How Mathematics Meets the World, by Tim Maudlin

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Philip Thrift

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Dec 7, 2019, 4:57:06 AM12/7/19
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How Mathematics Meets the World, by Tim Maudlin


Essay Abstract

The most obvious explanation for the power of mathematics as the language of physics is that the physical world has the right sort of structure to be represented mathematically. But what this in turn means depends on the mathematical language being used. I first briefly review some of the physical characteristics required in order to unambiguously describe a physical situation using integers, and then take up the much more difficult question of what characteristics are required to describe a situation using geometrical concepts. In the case of geometry, and particularly for the most basic form of geometry— topology—this is not clear. I discuss a new mathematical language for describing geometrical structure called the Theory of Linear Structures. This mathematical language is founded on a different primitive concept than standard topology, on the line rather than the open set. I explain how some other geometrical concepts can be defined in terms of lines, and how in a Relativistic setting time can be understood as the feature of physical reality that generates all geometrical facts. Whereas it is often said that Relativity spatializes time, from the perspective of the Theory of Linear Structures we can see instead that Relativity temporalizes space: all of the geometry flows from temporal structure. The Theory of Linear Structures also provides a mathematical language in which the fact that time is a fundamentally directed structure can be easily represented.




...
The standard answer derives from the standard mathematical tool used to describe the most basic geometrical structure of a space. If that mathematical tool, that mathematical language, is to provide an accurate characterization of the geometry physical space or physical space-time then physical space-time must have a structure corresponding to the fundamental concept in the mathematics. And a different mathematical language, built on a different primitive concept, requires that physical space-time have a different structure if it is to be accurately described. I will argue that standard geometry has been built on the wrong conceptual foundation to apply optimally to space-time. I will sketch an alternative geometrical language, and explain how it could directly reflect the structure of the physical world.
...
Physicists seeking such a mesh between mathematics and physics can only
alter one side of the equation. The physical world is as it is, and will not change at our command. But we can change the mathematical language used to formulate physics, and we can even seek to construct new mathematical languages that are better suited to represent the physical structure of the world. The Theory of Linear Structures, whatever else its virtues, provides and example of how this can be done. If it is correct, then we might see how the time itself creates the geometry of space-time, and also makes space-time exactly the sort of thing that is well described using this mathematical language.


@philipthrift

Brent Meeker

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Dec 7, 2019, 4:17:45 PM12/7/19
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On 12/7/2019 1:57 AM, Philip Thrift wrote:
Physicists seeking such a mesh between mathematics and physics can only
alter one side of the equation. The physical world is as it is, and will not change at our command.

It is generally overlooked that the above is not strictly true.  Physics has often moved phenomena from the category of "explained by science" to "accident of nature" and sometimes back.  For example Kepler thought the number of planets should be a consequence of natural law.  Newton dropped this from his theory.  The shape of continents was considered a geological accident...until Wegner showed they came from the breakup of a single continent.  The world may not change, but the part we take to be "law like" and the part we consider "accident of nature" are flexible.

Brent

Philip Thrift

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Dec 8, 2019, 3:09:52 AM12/8/19
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There is a hidden code of nature—the code written into its fabric. Our theories—our hypothetical code—are our evolving best-guess translations of the code of nature, which remains hidden from our knowledge—within nature-in-itself.

@philipthrift 

Bruno Marchal

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Dec 8, 2019, 6:43:21 AM12/8/19
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It is here that mechanism is at its best, as it delineates completely what is geographical/contingent, and what is necessary, for physics, for all universal machine (or all but finitely many exceptions of measure null).

And of course, mechanism explain easily what physics obey to math, as the physical appearances proceed from a mathematical phenomenon occurring in the arithmetical reality. We use mathematics because we are living in a mathematical reality. Note that the phenomenology is not entirely mathematical though, but psychological or theological.

Maudlin is a materialist, but at least he got right the deep incompatibility of physicalism with digital Mechanism (in its Olympia paper, published in 1989, I publish this in 1988, btw). 

