Quote by French Mathematician Charles Hermite

[Jason Resch]

Appears to predict the arithmetical reality:

"There exists, unless I am mistake, an entire world consisting of the totality of mathematical truths, which is accessible to us only through our intelligence, just as there exists the world of physical realities; each one is independent of us, both of them divinely created and appear different only because of the weakness of our mind; but, for a more powerful intelligence, they are one and the same thing, whose synthesis is partially revealed in that marvelous correspondence between abstract mathematics on the one hand and astronomy and all branches of physics on the other."

https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf on page 323.

Jason

[Philip Thrift]

"I have lived in the worlds of both mathematics and physics, and I never thought there was such a big difference between these two fields."

Gregory Chaitin

http://www.cs.virginia.edu/~robins/The_Limits_of_Reason_Chaitin_2006.pdf 

@philipthrift

[Bruno Marchal]

Yes, both Gödel and Chaitin miss the fact that with mechanism, physics becomes a subbranch of machine’s theology, or psychology (if you want, but also in its etymological sense: science of the soul or spirit).

The physical should be seen as a sphere, the mind/spirit/god is the volume of that sphere. This is an image. Eventually that border appears as a projective illusion from inside, like an horizon.It is the result of the first person indeterminacy on the universal dovetailing of on the sigma_1 truth (conceived extensionally).

In the first pass, God is the arithmetical truth, but the “enlightened” machine realise that it could be only the sigma_1 arithmetic (that she can defined, and it is absolutely undecidable for any universal machine and their consistent extension if there could be more than the sigma_1 reality.

Bruno

@philipthrift

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[Tomas Pales]

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles. It is a relation whereby the abstract object is a property of the concrete objects and the concrete objects are instances of the abstract object. The instantation relation is regarded as primitive, similarly like the composition relation between a collection of objects and the objects in the collection. The instantiation relation may appear more mysterious though, because while it is quite easy to visualize a collection, it is impossible to visualize an abstract object.

Abstract and concrete objects are existentially dependent on each other, because there can be no property without an object that has the property, and there can be no object that has no property.

 

[Lawrence Crowell]

On Wednesday, May 29, 2019 at 3:15:46 PM UTC-5, Jason wrote:

This is the opinion similar to what most mathematicians think. Mathematics is a system that has objective truth. I don't necessarily "believe this," but I can see its point and will tip my hat towards it. In physics we tend often to view mathematics as more similar to rules of chess, and where the use of the rules defines the game. Here the game being how to model the physical world. I can see this as well. There is the Brouwer constructionist idea of mathematics that is related to this. Hilbert thought that mathematics was something existing on its own, which is the objectivist opinion, objectivist not in line with the quasi-philosophy of Ayn Rand, which is related to Plato's ideas of there being ideal forms outside of physical forms. 

What is the relationship between physics and mathematics? I have not the slightest clue. I see this as similar to Garrison Keillor's Guy Noir who in the introduction would have, "On a dark night in a city that knows how to keep its secrets, one man searches for life's persistent questions. Guy Noir private eye." As I recall the quote. 

LC

[Philip Thrift]

In  the fictionalist philosophy of mathematics

https://plato.stanford.edu/entries/fictionalism-mathematics/

          there are no such things as abstract objects.

So such troubles do not arise.

@philipthrift

 

[Jason Resch]

Let's say reality is composed of two sets:

1. The set of all existent things

2. The set of all non-existent things

If nothing existed at all, then set one would be emtpy, while set two would contain everything.

Now take the nominalist position. Set one would contain the physical universe while set two would contain all abstract objects: arithmetical truth, executions of programs, histories of non-existent universes, etc.

What puzzles me, is that in the program executions and in the histories of non-existent universes you will find worlds where life evolves into more complex forms, you will find the risings and fallings of great civilizations, you will find literature written by the philosophers of those civilizations, their treatises on ontology, on why their universe is concrete while others are abstract, on the mysteries of consciousness and strangeness of qualia.  If all these things can be found in the abstract objects of the set of non-existent things, then how do we know we're not in an abstract object of that set of non-existent things?

Does it matter at all which set our universe resides in? Can moving an object from one set to another blink away or bring into being the first person experiences of the entities who inhabit such objects, or is their consciousness a property inherent to the object which cannot be taken away merely by moving it from one set to another?

Much to think about.

Jason

[Tomas Pales]

If there is no abstract triangle then there is no concrete triangle either, because what would it mean that there is a concrete triangle? That seems more of a trouble.

 

[Tomas Pales]

On Thursday, May 30, 2019 at 4:14:48 PM UTC+2, Jason wrote:

Let's say reality is composed of two sets:

1. The set of all existent things

2. The set of all non-existent things

If nothing existed at all, then set one would be emtpy, while set two would contain everything.

What do you mean by existent? How are existent things different from non-existent things?

[Jason Resch]

That's the $64K question, isn't it?  If "existence" is a difference that makes no difference, then it is a meaningless concept altogether.

If inherent properties such as the consciousness of a conscious object can no more be separated from the object than evenness could be removed from two, then just as two would be even whether or not it is abstract or instantiated, then conscious objects would still be conscious whether or not they were abstract or instantiated.

Jason

[Brent Meeker]

I wonder if philosophers have noticed that properties can be separated from objects in quantum mechanics, c.f. Cheshire Cat experiments?

Brent

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[Brent Meeker]

You're equivocating on "existent".  The set of all non-existent things is empty because non-existent things don't exist in one sense of the word.  But then you switch to the other sense of the word so that "non-existent"="imaginary" and conclude that there are lots of imaginary things and therefore lots of non-existent things.

Brent

Jason

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[Philip Thrift]

For the fictionalist, one can invent anything, including mathematics with different definitions of sets producing a multiverse of mathematical truths  (Joel David Hamkins) and logics that are inconsistent (Graham Priest). 

Matter (the universe we live in) gives what it gives and nothing more. 

