Otto



#2 jdk

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Posted 10 January 2020 - 04:25 PM

Crowdsourcing an essay for a class on ontology/epistemology? lol.gif  

 

I take issue with the first premise ("art, chance, and violence differ from nature), so I'd probably have to read this excerpt in context of the larger discussion to get a more complete understanding of what the author actually believes...this is serious chicken and egg territory. 


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#3 Gipht

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Posted 10 January 2020 - 04:45 PM

Father Wallace has  great intellect, insight and learning and is well worth listening to.  Many people, however, will question whether religion and science can be reconciled, or even if they need to be reconciled.  My understanding is limited,  and I am a humble creature.  Perhaps if I knew more, I would be even more humble.



#4 EJN

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Posted 10 January 2020 - 04:53 PM

A couple of quotes from Niels Bohr are appropriate here -
 

In physics we deal with states of affairs much simpler than those of psychology and yet we again and again learn that our task is not to investigate the essence of things—we do not at all know what this would mean, but to develop those concepts that allow us to speak with each other about the events of nature in a fruitful manner.


It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.


Mathematical physics is really concerned with correlations between objects/events and finding regularities (called dynamical relationships) which can be expressed as mathematical equations.

 


Edited by EJN, 10 January 2020 - 10:41 PM.


#5 Keith Rivich

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Posted 10 January 2020 - 05:11 PM

Nature doesn't care about our math. She does her own thing and we just try and keep up. 



#6 cst4

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Posted 10 January 2020 - 05:22 PM

Maybe I shouldn't pass judgement on an excerpt with such little context, but the whole argument of this particular paragraph seems meaningless to me.  Plus I disagree with the first sentence entirely... art, chance, and violence do not differ from nature as they only exist because there is a nature to exist in.  Maybe Wallace's intention is to show that these concepts are solely anthropogenic, but that does not mean that examples of each of these are not woven into the fabric of nature... art at its finest is the unfolding of the universe, the orbits of celestial bodies, the perfect balance of our ecosystems, the chemical complexity of life... it's the reason many believe in intelligent design, because it is too artfully crafted.  And if the universe exists outside a creator then I see chance as the only alternative.  And I do not understand claiming mathematics is an opposite of the natural... as Galileo said, "mathematics is the language in which God has written the universe."  Mathematical physics is simply diving deeper into the inner workings of concepts that natural philosophers explore from a higher level.  It's like one person strategically analyzing the style in which a poem was written while another is considering the symbolism and meaning of it all.  They are complimentary, not opposites. 


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#7 EJN

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Posted 10 January 2020 - 05:28 PM

Everything existing in the universe is the fruit of chance and necessity.

-- Democritus
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#8 Otto Piechowski

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Posted 10 January 2020 - 05:40 PM

By art, he means the Greek language concept of τέχνη (pronounced tech-nay) which forms part of the phonetic root of the word technology.  A τέχνη is an art in the sense of an activity which produces something; i.e. the carpentry that produces a chair or the playwright who creates a play.  The word art, here, though it would include much of what we call "the arts" today, is not limited to only that sense of art.  It includes any skilled activity which produces an artifact.

 

His meaning of the word chance and violence is best expressed in his own words, which follows:

 

“Chance is different from nature and indeed quite its opposite.  It is defined as an incidental or per accidens cause in things that are for an end and that happen seldom, rather than for the most part.  Moreoever, as happening seldom, the effect in chance is something neither intended nor expected by the agent.  Another definition of chance is that it is an interference between, or an intersection of, two lines of natural causality not determined, by the nature of either, to interfere with one another.  Such happens when, say, a cosmic ray strikes a gene and results in the production of abnormal offspring.  As the example suggests, chance events occur in nature and keep it from being completely determined in its operation.  A related concept is fortune or luck, which is said properly of events wherein an agent who acts with intelligence and will attains an unintended end.  The classic example is the person who is digging a grave and finds a buried treasure.  Unlike chance, fortune is called good or bad (misfortune) depending on the event that happens to the agent.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §17.  NATURE  //  [paragraph] 5  //   [page] 47)