Bruno



Brent

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Philip Thrift

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Dec 8, 2019, 6:56:28 AM12/8/19
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On Sunday, December 8, 2019 at 5:43:21 AM UTC-6, Bruno Marchal wrote:

We use mathematics because we are living in a mathematical reality. Note that the phenomenology is not entirely mathematical though, but psychological or theological.



Therein lies the camel's nose under the tent.

@philipthrift 

Brent Meeker

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Dec 8, 2019, 3:57:17 PM12/8/19
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On 12/8/2019 3:43 AM, Bruno Marchal wrote:

On 7 Dec 2019, at 22:17, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/7/2019 1:57 AM, Philip Thrift wrote:
Physicists seeking such a mesh between mathematics and physics can only
alter one side of the equation. The physical world is as it is, and will not change at our command.

It is generally overlooked that the above is not strictly true.  Physics has often moved phenomena from the category of "explained by science" to "accident of nature" and sometimes back.  For example Kepler thought the number of planets should be a consequence of natural law.  Newton dropped this from his theory.  The shape of continents was considered a geological accident...until Wegner showed they came from the breakup of a single continent.  The world may not change, but the part we take to be "law like" and the part we consider "accident of nature" are flexible.

It is here that mechanism is at its best, as it delineates completely what is geographical/contingent, and what is necessary, for physics, for all universal machine (or all but finitely many exceptions of measure null).

And of course, mechanism explain easily what physics obey to math, as the physical appearances proceed from a mathematical phenomenon occurring in the arithmetical reality. We use mathematics because we are living in a mathematical reality.

Sadly it explains easily as theologians usually do..."God did it." is an easy explanation for everything...assuming a God reality.

That's why scientists are impressed by predictions, but not so much by explanations.

Brent

Note that the phenomenology is not entirely mathematical though, but psychological or theological.

Maudlin is a materialist, but at least he got right the deep incompatibility of physicalism with digital Mechanism (in its Olympia paper, published in 1989, I publish this in 1988, btw). 

Bruno



Brent

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Bruno Marchal

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Dec 10, 2019, 7:51:24 AM12/10/19
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On 8 Dec 2019, at 21:57, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/8/2019 3:43 AM, Bruno Marchal wrote:

On 7 Dec 2019, at 22:17, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/7/2019 1:57 AM, Philip Thrift wrote:
Physicists seeking such a mesh between mathematics and physics can only
alter one side of the equation. The physical world is as it is, and will not change at our command.

It is generally overlooked that the above is not strictly true.  Physics has often moved phenomena from the category of "explained by science" to "accident of nature" and sometimes back.  For example Kepler thought the number of planets should be a consequence of natural law.  Newton dropped this from his theory.  The shape of continents was considered a geological accident...until Wegner showed they came from the breakup of a single continent.  The world may not change, but the part we take to be "law like" and the part we consider "accident of nature" are flexible.

It is here that mechanism is at its best, as it delineates completely what is geographical/contingent, and what is necessary, for physics, for all universal machine (or all but finitely many exceptions of measure null).

And of course, mechanism explain easily what physics obey to math, as the physical appearances proceed from a mathematical phenomenon occurring in the arithmetical reality. We use mathematics because we are living in a mathematical reality.

Sadly it explains easily as theologians usually do..."God did it." is an easy explanation for everything...assuming a God reality.

That is exactly my point, with “matter” instead of God. The physicalist say “matter selects the ‘conscious’ computation”, but they fail to give any rôle to that matter in the consciousness selection.

Either that selection process is Turing emulable, but then we are led to the mechanist formulation of the mind-body problem, or that selection process is not Turing emulable. In that case, either it is recoverable from the First Person Indeterminacy in arithmetic, in which case we are closer to the mechanist explanation of the origin of the physical laws, or it does not, and that is what we can tested.




That's why scientists are impressed by predictions, but not so much by explanations.

An explanation without a prediction is a waste of time. We agree on this. But my whole point is that Mechanism vs Materialism is testable, and that the facts confirms Mechanism, and refute Materialism (as guessed by many theologian at the time this was done by scientists, indeed).