There is a story today about rare earth minerals:

https://www.cnn.com/2019/05/30/investing/rare-earths-china-trade-war/

I suppose for those who think that matter doesn't exist, a shortage of rare earth minerals cannot be a problem. Maybe someday we build a matter compiler that can make them.

@philipthrift 

[Philip Thrift]

Quantum Cheshire Cat effect may be explained by standard quantum mechanics.

https://phys.org/news/2015-06-quantum-cheshire-cat-effect-standard.html

@philipthrift

[Tomas Pales]

On Thursday, May 30, 2019 at 8:02:12 PM UTC+2, Brent wrote:

I wonder if philosophers have noticed that properties can be separated from objects in quantum mechanics, c.f. Cheshire Cat experiments?

What does it mean that a property is "separated" from an object? That an object loses a property? That happens all the time.

[Tomas Pales]

On Thursday, May 30, 2019 at 6:33:30 PM UTC+2, Jason wrote:

On Thu, May 30, 2019 at 9:54 AM Tomas Pales <litew...@gmail.com> wrote:

On Thursday, May 30, 2019 at 4:14:48 PM UTC+2, Jason wrote:

Let's say reality is composed of two sets:

1. The set of all existent things

2. The set of all non-existent things

If nothing existed at all, then set one would be emtpy, while set two would contain everything.

What do you mean by existent? How are existent things different from non-existent things?

That's the $64K question, isn't it?  If "existence" is a difference that makes no difference, then it is a meaningless concept altogether.

Yes, every object can be defined by its relations to all other objects, so the concept of "existence" boils down to the definition of the object. The only objects that don't exist are those that are defined inconsistently, for example if they have a property that they don't have. But those are not even objects; they are nothing.

[Jason Resch]

On Thu, May 30, 2019 at 1:13 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 5/30/2019 7:14 AM, Jason Resch wrote:

On Thursday, May 30, 2019, Philip Thrift <cloud...@gmail.com> wrote:

On Thursday, May 30, 2019 at 7:50:37 AM UTC-5, Tomas Pales wrote:

On Wednesday, May 29, 2019 at 10:15:46 PM UTC+2, Jason wrote:

Appears to predict the arithmetical reality:

"There exists, unless I am mistake, an entire world consisting of the totality of mathematical truths, which is accessible to us only through our intelligence, just as there exists the world of physical realities; each one is independent of us, both of them divinely created and appear different only because of the weakness of our mind; but, for a more powerful intelligence, they are one and the same thing, whose synthesis is partially revealed in that marvelous correspondence between abstract mathematics on the one hand and astronomy and all branches of physics on the other."

https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf on page 323.

Jason

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles. It is a relation whereby the abstract object is a property of the concrete objects and the concrete objects are instances of the abstract object. The instantation relation is regarded as primitive, similarly like the composition relation between a collection of objects and the objects in the collection. The instantiation relation may appear more mysterious though, because while it is quite easy to visualize a collection, it is impossible to visualize an abstract object.

Abstract and concrete objects are existentially dependent on each other, because there can be no property without an object that has the property, and there can be no object that has no property.

In  the fictionalist philosophy of mathematics

https://plato.stanford.edu/entries/fictionalism-mathematics/

          there are no such things as abstract objects.

So such troubles do not arise.

Let's say reality is composed of two sets:

1. The set of all existent things

2. The set of all non-existent things

If nothing existed at all, then set one would be emtpy, while set two would contain everything.

Now take the nominalist position. Set one would contain the physical universe while set two would contain all abstract objects: arithmetical truth, executions of programs, histories of non-existent universes, etc.

What puzzles me, is that in the program executions and in the histories of non-existent universes you will find worlds where life evolves into more complex forms, you will find the risings and fallings of great civilizations, you will find literature written by the philosophers of those civilizations, their treatises on ontology, on why their universe is concrete while others are abstract, on the mysteries of consciousness and strangeness of qualia.  If all these things can be found in the abstract objects of the set of non-existent things, then how do we know we're not in an abstract object of that set of non-existent things?

Does it matter at all which set our universe resides in? Can moving an object from one set to another blink away or bring into being the first person experiences of the entities who inhabit such objects, or is their consciousness a property inherent to the object which cannot be taken away merely by moving it from one set to another?

Much to think about.

You're equivocating on "existent".  The set of all non-existent things is empty because non-existent things don't exist in one sense of the word.

If the set of non-existent things were empty, then everything would exist, by definition.

 

  But then you switch to the other sense of the word so that "non-existent"="imaginary" and conclude that there are lots of imaginary things and therefore lots of non-existent things.

Could you define what you mean by "non-existent"?  I don't think I used imaginary anywhere in my reasoning. Imaginary requires an imaginer, and concerns subjective ideas or thoughts of that imaginer.

I think there are clearly two distinct classes of common-sense meaning when it comes to existent vs. non-existent, and there are different words with different connotations, but roughly:

Existent,     Non-existent

Actual,       Possible

Real,          Unreal

Concrete,  Abstract

Instantiated,  Unsubstantiated

Imaginary isn't applicable here because the objects for which I describe are objective.  That is, two independent minds could study such an object in question, and both reach the same conclusions regarding it and its properties.  This isn't true for imaginary objects, but it is possible for sufficiently well defined objects that are claimed to be "non-existent", "possible", "unreal", "abstract", or "unsubstantiated".

Jason

[Jason Resch]

I didn't say matter doesn't exist. I only point out that the property you call "existence" doesn't seem to do anything.

See Minsky's point here: https://www.youtube.com/watch?v=hVJwzVD3jEs

Jason

 

@philipthrift 

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[Brent Meeker]

arXiv:1312.3775v1 [quant-ph] 13 Dec 2013

Brent

[Brent Meeker]

If rare-earths exist you can make things out of them.  Otherwise you can't.