 

“Violence, i.e., compulsion or force, is even more opposed to nature than is chance.  The violent arises not from an intrinsic principle, as does the natural, but from an extrinsic principle, and in such a way that the thing suffering the violence contributes nothing to the result.  The action of the extrinsic principle either prevents the thing acted upon from following its own inclinations or forces it to act contrary to them.  These inclinations are intrinsic sources of activity, e.g., the will for rational life, the appetites for sentient life, and the tendency of form or nature for vegetative life and for non-vital activities and reactivities.  Just as such inclinations give rise to natural movements, so force or compulsion gives rise to violent movements.  It is to be noted, however, that when one is dealing with the inanimate, where the ends intended by nature are not always clearly discernible, the distinction between natural and violent movements becomes much less sharp than in the sphere of human activity and even of living things in general.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §17.  NATURE  //  [paragraph] 6  //   [pages] 47 and 48)


Edited by Otto Piechowski, 10 January 2020 - 05:41 PM.


#9 Sleep Deprived

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Posted 10 January 2020 - 05:50 PM

Nature doesn't care about our math. She does her own thing and we just try and keep up. 

I have my degree in Physics, and I was always amazed that something would simply 'happen' in nature (all on its own, without any thought - think of the apple falling from the tree) and we would apply math to it to explain  the phenomenon.  Some of the math for some events/things is profoundly complicated.  There are plenty of things that happen that we cannot yet apply math to - that 'math' hasn't been invented yet.  We can explain the motion of the apple mathematically, how it absorbs/emits heat mathematically, probably how it rots mathematically, but nowhere do we really explain 'apple'.  More fundamental is time - we have all kinds of equations with time as a factor, yet, what is time?  There is no Time Atom, or any Time Wavelength - at the core of it, what is time?  No one has ever adequately explained it.

 

It seems that no matter what the event, we can explain certain aspects of it in terms of math equations.  The job of a physicist is to find the math that explains the phenomenon that he is trying to quantify.  Nature simply happens.  We try to apply math to it.

 

We have known for a long time that nature doesn't always act the same way in certain cases.  Heisenberg's Uncertainty Principle alludes to this.  Chaos Theory is another attempt to try to explain some of these things.

 

In the end, was Nature 'designed'?  Was the Greatest Mathematician Ever responsible for all that we see?  Or is everything we know and see simply a 'happening', without a captain at the helm?  Did the 'designer' create all the physical laws, constants, matter, and energy, then simply step back and let it all run forward?  Are we on autopilot?  Are there multiple (even infinite) universes out there, each with their own (different) physical laws and different physical constants?  Have most of those universes imploded before they even got off the ground because 'their' physical laws are incompatible with continued existence?  Is OUR universe really the only one that has lasted more than a millisecond?  Whatever a millisecond is.


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#10 jdk

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Posted 10 January 2020 - 06:08 PM

“Chance is different from nature and indeed quite its opposite.  It is defined as an incidental or per accidens cause in things that are for an end and that happen seldom, rather than for the most part.  

 

This is probably invoking the anthropic principcle, and not in a good way. 

 

I have my degree in Physics, and I was always amazed that something would simply 'happen' in nature (all on its own, without any thought - think of the apple falling from the tree) and we would apply math to it to explain  the phenomenon. 

Boltzmann is so sad right nowbawling.gif lol.gif

 

Statistical fluctuations in the realm of cosmological evolution has fascinated me ever since I read about it in one of Sean Carroll's books. Especially the idea of a "Boltzmann brain," which is one (admittedly not popular) explanation for the "apple."

 

More fundamental is time - we have all kinds of equations with time as a factor, yet, what is time?  There is no Time Atom, or any Time Wavelength - at the core of it, what is time?  

 

Isn't time just a dimension? The fundamental equations of physics work perfectly well backwards as they do forwards (or so I'm told). You could think of the same absurd questions to ask of the more conventional spatial directions. "What is "down?""