Bruno




Brent

Note that the phenomenology is not entirely mathematical though, but psychological or theological.

Maudlin is a materialist, but at least he got right the deep incompatibility of physicalism with digital Mechanism (in its Olympia paper, published in 1989, I publish this in 1988, btw). 

Bruno



Brent

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Brent Meeker

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Dec 10, 2019, 3:39:55 PM12/10/19
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On 12/10/2019 4:51 AM, Bruno Marchal wrote:

On 8 Dec 2019, at 21:57, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/8/2019 3:43 AM, Bruno Marchal wrote:

On 7 Dec 2019, at 22:17, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/7/2019 1:57 AM, Philip Thrift wrote:
Physicists seeking such a mesh between mathematics and physics can only
alter one side of the equation. The physical world is as it is, and will not change at our command.

It is generally overlooked that the above is not strictly true.  Physics has often moved phenomena from the category of "explained by science" to "accident of nature" and sometimes back.  For example Kepler thought the number of planets should be a consequence of natural law.  Newton dropped this from his theory.  The shape of continents was considered a geological accident...until Wegner showed they came from the breakup of a single continent.  The world may not change, but the part we take to be "law like" and the part we consider "accident of nature" are flexible.

It is here that mechanism is at its best, as it delineates completely what is geographical/contingent, and what is necessary, for physics, for all universal machine (or all but finitely many exceptions of measure null).

And of course, mechanism explain easily what physics obey to math, as the physical appearances proceed from a mathematical phenomenon occurring in the arithmetical reality. We use mathematics because we are living in a mathematical reality.

Sadly it explains easily as theologians usually do..."God did it." is an easy explanation for everything...assuming a God reality.

That is exactly my point, with “matter” instead of God. The physicalist say “matter selects the ‘conscious’ computation”, but they fail to give any rôle to that matter in the consciousness selection.

These physicalists you are always refuting are strawmen.  No scientist or philosopher I've read says, “matter selects the ‘conscious’ computation”.  Materialists say consciousness is process, and as such is realized in matter, but is not itself matter.  This is well supported by empirical observations of everything from drunkeness to brain surgery.

Brent


Either that selection process is Turing emulable, but then we are led to the mechanist formulation of the mind-body problem, or that selection process is not Turing emulable. In that case, either it is recoverable from the First Person Indeterminacy in arithmetic, in which case we are closer to the mechanist explanation of the origin of the physical laws, or it does not, and that is what we can tested.




That's why scientists are impressed by predictions, but not so much by explanations.

An explanation without a prediction is a waste of time. We agree on this. But my whole point is that Mechanism vs Materialism is testable, and that the facts confirms Mechanism, and refute Materialism (as guessed by many theologian at the time this was done by scientists, indeed).

Bruno




Brent

Note that the phenomenology is not entirely mathematical though, but psychological or theological.

Maudlin is a materialist, but at least he got right the deep incompatibility of physicalism with digital Mechanism (in its Olympia paper, published in 1989, I publish this in 1988, btw). 

Bruno



Brent

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Philip Thrift

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Dec 10, 2019, 6:06:17 PM12/10/19
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On Tuesday, December 10, 2019 at 2:39:55 PM UTC-6, Brent wrote:
Materialists say consciousness is process, and as such is realized in matter, but is not itself matter.  This is well supported by empirical observations of everything from drunkenness to brain surgery.

Brent



No materialist would say there are processes and matter and that processes are not matter. If they did, they would be a kind of dualist, not a materialist.

@philipthrift 

Brent Meeker

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Dec 10, 2019, 7:05:14 PM12/10/19
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On 12/10/2019 3:06 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 2:39:55 PM UTC-6, Brent wrote:
Materialists say consciousness is process, and as such is realized in matter, but is not itself matter.  This is well supported by empirical observations of everything from drunkenness to brain surgery.

Brent



No materialist would say there are processes and matter and that processes are not matter.

Sure they would.  Just as JKC said race cars are fast but being fast isn't a race car, it's a process.