Brent

[Philip Thrift]

We know that a molecule's histories can interfere with each other:

https://en.wikipedia.org/wiki/Double-slit_experiment

In 2013, the double-slit experiment was successfully performed with molecules that each comprised 810 atoms (whose total mass was over 10,000 atomic mass units).

 

Does this mean that a molecule's properties can be separated from itself?

@philipthrift

[Brent Meeker]

That's a non-sequitur.  A double-slit experiment is not the same as a Cheshire cat experiment.

Brent

[Tomas Pales]

So, they claim that a neutron can be spatially separated from its spin if they perform a "weak measurement". A weak measurement does not collapse the wave function, does it? So the neutron is still spread out as a wave and so is its spin, no?

[Jason Resch]

So what of rare earths on beyond the cosmological horizon? Or in other branches of the wavefunction?

Jason

 

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[Philip Thrift]

The same QM principles apply. It's just plain quantum mechanics going on whether it's a particle of molecule, or which experiment is being done:

[Philip Thrift]

On Thursday, May 30, 2019 at 4:35:14 PM UTC-5, Philip Thrift wrote:

On Thursday, May 30, 2019 at 3:30:56 PM UTC-5, Brent wrote:

On 5/30/2019 1:17 PM, Philip Thrift wrote:

On Thursday, May 30, 2019 at 3:03:30 PM UTC-5, Brent wrote:

On 5/30/2019 11:47 AM, Tomas Pales wrote:

On Thursday, May 30, 2019 at 8:02:12 PM UTC+2, Brent wrote:

I wonder if philosophers have noticed that properties can be separated from objects in quantum mechanics, c.f. Cheshire Cat experiments?

What does it mean that a property is "separated" from an object? That an object loses a property? That happens all the time.

arXiv:1312.3775v1 [quant-ph] 13 Dec 2013

Brent

We know that a molecule's histories can interfere with each other:

https://en.wikipedia.org/wiki/Double-slit_experiment

In 2013, the double-slit experiment was successfully performed with molecules that each comprised 810 atoms (whose total mass was over 10,000 atomic mass units).

 

Does this mean that a molecule's properties can be separated from itself?

That's a non-sequitur.  A double-slit experiment is not the same as a Cheshire cat experiment.

Brent

The same QM principles apply. It's just plain quantum mechanics going on whether it's a particle 

>                                                                                                                                                            or 

[Philip Thrift]

The "Cheshire Cat" claim that a property can be separated from the particle is just pseudoscience, as far as I can tell.

@philipthrift  

[Brent Meeker]

Although it is not so spread out that the spin is not separated.  But, yes, that's why the interpretation is controversial.

Brent

[Brent Meeker]

So rare Earths here don't exist.

Brent

[Brent Meeker]

On 5/30/2019 2:47 PM, Philip Thrift wrote:

On Thursday, May 30, 2019 at 4:38:10 PM UTC-5, Philip Thrift wrote:

On Thursday, May 30, 2019 at 4:35:14 PM UTC-5, Philip Thrift wrote:

On Thursday, May 30, 2019 at 3:30:56 PM UTC-5, Brent wrote:

On 5/30/2019 1:17 PM, Philip Thrift wrote:

On Thursday, May 30, 2019 at 3:03:30 PM UTC-5, Brent wrote:

On 5/30/2019 11:47 AM, Tomas Pales wrote:

On Thursday, May 30, 2019 at 8:02:12 PM UTC+2, Brent wrote:

I wonder if philosophers have noticed that properties can be separated from objects in quantum mechanics, c.f. Cheshire Cat experiments?

What does it mean that a property is "separated" from an object? That an object loses a property? That happens all the time.

arXiv:1312.3775v1 [quant-ph] 13 Dec 2013

Brent

We know that a molecule's histories can interfere with each other:

https://en.wikipedia.org/wiki/Double-slit_experiment

In 2013, the double-slit experiment was successfully performed with molecules that each comprised 810 atoms (whose total mass was over 10,000 atomic mass units).

 

Does this mean that a molecule's properties can be separated from itself?

That's a non-sequitur.  A double-slit experiment is not the same as a Cheshire cat experiment.

Brent

The same QM principles apply. It's just plain quantum mechanics going on whether it's a particle 

>                                                                                                                                                            or 

molecule, or which experiment is being done:

Quantum Cheshire Cat effect may be explained by standard quantum mechanics.

@philipthrift

You imply that detecting the spin on a path different from the object is somehow contrary to standard quantum mechanics.  I don't see that.  It's just contrary to an assumption about the interaction of position measurements and spin measurements, i.e. the assumption that they have to happen at the same place.  It's no more strange than violating the assumption that a particle can't go thru two different slits at the same time.

"In no way this is a definitive answer," Corrêa said. "As usual in science, new explanations can always show up and are always welcome, and that's what characterizes its development. In fact, we can't even say that we proved the authors wrong in their interpretation—we simply provided a different interpretation of the results.


Brent

The "Cheshire Cat" claim that a property can be separated from the particle is just pseudoscience, as far as I can tell.

@philipthrift  

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[Jason Resch]

Is existence an intrinsic property or a relative one?

Jason 

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[Bruce Kellett]

On Fri, May 31, 2019 at 9:20 AM Jason Resch <jason...@gmail.com> wrote:

Is existence an intrinsic property or a relative one?

Existence isn't a property!

Bruce 

[Lawrence Crowell]

On Thursday, May 30, 2019 at 1:28:19 PM UTC-5, Philip Thrift wrote:

Quantum Cheshire Cat effect may be explained by standard quantum mechanics.

https://phys.org/news/2015-06-quantum-cheshire-cat-effect-standard.html

@philipthrift

Of course it is ordinary quantum mechanics. In the Heisenberg representation of an operator the evolution is dO/dt = i[O, H]. Different observables will have different commutation properties with the Hamiltonian and thus may evolve separately.

 

On Thursday, May 30, 2019 at 1:02:12 PM UTC-5, Brent wrote:

I wonder if philosophers have noticed that properties can be separated from objects in quantum mechanics, c.f. Cheshire Cat experiments?