#11 ButterFly

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Posted 10 January 2020 - 09:39 PM

The fundamental equations of physics work perfectly well backwards as they do forwards (or so I'm told).

The nuetrino cares not what you were told.  If the equations of physics worked perfectly well backwards as they do forwards, one could unstir a cup of coffee.


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#12 ButterFly

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Posted 10 January 2020 - 09:46 PM

Back to OP, it seems that this passage is highlighting the imprecision of language, despite its usefulness.

 

<<This sentence is a lie.>>

 

We know what this sentence means, but it still does not make sense.  If we solve Newton's equations for a ball thrown in the air and slightly forward, the math tells us it never stops moving.  That makes no sense in reality.  We have not yet told the math about "floor".  The math helped us arrive at an hypothesis, even though it was wrong.  The math gets modified - not the universe.  In other words, we better describe the universe as it is.

 

Sometimes it works the other way.  It is not likely that anyone would have arrived at the Maxwell relations without mathematics.  We could believe the math and test it.  It worked!  There was no real reason why it had to work.  There could have been an unseen "floor" somewhere.


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#13 jdk

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Posted 10 January 2020 - 09:58 PM

The nuetrino cares not what you were told.  If the equations of physics worked perfectly well backwards as they do forwards, one could unstir a cup of coffee.

I could be wrong, but I think I'm accurately paraphrasing good authority. Carroll's entire book is basically devoted to explaining how things that are perfectly invariant under time reversal nonetheless give rise to what we perceive as macroscopic irreversibility (like your cup of coffee). A topic for another thread I guess.



#14 DaveC2042

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Posted 10 January 2020 - 10:03 PM

“Art, chance, and violence differ from nature and so aid in its definition, but a perhaps more significant opposite of the natural or the physical in our day is the mathematical."

 

I can't understand this at all, possibly because there are a bunch of terms that don't seem to be defined.  If, by nature, we simply mean the physical world which is the subject of science, how do 'art, chance and violence' 'differ from it', and why is that meaningful?  Specifically:

  • Is 'art' really just  word for science, or is it human endeavour?  If the former, sure, I guess, - is this just saying the thing studied and the study of the thing are not the same?  If the latter, why is this not part of nature?
  • Does 'chance' mean random and unpredictable behaviour?  If so, why is this not simply an aspect of nature?
  • What does 'violence' mean here?  Why is it not simply an aspect of nature?
  • How is maths the 'opposite' of the natural?  This is not a use of the term I am familiar with.

 

"This opposition becomes important when differentiating natural science from mathematical knowledge as this is applied to nature.  In mathematical physics, for example, the object of consideration is not the natural as such but rather the sensible or physical as compounded with the quantified or mathematical."

 

 

How is the 'natural' not 'physical'?  As someone with a physics degree, they look pretty like the same thing to me.  The natural world and the physical world are simply the universe we are in and its contents, behaving as they do.  I see a minor semantic difference in that if a discussion involved supernatural speculation, I'd talk about the 'natural' to highlight that distinction, but there doesn't seem to be any real difference.

 

 

"It is for this reason that mathematical physics is called a mixed science.  The middle terms or explanatory factors it employs are physico-mathematical, but the formality under which it demonstrates is mathematical and its conclusions are only terminatively physical.  The mathematical physicist must measure motion or time in order to treat it; the philosopher of nature has the problem of defining motion or time regardless of how it is measured.  Again, the results attained by the mathematical physicist require interpretation if one is to give a physical reason or explanation for the facts he knows in only their mathematical reasons.  Such interpretation, it can be argued, is itself external to mathematical physics; it is properly the function of the science of nature, where the physical causes of natural things are sought.  The mathematical physicist may himself take on this function, but it is noteworthy that difficult problems of interpretation are increasingly becoming the domain of the philosopher of science.”