Brent

If they did, they would be a kind of dualist, not a materialist.

@philipthrift 
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Philip Thrift

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Dec 10, 2019, 8:13:05 PM12/10/19
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On Tuesday, December 10, 2019 at 6:05:14 PM UTC-6, Brent wrote:


On 12/10/2019 3:06 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 2:39:55 PM UTC-6, Brent wrote:
Materialists say consciousness is process, and as such is realized in matter, but is not itself matter.  This is well supported by empirical observations of everything from drunkenness to brain surgery.

Brent



No materialist would say there are processes and matter and that processes are not matter.

Sure they would.  Just as JKC said race cars are fast but being fast isn't a race car, it's a process.

Brent



A fast car is still a car. Fast matter is still matter. A conscious brain is still a brain.

A parked (not moving at all) car is still a car, too. A parked car is no more or less of a car than a fast car. (What process is occurring with a parked car? Is 'stationary' a process?)

'fast',  'conscious', 'parked', 'stationary' have no existence of their own.

@philipthrift

Brent Meeker

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Dec 10, 2019, 8:27:59 PM12/10/19
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Are they matter?  No.  Do they exist?  Yes.

Brent

Philip Thrift

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Dec 10, 2019, 8:37:23 PM12/10/19
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Show me where fast exists. What are its spacetime coordinates?


Nominalism is the doctrine that abstract concepts, general terms or universals have no independent existence but exist only as names. Therefore, various objects labeled by the same term have nothing in common but their name. Put another way, only actual physical particulars are real, and universals exist only subsequent to particular things, being just verbal abstractions.

Nominalism arose in reaction to the problem of universals and in particular to Plato's solution to it, known as Platonic Realism, which holds that abstract objects like universals and Forms exist in their own right and are wholly independent of the physical world, and that particular physical objects merely exemplify or instantiate the universal. Nominalists ask exactly where this universal realm might be, and find it unusual and unlikely that there could be a single thing that exists in multiple places simultaneously.


@philipthrift 

Brent Meeker

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Dec 10, 2019, 8:53:35 PM12/10/19
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On 12/10/2019 5:37 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 7:27:59 PM UTC-6, Brent wrote:


On 12/10/2019 5:13 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 6:05:14 PM UTC-6, Brent wrote:


On 12/10/2019 3:06 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 2:39:55 PM UTC-6, Brent wrote:
Materialists say consciousness is process, and as such is realized in matter, but is not itself matter.  This is well supported by empirical observations of everything from drunkenness to brain surgery.

Brent



No materialist would say there are processes and matter and that processes are not matter.

Sure they would.  Just as JKC said race cars are fast but being fast isn't a race car, it's a process.

Brent



A fast car is still a car. Fast matter is still matter. A conscious brain is still a brain.

A parked (not moving at all) car is still a car, too. A parked car is no more or less of a car than a fast car. (What process is occurring with a parked car? Is 'stationary' a process?)

'fast',  'conscious', 'parked', 'stationary' have no existence of their own.

Are they matter?  No.  Do they exist?  Yes.

Brent


Show me where fast exists. What are its spacetime coordinates?

It's an attribute not a thing.  So it exists where things have space coordinates changing relative to time coordinates (as you well know).

And I don't need  lecture on nominalism.

Brent



Nominalism is the doctrine that abstract concepts, general terms or universals have no independent existence but exist only as names. Therefore, various objects labeled by the same term have nothing in common but their name. Put another way, only actual physical particulars are real, and universals exist only subsequent to particular things, being just verbal abstractions.

Nominalism arose in reaction to the problem of universals and in particular to Plato's solution to it, known as Platonic Realism, which holds that abstract objects like universals and Forms exist in their own right and are wholly independent of the physical world, and that particular physical objects merely exemplify or instantiate the universal. Nominalists ask exactly where this universal realm might be, and find it unusual and unlikely that there could be a single thing that exists in multiple places simultaneously.