There is no real distinction between an object and its properties in quantum mechanics.

LC

[Philip Thrift]

On Thursday, May 30, 2019 at 5:42:45 PM UTC-5, Brent wrote:

On 5/30/2019 2:47 PM, Philip Thrift wrote:

On Thursday, May 30, 2019 at 4:38:10 PM UTC-5, Philip Thrift wrote:

Quantum Cheshire Cat effect may be explained by standard quantum mechanics.

@philipthrift

You imply that detecting the spin on a path different from the object is somehow contrary to standard quantum mechanics.  I don't see that.  It's just contrary to an assumption about the interaction of position measurements and spin measurements, i.e. the assumption that they have to happen at the same place.  It's no more strange than violating the assumption that a particle can't go thru two different slits at the same time.

"In no way this is a definitive answer," Corrêa said. "As usual in science, new explanations can always show up and are always welcome, and that's what characterizes its development. In fact, we can't even say that we proved the authors wrong in their interpretation—we simply provided a different interpretation of the results.


Brent

'Quantum Cheshire Cat' as Simple Quantum Interference

Raul Corrêa, Marcelo França Santos, C. H. Monken, Pablo L. Saldanha

https://arxiv.org/abs/1409.0808

In a recent work, Aharonov et al. suggested that a photon could be separated from its polarization in an experiment involving pre- and post-selection [New J. Phys 15, 113015 (2013)]. They named the effect 'quantum Cheshire Cat', in a reference to the cat that is separated from its grin in the novel Alice's Adventures in Wonderland. Following these ideas, Denkmayr et al. performed a neutron interferometric experiment and interpreted the results suggesting that neutrons were separated from their spin. Here we show that these results can be interpreted as simple quantum interference, with no separation between the quantum particle and its internal degree of freedom. We thus hope to clarify the phenomenon with this work, by removing these apparent paradoxes. 

The "Cheshire Cat" claim that a property can be separated from the particle is just pseudoscience, as far as I can tell.

@philipthrift  

--

no more strange than violating the assumption that a particle can't go thru two different slits at the same time

So an 810-atom molecule that is sent from source to screen does that too?

The experiment can be done with entities much larger than electrons and photons, although it becomes more difficult as size increases. The largest entities for which the double-slit experiment has been performed were molecules that each comprised 810 atoms (whose total mass was over 10,000 atomic mass units).

A lot of quantum pseudoscience is made with misguided interpretations.

@philipthrift

[Tomas Pales]

On Friday, May 31, 2019 at 1:20:33 AM UTC+2, Jason wrote:

Is existence an intrinsic property or a relative one?

The most general definition of existence is that existence is logical consistency or identity: an object exists iff it is what it is and is not what it is not. This means that an object must be consistently defined in relations to all other objects ('relative' existence) and it must also be something that stands in those relations (being this something is 'intrinsic' existence).

 

[Bruno Marchal]

On 30 May 2019, at 14:50, Tomas Pales <litew...@gmail.com> wrote:

On Wednesday, May 29, 2019 at 10:15:46 PM UTC+2, Jason wrote:

Appears to predict the arithmetical reality:

"There exists, unless I am mistake, an entire world consisting of the totality of mathematical truths, which is accessible to us only through our intelligence, just as there exists the world of physical realities; each one is independent of us, both of them divinely created and appear different only because of the weakness of our mind; but, for a more powerful intelligence, they are one and the same thing, whose synthesis is partially revealed in that marvelous correspondence between abstract mathematics on the one hand and astronomy and all branches of physics on the other."

https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf on page 323.

Jason

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles.

In philosophy base on the assumption that there is a primitively Aristotelian reality.

Note that in math, an instantiation is when you replace a variable by a “concrete” number.

With mechanism assumed in the cognitive science, the physical reality is projection in the mind of the universal Turing machine (which probably exist in elementary arithmetic). Physics is not the fundamental science, once you bet on mechanism (like Darwin did).

It is a relation whereby the abstract object is a property of the concrete objects and the concrete objects are instances of the abstract object. The instantation relation is regarded as primitive, similarly like the composition relation between a collection of objects and the objects in the collection. The instantiation relation may appear more mysterious though, because while it is quite easy to visualize a collection, it is impossible to visualize an abstract object.

Abstract and concrete objects are existentially dependent on each other, because there can be no property without an object that has the property, and there can be no object that has no property.

OK. 

But that view can be shown inconsistent with the idea that the brain does not use magic to function. You need a non-mechanist theory of mind to make sense of this. With mechanism, physics emerges from a statistic of number dreams (so to speak, they are computations with a notion of being seen from inside arithmetic) which are (provably when assuming mechanism) realised in the elementary arithmetical reality.

The number 17 is, for a mechanist, more concrete than the moon, which only seems concrete because the brain is programmed to make us feel that way.

Bruno

 

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[Bruno Marchal]

On 30 May 2019, at 15:28, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Wednesday, May 29, 2019 at 3:15:46 PM UTC-5, Jason wrote:

Appears to predict the arithmetical reality:

"There exists, unless I am mistake, an entire world consisting of the totality of mathematical truths, which is accessible to us only through our intelligence, just as there exists the world of physical realities; each one is independent of us, both of them divinely created and appear different only because of the weakness of our mind; but, for a more powerful intelligence, they are one and the same thing, whose synthesis is partially revealed in that marvelous correspondence between abstract mathematics on the one hand and astronomy and all branches of physics on the other."

https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf on page 323.

Jason

This is the opinion similar to what most mathematicians think. Mathematics is a system that has objective truth. I don't necessarily "believe this," but I can see its point and will tip my hat towards it. In physics we tend often to view mathematics as more similar to rules of chess, and where the use of the rules defines the game. Here the game being how to model the physical world. I can see this as well. There is the Brouwer constructionist idea of mathematics that is related to this. Hilbert thought that mathematics was something existing on its own, which is the objectivist opinion, objectivist not in line with the quasi-philosophy of Ayn Rand, which is related to Plato's ideas of there being ideal forms outside of physical forms. 