 

This seems very confused.  Firstly, it seems to rest on the existence of an idealised 'mathematical physicist' who sits around doing formal maths in splendid isolation.  This is not really what these people do - they are normally very engaged with what experimenters / observers are doing, with much back-and-forth communication.  Secondly, what is a 'philosopher of nature' that is distinct from a mathematical physicist?  My experience is that mathematical physicists are very engaged with the philosophy of science, and perfectly capable of thinking about it in a pretty sophisticated way.  I'd note there are plenty of (at least self-proclaimed) philosophers who talk about science from a position of little knowledge - google objections to relativity or quantum mechanics.  Thirdly, what is 'the science of nature' that is distinct from mathematical physics?  Modern science is an integrated body of knowledge - maths, physics, chemistry, biology, geology etc are all inextricably linked to each other and any scientists worth the name understands these linkages and uses them to guide inquiry.

 

Here is a good example of how these things are linked.  Paul Dirac's eponymous equation started life as a purely formal mathematical attempt to come up with a version of the Schrodinger Equation that was relativistic.  Having succeeded, Dirac then sat on it for quite a while, because it's interpretation was very troubling.  He eventually postulated the existence of antimatter to resolve this, and published.  He pointed out that antimatter could be tested for experimentally and encouraged experimenters to go ahead and do it - they did and verified it.  The Dirac Equation also, provided a beautiful explanation of spin as a relativistic effect - again this is a very real thing.  Also, Dirac and his contemporaries spent vast amounts of time and effort worrying about the philosophical implications of QM.

 

Maybe the rest of the book precisely defines these things in a way that makes sense and leads to a worthwhile point, but I'm sceptical.  It looks to my like a very rhetorical piece, with the intention of casting science as an inferior activity to philosophy.


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#15 DaveC2042

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Posted 10 January 2020 - 10:19 PM

One more observation.

 

"The mathematical physicist must measure motion or time in order to treat it; the philosopher of nature has the problem of defining motion or time regardless of how it is measured."

 

This looks like a straw man.  Physicists do have multiple ways of 'measuring' these things - that's one of the ways you can tell you are dealing with something real.  A major premise of any good physical theory is that the things it treats are invariants, which don't depend on the particular way you measure them.

 

Or is the suggestion that a philosopher can define things that cannot be measured or observed?  To each their own, but it strikes me as a pointless activity.



#16 EJN

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Posted 10 January 2020 - 11:09 PM

I found the quote I was looking for earlier, from Eugene Wigner, the 1963 recipient of the Nobel Prize

for physics.

 

 

 

Physics does not even try  to give us complete information about the events around us -

it gives information about the correlations between those events.

 

Wigner also wrote a famous paper titled "The Unreasonable Effectiveness of Mathematics in the

Natural Sciences."

 

You can read it here.

 

 

 

When I had a full head of hair, nearly shoulder length, I took a political science class. What I remember

is that the textbooks used an awful lot of words to say...very little. When I read the quotes here from Wallace,

it gives me the same impression. Sometimes I get the impression that philosophers use lots of words

to give the impression of being erudite and profound without really saying much of anything, or are

being deliberately ambiguous.

YMMV.


Edited by EJN, 10 January 2020 - 11:47 PM.

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#17 jdk

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Posted 11 January 2020 - 12:02 AM

I found the quote I was looking for earlier, from Eugene Wigner, the 1963 recipient of the Nobel Prize

for physics.

This is probably the most salient point, given that the line of reasoning (to the extent you can follow it) in the OP's post is probably headed towards some conclusion regarding the propriety of developing normative boundaries based on purely "observational" or "computational" inquiry. 

 

When I had a full head of hair, nearly shoulder length, I took a political science class. What I remember

is that the textbooks used an awful lot of words to say...very little. When I read the quotes here from Wallace,

it gives me the same impression. Sometimes I get the impression that philosophers use lots of words

to give the impression of being erudite and profound without really saying much of anything, or are

being deliberately ambiguous.

YMMV.

 

lol.gif This is why law schools try to recruit people with coding backgrounds; legal scholarship can easily run into the same extravagance, and most people appreciate the idea of judging the merit of a brief or memo as if they were debugging code...even if that analogy has sooooooooooo many problems. 