@philipthrift 
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Philip Thrift

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Dec 11, 2019, 2:53:52 AM12/11/19
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On Tuesday, December 10, 2019 at 7:53:35 PM UTC-6, Brent wrote:


On 12/10/2019 5:37 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 7:27:59 PM UTC-6, Brent wrote:


On 12/10/2019 5:13 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 6:05:14 PM UTC-6, Brent wrote:


On 12/10/2019 3:06 PM, Philip Thrift wrote:


On Tuesday, December 10, 2019 at 2:39:55 PM UTC-6, Brent wrote:
Materialists say consciousness is process, and as such is realized in matter, but is not itself matter.  This is well supported by empirical observations of everything from drunkenness to brain surgery.

Brent



No materialist would say there are processes and matter and that processes are not matter.

Sure they would.  Just as JKC said race cars are fast but being fast isn't a race car, it's a process.

Brent



A fast car is still a car. Fast matter is still matter. A conscious brain is still a brain.

A parked (not moving at all) car is still a car, too. A parked car is no more or less of a car than a fast car. (What process is occurring with a parked car? Is 'stationary' a process?)

'fast',  'conscious', 'parked', 'stationary' have no existence of their own.

Are they matter?  No.  Do they exist?  Yes.

Brent


Show me where fast exists. What are its spacetime coordinates?

It's an attribute not a thing.  So it exists where things have space coordinates changing relative to time coordinates (as you well know).

And I don't need  lecture on nominalism.

Brent



That works for 'fast' -  "it exists where things have space coordinates changing relative to time coordinates".

Is a running river matter? Is a an ocean wave matter? They 'things have space coordinates changing relative to time coordinates".

According to what you wrote (about matter+process) above the answer would be that they are only partly matter.


What about 'stationary'? Where is that?


it exists where things have space coordinates unchanging relative to time coordinates ?


@philipthrift

Bruno Marchal

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Dec 11, 2019, 12:11:38 PM12/11/19
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On 10 Dec 2019, at 21:39, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/10/2019 4:51 AM, Bruno Marchal wrote:

On 8 Dec 2019, at 21:57, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/8/2019 3:43 AM, Bruno Marchal wrote:

On 7 Dec 2019, at 22:17, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:



On 12/7/2019 1:57 AM, Philip Thrift wrote:
Physicists seeking such a mesh between mathematics and physics can only
alter one side of the equation. The physical world is as it is, and will not change at our command.

It is generally overlooked that the above is not strictly true.  Physics has often moved phenomena from the category of "explained by science" to "accident of nature" and sometimes back.  For example Kepler thought the number of planets should be a consequence of natural law.  Newton dropped this from his theory.  The shape of continents was considered a geological accident...until Wegner showed they came from the breakup of a single continent.  The world may not change, but the part we take to be "law like" and the part we consider "accident of nature" are flexible.

It is here that mechanism is at its best, as it delineates completely what is geographical/contingent, and what is necessary, for physics, for all universal machine (or all but finitely many exceptions of measure null).

And of course, mechanism explain easily what physics obey to math, as the physical appearances proceed from a mathematical phenomenon occurring in the arithmetical reality. We use mathematics because we are living in a mathematical reality.

Sadly it explains easily as theologians usually do..."God did it." is an easy explanation for everything...assuming a God reality.

That is exactly my point, with “matter” instead of God. The physicalist say “matter selects the ‘conscious’ computation”, but they fail to give any rôle to that matter in the consciousness selection.

These physicalists you are always refuting are strawmen.  No scientist or philosopher I've read says, “matter selects the ‘conscious’ computation”. 


Because they are not even aware of the computations in arithmetic. But when the physicalist attempt to explain the mind, they invoke their god “primary matter” to claim, like John clark, that “consciousness” is what piece of matter do when organised in the right way. If that is the case in virtue of emulating the relevant computation, that consciousness will appear in arithmetic, and physics will have to be re-explained by the first person statistics on all “relative” computations.





Materialists say consciousness is process, and as such is realized in matter, but is not itself matter. 

Materialists who try to solve the problem comes up with many theories, and few are testable? But with mechanism, “realised in matter” simply does not work, unless you attribute some magical abilities to such “matter”. 