What is the relationship between physics and mathematics?

With mechanism, or even just form of platonism, that is easily answered. We are mathematical being living in a mathematical reality. it is absolutely undecidable if there is more than the arithmetical truth, and with mechanism, it is obligatory to not assume more than very elementary arithmetic. We can’t even assume PA for the ontology. PA is assumed only for the observer.

The physical reality is a lawful illusion by Turing machine, or combinator, or number ..

Bruno

I have not the slightest clue. I see this as similar to Garrison Keillor's Guy Noir who in the introduction would have, "On a dark night in a city that knows how to keep its secrets, one man searches for life's persistent questions. Guy Noir private eye." As I recall the quote. 

LC

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[Bruno Marchal]

On 30 May 2019, at 16:52, Tomas Pales <litew...@gmail.com> wrote:

On Thursday, May 30, 2019 at 3:32:41 PM UTC+2, Philip Thrift wrote:

On Thursday, May 30, 2019 at 7:50:37 AM UTC-5, Tomas Pales wrote:

On Wednesday, May 29, 2019 at 10:15:46 PM UTC+2, Jason wrote:

Appears to predict the arithmetical reality:

"There exists, unless I am mistake, an entire world consisting of the totality of mathematical truths, which is accessible to us only through our intelligence, just as there exists the world of physical realities; each one is independent of us, both of them divinely created and appear different only because of the weakness of our mind; but, for a more powerful intelligence, they are one and the same thing, whose synthesis is partially revealed in that marvelous correspondence between abstract mathematics on the one hand and astronomy and all branches of physics on the other."

https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf on page 323.

Jason

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles. It is a relation whereby the abstract object is a property of the concrete objects and the concrete objects are instances of the abstract object. The instantation relation is regarded as primitive, similarly like the composition relation between a collection of objects and the objects in the collection. The instantiation relation may appear more mysterious though, because while it is quite easy to visualize a collection, it is impossible to visualize an abstract object.

Abstract and concrete objects are existentially dependent on each other, because there can be no property without an object that has the property, and there can be no object that has no property.

In  the fictionalist philosophy of mathematics

https://plato.stanford.edu/entries/fictionalism-mathematics/

          there are no such things as abstract objects.

So such troubles do not arise.

If there is no abstract triangle then there is no concrete triangle either, because what would it mean that there is a concrete triangle? That seems more of a trouble.

Agreed.

Now, we could say that there is no concrete object. Concreteness is when abstraction seen from inside. But usually I consider natural numbers, or programs, as concrete primitive objects, but each soul is multiplied in the infinities of computations that we get when we assume the (natural) numbers.

Bruno

 

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[Bruno Marchal]

On 30 May 2019, at 16:54, Tomas Pales <litew...@gmail.com> wrote:

On Thursday, May 30, 2019 at 4:14:48 PM UTC+2, Jason wrote:

Let's say reality is composed of two sets:

1. The set of all existent things

2. The set of all non-existent things

If nothing existed at all, then set one would be emtpy, while set two would contain everything.

What do you mean by existent? How are existent things different from non-existent things?

Yes, that is a bit weird.

Let me give exemples of non existent thing: a unicorn with two corns, A cat is is also a dog, a saure without corner, a triangle with four sides, a proof of an inconsistency in RA, a French who is higher than Mt-Everest, etc.

If mechanism is true, then an ontological physical universe is another example.

The set of non existent things is empty, almost by definition. I would say.

Bruno

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[Bruno Marchal]

On 30 May 2019, at 20:18, Philip Thrift <cloud...@gmail.com> wrote:

On Thursday, May 30, 2019 at 9:14:48 AM UTC-5, Jason wrote:

On Thursday, May 30, 2019, Philip Thrift <cloud...@gmail.com> wrote:

On Thursday, May 30, 2019 at 7:50:37 AM UTC-5, Tomas Pales wrote:

On Wednesday, May 29, 2019 at 10:15:46 PM UTC+2, Jason wrote:

Appears to predict the arithmetical reality:

"There exists, unless I am mistake, an entire world consisting of the totality of mathematical truths, which is accessible to us only through our intelligence, just as there exists the world of physical realities; each one is independent of us, both of them divinely created and appear different only because of the weakness of our mind; but, for a more powerful intelligence, they are one and the same thing, whose synthesis is partially revealed in that marvelous correspondence between abstract mathematics on the one hand and astronomy and all branches of physics on the other."

https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf on page 323.

Jason

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles. It is a relation whereby the abstract object is a property of the concrete objects and the concrete objects are instances of the abstract object. The instantation relation is regarded as primitive, similarly like the composition relation between a collection of objects and the objects in the collection. The instantiation relation may appear more mysterious though, because while it is quite easy to visualize a collection, it is impossible to visualize an abstract object.

Abstract and concrete objects are existentially dependent on each other, because there can be no property without an object that has the property, and there can be no object that has no property.

In  the fictionalist philosophy of mathematics

https://plato.stanford.edu/entries/fictionalism-mathematics/

          there are no such things as abstract objects.

So such troubles do not arise.

Let's say reality is composed of two sets:

1. The set of all existent things

2. The set of all non-existent things

If nothing existed at all, then set one would be emtpy, while set two would contain everything.

Now take the nominalist position. Set one would contain the physical universe while set two would contain all abstract objects: arithmetical truth, executions of programs, histories of non-existent universes, etc.

What puzzles me, is that in the program executions and in the histories of non-existent universes you will find worlds where life evolves into more complex forms, you will find the risings and fallings of great civilizations, you will find literature written by the philosophers of those civilizations, their treatises on ontology, on why their universe is concrete while others are abstract, on the mysteries of consciousness and strangeness of qualia.  If all these things can be found in the abstract objects of the set of non-existent things, then how do we know we're not in an abstract object of that set of non-existent things?