Edited by jdk, 11 January 2020 - 12:04 AM.


#18 EJN

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Posted 11 January 2020 - 02:14 AM

“Art, chance, and violence differ from nature and so aid in its definition"

 

Here is an example of the type of logic which drives me nuts. If I rephrased it

"Aardvarks, hedgehogs, and skunks differ from cows and so aid in their definition"

would this make any sense at all? Saying what something is not tells you nothing

about what it is.


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#19 jdk

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Posted 11 January 2020 - 10:50 AM

Here is an example of the type of logic which drives me nuts. If I rephrased it

"Aardvarks, hedgehogs, and skunks differ from cows and so aid in their definition"

would this make any sense at all? Saying what something is not tells you nothing

about what it is.

That actually makes way more sense than the original statement lol.gif Yours at least has some breathing room for common intuition...the quote above is simply conclusory. 



#20 Otto Piechowski

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Posted 11 January 2020 - 11:18 AM

Modern science is silent on the reality of nature, in general, and of essences, in particular.  It is silent because these are philosophical concepts; not scientific.

 

 

Concerning essence(s):  Knowing what scholastic/classical philosophy means by "essence" is helpful for understanding Wallace's comments.  Every thing has its own essence.  That essence is the product of four intrinsic causes, one of which is the purpose/end/goal/perfection of the given thing.  In Greek, this purpose/end/goal/perfection-cause is known as τἑλος (pronounced tay-loss) which is a part of the phonetic root of the word teleology.

 

By its nature, a thing has a tendency to gravitate toward its intrinsic τἑλος.  However, a thing's progression to its τἑλος can be interrupted by art, chance, or violence.

 

 

Concerning nature:  The English word "nature" is derived from the Latin language word natura which, in turn, was the Latin language translation of the Greek word/term/concept φὑσις (pronounced foo-cease) which is the phonetic root of our English word physics.

 

The human awareness of the existence of nature only comes about with the ability of humans to make things and with the awareness that they are making things.  Nature is then seen as the other part of reality (which pre-existed human-made-things) which does not consist of those things which are made by humans.

 

Just as the awareness of self is dependent on the awareness of other(s), the awareness of nature comes into being only when/after humans become able to make things and aware they are making things.



#21 jdk

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Posted 11 January 2020 - 11:36 AM

Every thing has its own essence.  That essence is the product of four intrinsic causes, one of which is the purpose/end/goal/perfection of the given thing.  In Greek, this purpose/end/goal/perfection-cause is known as τἑλος (pronounced tay-loss) which is a part of the phonetic root of the word teleology.

 

By its nature, a thing has a tendency to gravitate toward its intrinsic τἑλος.  However, a thing's progression to its τἑλος can be interrupted by art, chance, or violence.

Even if this old school natural law understanding is true (which I don't concede), the next step is to realize that there are no objective standards for divining the "true purpose" of a thing, and that most - if not all - efforts to do so are disingenuous, self-serving, and conclusory.



#22 llanitedave

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Posted 11 January 2020 - 01:12 PM

I don't think the idea of "essence" can be applied to any tangible thing.  It can only be applied to ideas with meaning, as a distillation of that meaning.  A sparrow has no meaning.  It just is.  And since "meaning" is something assigned by humans, and culturally and socially contingent, so "essence" is also artificial.



#23 Jim_V

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Posted 11 January 2020 - 03:02 PM

Modern science is silent on the reality of nature,

 


 

"the phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations"

 

How is science silent on nature? Science describes much of nature.

 

Philosophical discussions are just that Philosophical.  Conjoining Philosophy and Science is not very malleable, and to me should be avoided.


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#24 EJN

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Posted 11 January 2020 - 04:38 PM

Modern science is silent on the reality of nature, in general, and of essences, in particular.  It is silent because these are philosophical concepts; not scientific.