This is well supported by empirical observations of everything from drunkeness to brain surgery.

The empirical evidences supports Mechanism. I don’t see any evidences for physicalism. It fails on the mind, or identify 1p and 3p, or make everything conscious, without any real theory, unlike mechanism, whose theory is computer science, arithmetic, intensional arithmetic, mathematical logic, even Artificial Intelligence, as this domain will be more and more experimental, in all directions.

The claim that there exist a fundamental-ontological-primary universe only add insuperable complexity to the Mechanist approach and formulation of the mind body problem.

You are right, the physicalist does not even realise that they use Matter in the same invalid way that some pseudo-religious person invoke God in a metaphysical explanation. The reason is that they take the primitive existence of the physical for granted, and that is not valid when we adopt the scientific attitude in this domain. I am aware that the bad habit lasts for more than 1500 years. A chance I am patient.

Note for John Clark:  I will (try) to answer your post tomorrow.

Bruno





Philip Thrift

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Dec 11, 2019, 1:20:54 PM12/11/19
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On Wednesday, December 11, 2019 at 11:11:38 AM UTC-6, Bruno Marchal wrote:

The empirical evidences supports Mechanism. I don’t see any evidences for physicalism. It fails on the mind, or identify 1p and 3p, or make everything conscious, without any real theory, unlike mechanism, whose theory is computer science, arithmetic, intensional arithmetic, mathematical logic, even Artificial Intelligence, as this domain will be more and more experimental, in all directions.

The claim that there exist a fundamental-ontological-primary universe only add insuperable complexity to the Mechanist approach and formulation of the mind body problem.

You are right, the physicalist does not even realise that they use Matter in the same invalid way that some pseudo-religious person invoke God in a metaphysical explanation. The reason is that they take the primitive existence of the physical for granted, and that is not valid when we adopt the scientific attitude in this domain. I am aware that the bad habit lasts for more than 1500 years. A chance I am patient.

Note for John Clark:  I will (try) to answer your post tomorrow.

Bruno




There is a 'test' for the matterless  theory:

Why panpsychism can’t just go away

Basically: If consciousness can arise in a simulation (of all particles), then panpsychism is false and mechanism is true.

@philipthrift
 

Brent Meeker

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Dec 11, 2019, 3:57:09 PM12/11/19
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No problem.  It just shows that things are made of particles that have intrinsic proto-stationarity.

Brent
P.S. Have you noticed that speed is a fundamental dimension in SI, but position isn't .

Brent Meeker

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Dec 11, 2019, 6:33:34 PM12/11/19
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On 12/11/2019 9:11 AM, Bruno Marchal wrote:
>
>
>> Materialists say consciousness is process, and as such is realized in
>> matter, but is not itself matter.
>
> Materialists who try to solve the problem comes up with many theories,
> and few are testable? But with mechanism, “realised in matter” simply
> does not work, unless you attribute some magical abilities to such
> “matter”.

It's quite testable.  Mess with the matter of the brain and the mind is
affected.  Whether you think that is "magical" or not is just semantics.

Brent

Philip Thrift

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Dec 12, 2019, 4:45:33 AM12/12/19
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There is an ontological fad called trope theory - everything is a bindle of properties (tropes):

Trope theory is the view that reality is (wholly or partly) made up from tropes. Tropes are things like the particular shape, weight, and texture of an individual object. Because tropes are particular, for two objects to ‘share’ a property (for them both to exemplify, say, a particular shade of green) is for each to contain (instantiate, exemplify) a greenness-trope, where those greenness-tropes, although numerically distinct, nevertheless exactly resemble each other.


@philipthrift 

Bruno Marchal

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Dec 12, 2019, 7:19:58 AM12/12/19
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So, basically we agree. 

Materialism will disappear, because it entails pantheism, which explains nothing, Imo. I believe in numbers, and I don’ believe that any number can think, per se. 

So, I cannot really embrace pantheism, unless using some semantical stretching.

Only Turing universal relation can process thoughts, in the frame of the theory that I study.

Bruno




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