Does it matter at all which set our universe resides in? Can moving an object from one set to another blink away or bring into being the first person experiences of the entities who inhabit such objects, or is their consciousness a property inherent to the object which cannot be taken away merely by moving it from one set to another?

Much to think about.

Jason

For the fictionalist, one can invent anything, including mathematics with different definitions of sets producing a multiverse of mathematical truths  (Joel David Hamkins) and logics that are inconsistent (Graham Priest). 

Matter (the universe we live in) gives what it gives and nothing more. 

There is a story today about rare earth minerals:

https://www.cnn.com/2019/05/30/investing/rare-earths-china-trade-war/

I suppose for those who think that matter doesn't exist, a shortage of rare earth minerals cannot be a problem. Maybe someday we build a matter compiler that can make them.

@philipthrift 

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[Bruno Marchal]

Apology for the preceding sending error. Comment below.

On 30 May 2019, at 20:18, Philip Thrift <cloud...@gmail.com> wrote:

On Thursday, May 30, 2019 at 9:14:48 AM UTC-5, Jason wrote:

On Thursday, May 30, 2019, Philip Thrift <cloud...@gmail.com> wrote:

On Thursday, May 30, 2019 at 7:50:37 AM UTC-5, Tomas Pales wrote:

On Wednesday, May 29, 2019 at 10:15:46 PM UTC+2, Jason wrote:

Appears to predict the arithmetical reality:

"There exists, unless I am mistake, an entire world consisting of the totality of mathematical truths, which is accessible to us only through our intelligence, just as there exists the world of physical realities; each one is independent of us, both of them divinely created and appear different only because of the weakness of our mind; but, for a more powerful intelligence, they are one and the same thing, whose synthesis is partially revealed in that marvelous correspondence between abstract mathematics on the one hand and astronomy and all branches of physics on the other."

https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf on page 323.

Jason

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles. It is a relation whereby the abstract object is a property of the concrete objects and the concrete objects are instances of the abstract object. The instantation relation is regarded as primitive, similarly like the composition relation between a collection of objects and the objects in the collection. The instantiation relation may appear more mysterious though, because while it is quite easy to visualize a collection, it is impossible to visualize an abstract object.

Abstract and concrete objects are existentially dependent on each other, because there can be no property without an object that has the property, and there can be no object that has no property.

In  the fictionalist philosophy of mathematics

https://plato.stanford.edu/entries/fictionalism-mathematics/

          there are no such things as abstract objects.

So such troubles do not arise.

But other troubles arises. What is non fiction? For example. That will of course depends on your metaphysical assumption.

Let's say reality is composed of two sets:

1. The set of all existent things

2. The set of all non-existent things

If nothing existed at all, then set one would be emtpy, while set two would contain everything.

Now take the nominalist position. Set one would contain the physical universe while set two would contain all abstract objects: arithmetical truth, executions of programs, histories of non-existent universes, etc.

What puzzles me, is that in the program executions and in the histories of non-existent universes you will find worlds where life evolves into more complex forms, you will find the risings and fallings of great civilizations, you will find literature written by the philosophers of those civilizations, their treatises on ontology, on why their universe is concrete while others are abstract, on the mysteries of consciousness and strangeness of qualia.  If all these things can be found in the abstract objects of the set of non-existent things, then how do we know we're not in an abstract object of that set of non-existent things?

Does it matter at all which set our universe resides in? Can moving an object from one set to another blink away or bring into being the first person experiences of the entities who inhabit such objects, or is their consciousness a property inherent to the object which cannot be taken away merely by moving it from one set to another?

Much to think about.

Jason

For the fictionalist, one can invent anything, including mathematics with different definitions of sets producing a multiverse of mathematical truths  (Joel David Hamkins) and logics that are inconsistent (Graham Priest). 

Fictionalism become a bad name for phenomenology. Graham Priest paraconsistent logics are interesting for natural language study, but misleading for metaphysics, as it leads to relativisme.

Matter (the universe we live in) gives what it gives and nothing more. 

There is a story today about rare earth minerals:

https://www.cnn.com/2019/05/30/investing/rare-earths-china-trade-war/

I suppose for those who think that matter doesn't exist,

Nobody says that matter does not exist. That would be denying simple facts. The point is that matter has phenomenological existence.

I thing we should never use the term ‘exist” without making precise if we talk about ontological existence, or phenomenological existence. With mechanism there are eight important different notion of phenomenological existence, and one simple notion of ontological existence valid only for numbers.

Bruno

[Bruno Marchal]

It is very wise to think so. Mathematical logic is almost entirely based on that idea.

In logic “existence” is a disjunction applied to the domain of discourse. For example, to say that a natural number x having some property  P exists means that the infinite disjunction 

P(0) v P(1) v P(2) v P(3) v P(4) v P(5) v P(6) v ...

is true.

This is a very useful idea which eliminates inessential essentialism. The unavoidable essentialism coming back with incompleteness is quite enough.

Bruno

Bruce 

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[Brent Meeker]

On 5/31/2019 2:51 AM, Bruno Marchal wrote:
>> I suppose for those who think that matter doesn't exist,
>
> Nobody says that matter does not exist. That would be denying simple
> facts. The point is that matter has phenomenological existence.
>
> I thing we should never use the term ‘exist” without making precise if
> we talk about ontological existence, or phenomenological existence.

Right.  And that of course also applies to "non-existence".  And
ontologies are theory dependent.  To often the theory is assumed
implicitly and "exist" is use equivocally.

> With mechanism there are eight important different notion of
> phenomenological existence, and one simple notion of ontological
> existence valid only for numbers.
>

And that "ontological existence" is in the context of the theory of
countable things, i.e. the natural numbers.

Brent

[Tomas Pales]

On Friday, May 31, 2019 at 11:04:53 AM UTC+2, Bruno Marchal wrote:

On 30 May 2019, at 14:50, Tomas Pales <litew...@gmail.com> wrote:

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles.