 

 

Concerning essence(s):  Knowing what scholastic/classical philosophy means by "essence" is helpful for understanding Wallace's comments. Every thing has its own essence.  That essence is the product of four intrinsic causes, one of which is the purpose/end/goal/perfection of the given thing.  In Greek, this purpose/end/goal/perfection-cause is known as τἑλος (pronounced tay-loss) which is a part of the phonetic root of the word teleology.

 

By its nature, a thing has a tendency to gravitate toward its intrinsic τἑλος.  However, a thing's progression to its τἑλος can be interrupted by art, chance, or violence.

 

Lets look at the "essence" of a rock.

 

First we could say it's not an aardvark, hedgehog, skunk, or cow. Not helpful.

 

If we were the ancient Greeks, we could say it's not air, fire, or water, so it must be earth. Ok...

 

From the above definition - 

purpose - to be a rock

end - erode to sand or dirt

goal - to fly like an eagle? 

perfection - no, it's got chips

 

Lets look at it from a modern perspective.

A rock is a composite object composed of various minerals. What is a mineral? A chemical compound

composed of various elements. What is a chemical compound? A molecule composed of atoms of

different elements. What is an element? It is composed of unique, identical atoms.

 

Now we've gotten somewhere. But wait....

 

What is an atom? It is a composite structure composed of a cloud of electrons around a nucleus

of protons and neutrons. What holds it together? Electrons are negatively charged, and the

electromagnetic force attracts them to the positively charged protons. However electrons are only

found in specific stationary states (orbitals), so they don't fall into the nucleus. The nucleus is held

together by the strong nuclear force.

 

Are electrons, protons, & neutrons fundamental particles?

To the best of our knowledge, an electron is a fundamental particle of a class called leptons.

Protons and neutrons, however, are composed of 3 quarks. Are quarks fundamental? To the

best of our knowledge, yes.

 

What are leptons and quarks, what is their "essence?"

 

Well, we can categorize them by their properties, such as charge, spin, isospin, etc.,

which forces they interact with and which ones they don't. For example, leptons do

not interact with the strong nuclear force.

 

Next we have to go to quantum field theory (QFT). Particles are excited states in the underlying field.

How do we know they are fundamental? Because they are irreducible representations on the

Poincare group.

 

Huh?

 

At this stage we are dealing with mathematical representations, and so far this is the only way

to talk about things at this level in a coherent way. So at the very bottom of the chain you have...

mathematics!

 

A NASA physicist named Max Tegmark has proposed that at the most fundamental level, the

universe is a physical manifestation of a mathematical structure, with the mathematical

structure being isomorphic to the physical objects. It is a controversial, but interesting, idea.


Edited by EJN, 11 January 2020 - 08:44 PM.

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#25 DaveC2042

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Posted 11 January 2020 - 05:54 PM

Modern science is silent on the reality of nature, in general, and of essences, in particular. It is silent because these are philosophical concepts; not scientific.


Concerning essence(s): Knowing what scholastic/classical philosophy means by "essence" is helpful for understanding Wallace's comments. Every thing has its own essence. That essence is the product of four intrinsic causes, one of which is the purpose/end/goal/perfection of the given thing. In Greek, this purpose/end/goal/perfection-cause is known as τἑλος (pronounced tay-loss) which is a part of the phonetic root of the word teleology.

By its nature, a thing has a tendency to gravitate toward its intrinsic τἑλος. However, a thing's progression to its τἑλος can be interrupted by art, chance, or violence.


Concerning nature: The English word "nature" is derived from the Latin language word natura which, in turn, was the Latin language translation of the Greek word/term/concept φὑσις (pronounced foo-cease) which is the phonetic root of our English word physics.

The human awareness of the existence of nature only comes about with the ability of humans to make things and with the awareness that they are making things. Nature is then seen as the other part of reality (which pre-existed human-made-things) which does not consist of those things which are made by humans.

Just as the awareness of self is dependent on the awareness of other(s), the awareness of nature comes into being only when/after humans become able to make things and aware they are making things.


Otto, this 'essence' stuff is hundreds of years out of date.
  • llanitedave likes this


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