In philosophy base on the assumption that there is a primitively Aristotelian reality.

Note that in math, an instantiation is when you replace a variable by a “concrete” number.

 

Yes. I didn't want to make my point about the instantiation relation too long but there is a hierarchy of abstract objects from the most abstract to the least abstract and under them are concrete objects. For example, "mathematical object" is instantiated in "number", which is instantiated in a specific number, for example in number 2, which is instantiated in the concrete relation between two concrete flowers. Concrete objects are the bottom of instantiation because concrete objects have no instances. Number 2 is instantiated in the relation between any two objects, or abstract flower is instantiated in any concrete flower, but a concrete flower has no instances; it cannot be said that the flower that is growing under my window is a property of something else.

An interesting question is whether there are abstract objects that never bottom out in concrete objects. Similarly like for the composition relation where you have a collection of collections of collections etc. ad infinitum, never bottoming out in empty collections. But I guess these infinite chains are subject to Godel's second incompleteness theorem so we may never know whether they are consistent and thus whether they exist.

As for the most abstract object, I would say it is "existence" because it is instantiated in every object, including in itself. Existence is just the principle of logical consistency or identity. Inconsistent objects don't exist because they are not even objects. What kind of object is a "triangle that is not a triangle"? It's nothing. As you said, the set of inconsistent objects is empty.

The number 17 is, for a mechanist, more concrete than the moon, which only seems concrete because the brain is programmed to make us feel that way.

Number 17 is the property of the relation among any 17 objects. The moon orbiting our planet is not a property of anything. Therefore number 17 is an abstract object and the moon is a concrete object.

[Tomas Pales]

On Friday, May 31, 2019 at 9:12:48 PM UTC+2, Brent wrote:

Right.  And that of course also applies to "non-existence".  And
ontologies are theory dependent.  To often the theory is assumed
implicitly and "exist" is use equivocally.

I think the most general ontology is based on three relations: (1) similarity, (2) instantiation, and (3) composition.

(1) Similarity between objects means that the objects have some same properties and some different properties. Any relation is an instance of the similarity relation.

(2) Instantiation is the relation between an abstract object (property) and a less abstract object (which has the more abstract object as a property), or between an abstract object (property) and a concrete object (which has the abstract object as a property and is not a property of anything).

(3) Composition is the relation between a collection and an object in that collection.

These three relations seem mutually interwoven but not reducible to each other: instantiation and composition need similarity (because any object and its property, or any collection and an object in it, must be similar); similarity and composition need instantiation (because any similar objects, or any collection and an object in it, must have properties); and instantiation and similarity need composition (because any object and its property, or any similar objects, must compose a collection).

And if there are relations, there must also be objects (relata) that stand in these relations. Relata may be relations but there must also be relata that are non-relations, because otherwise relations would not make sense: there cannot be just similarity relations between similarity relations; relations must be grounded in non-relations. Mathematics, logic, and mathematical foundations such as set theory, category theory or type theory study relations and their structures. The unstructured nature of non-relations seems to make them (or at least some of them) candidates for qualities of consciousness (qualia).

[Bruno Marchal]

OK. And with mechanism, the point is that we cannot assume more than the natural numbers in the ontology. The non countable things will comes in the first person perspective through the non recursively countable, and limits.

I am just illustrating this to my student, by showing that “simple” arithmetical relation can only be proved by doing a transfinite induction up to epsilon-zero, and unavoidable by even a theory as rich as PA. I use Goodstein's sequences. May be I can say more on this one day, but people should study a bit of mathematical logic.

Bruno



>
> Brent

>
>
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[Bruno Marchal]

On 31 May 2019, at 22:27, Tomas Pales <litew...@gmail.com> wrote:

On Friday, May 31, 2019 at 11:04:53 AM UTC+2, Bruno Marchal wrote:

On 30 May 2019, at 14:50, Tomas Pales <litew...@gmail.com> wrote:

In philosophy, the relation between abstract and concrete objects is called "instantiation", for example between the abstract triangle and concrete triangles.

In philosophy base on the assumption that there is a primitively Aristotelian reality.

Note that in math, an instantiation is when you replace a variable by a “concrete” number.

 

Yes. I didn't want to make my point about the instantiation relation too long but there is a hierarchy of abstract objects from the most abstract to the least abstract and under them are concrete objects. For example, "mathematical object" is instantiated in "number", which is instantiated in a specific number, for example in number 2, which is instantiated in the concrete relation between two concrete flowers. Concrete objects are the bottom of instantiation because concrete objects have no instances. Number 2 is instantiated in the relation between any two objects, or abstract flower is instantiated in any concrete flower, but a concrete flower has no instances; it cannot be said that the flower that is growing under my window is a property of something else.

An interesting question is whether there are abstract objects that never bottom out in concrete objects. Similarly like for the composition relation where you have a collection of collections of collections etc. ad infinitum, never bottoming out in empty collections. But I guess these infinite chains are subject to Godel's second incompleteness theorem so we may never know whether they are consistent and thus whether they exist.

Keep in mind that the consistent machine is able to prove its own Gödel theorem. That is why the ontology will admit bottom and be well-founded, but the non-bottom aspect of reality will be unavoidable in the first person perspective, somehow.

As for the most abstract object, I would say it is "existence" because it is instantiated in every object, including in itself.

Hmm… That makes sense, perhaps, in rich ontologies à la NF (Quine’s New Foundation), where the universe (of sets) can be a set. Something similar can be emulated in ZF using anti-foundation axioms, but I avoid them, for technical reason, and because it could only be a variation of simpler things occurring in the phenomenology. With mechanism, the ontology os well-founded.

Existence is just the principle of logical consistency or identity.

Almost. Peano arithmetic is consistent with the proposition that Peano arithmetic is inconsistent. Consistency is shown rather cheap, and far away from Truth, which is the key notion, but of course not a very obvious one. 

Inconsistent objects don't exist because they are not even objects. What kind of object is a "triangle that is not a triangle"? It's nothing. As you said, the set of inconsistent objects is empty.

The number 17 is, for a mechanist, more concrete than the moon, which only seems concrete because the brain is programmed to make us feel that way.

Number 17 is the property of the relation among any 17 objects. The moon orbiting our planet is not a property of anything. Therefore number 17 is an abstract object and the moon is a concrete object.

Here I disagree. 17 is very concrete. It the successor of 16, which is very concrete, etc. With mechanism, 0, 1, 2, 3, … are taken as the most concrete “really existing” object. The moon, and yourself are extremely abstract type, having only phenomenological existence. There are reason why it needs to be like that, but I will refer, at least now, to my papers for the why. (I will have to go soon). To be continued …

Bruno

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[Tomas Pales]

On Saturday, June 1, 2019 at 10:06:31 AM UTC+2, Bruno Marchal wrote:

On 31 May 2019, at 22:27, Tomas Pales <litew...@gmail.com> wrote:

Existence is just the principle of logical consistency or identity.

Almost. Peano arithmetic is consistent with the proposition that Peano arithmetic is inconsistent. Consistency is shown rather cheap, and far away from Truth, which is the key notion, but of course not a very obvious one. 

If PA is consistent, it exists. If PA is not consistent, it doesn't exist. But since PA is subject to Godel's second incompleteness theorem, we may never know, right?

 

Here I disagree. 17 is very concrete. It the successor of 16, which is very concrete, etc. With mechanism, 0, 1, 2, 3, … are taken as the most concrete “really existing” object. The moon, and yourself are extremely abstract type, having only phenomenological existence.

This is what I mean by "abstract" and "concrete":

abstract: has instances/examples (is a property)

concrete: has no instances/examples (is not a property)

Number 17 has instances/examples in any collection of 17 objects (is a property of any collection of 17 objects). Therefore number 17 is an abstract object.

Our moon has no instances/examples (is not a property of any object, just as Bruno Marchal is not a property of any object). Therefore our moon is a concrete object.

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[Bruno Marchal]

On 1 Jun 2019, at 11:27, Tomas Pales <litew...@gmail.com> wrote:

On Saturday, June 1, 2019 at 10:06:31 AM UTC+2, Bruno Marchal wrote:

On 31 May 2019, at 22:27, Tomas Pales <litew...@gmail.com> wrote:

Existence is just the principle of logical consistency or identity.

Almost. Peano arithmetic is consistent with the proposition that Peano arithmetic is inconsistent. Consistency is shown rather cheap, and far away from Truth, which is the key notion, but of course not a very obvious one. 

If PA is consistent, it exists. If PA is not consistent, it doesn't exist.

If PA is consistent, a Model of PA exists. Most people believe that PA is consistent, because they have learned the standard model (N, 0, +, x) at school.

But since PA is subject to Godel's second incompleteness theorem, we may never know, right?

Even PA knows it. What Gödel’s show is that not theory/machine can prove its own consistency.

If PA would inconsistent, it would still exist. Inconsistent people, machine and numbers exists already in the model of RA (which is much weaker than PA).

 

Here I disagree. 17 is very concrete. It the successor of 16, which is very concrete, etc. With mechanism, 0, 1, 2, 3, … are taken as the most concrete “really existing” object. The moon, and yourself are extremely abstract type, having only phenomenological existence.

This is what I mean by "abstract" and "concrete":

abstract: has instances/examples (is a property)

concrete: has no instances/examples (is not a property)

Number 17 has instances/examples in any collection of 17 objects (is a property of any collection of 17 objects). Therefore number 17 is an abstract object.

Our moon has no instances/examples (is not a property of any object, just as Bruno Marchal is not a property of any object). Therefore our moon is a concrete object.

I can accept such definition. Then 0, 1, 2, … are concrete. Prime becomes a property and is abstract in that setting, but then computers are even more abstract and physical computer still even more, and the moon can be said to instantiate the theory of the moon, unless you postulate that there is “really” a moon out there, which is incoherent with the mechanist hypothesis, where the numbers (or Turing equivalent). (If you are aware that mechanism and materialism oppose each other logically (see my papers if not, it is still rather ignored).

Bruno

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[Bruno Marchal]

Tomas,

Let me add this. Gödel’s theorem does not add any doubt on arithmetic. On the contrary it free arithmetic from reductionist theories of Arithmetic. 

Rich theories like PA or ZF proves their own second incompleteness theorem: they prove that if they are consistent then they cannot rove that their are consistent, making “consistency” already a bit like consciousness (indeed conscious reasoner comes up often with the idea that a conscious entity cannot prove its consciousness to another entity). 

IF PA was inconsistent, it would of course proves its consistency, for no avail, bacuse it would not have any model and be senseless. So Gödel’s theorem is more like giving more trust in the mathematical theories, because it shows that somehow, the mathematical theories and the ‘rich) machine are rather well aware of their limitation, and that explain also why personal semantic (rich model encompassing ourselves) requires some act of faith. We are not conscious of this, because the brain, for survival propose, makes such act of faith instinctive. If the lamb doubt its experience of the wolf, its chance of surviving will decline. That explains also why it is hard for most people to doubt on some matter, because we are all brain wired, so to speak,  to not doubt too much.

With Mechanism, Gödel’s theorem apply to us, as far as we are consistent/sound. That is beauty of it; it illustrates that reason can discover its own limitation, and why we need some faith to believe in any reality (equivalent with self-consistency).

By machine theology, I always mean something very specific: the G* logic discovered by Solovay. It is the true part of the logic of machine (and other entities) provability/consistency. Solovay knew about G, which concerns the provable part of G*. So, science has discovered that for all (enough rich) machine, there is a surrational part in between the rational and the irrational (false and/or refutable).

Reason explain the reason why reality is larger than what reason can justify, and this happens even when we limited ourself to arithmetic.

Gödel’s theorem can be see as the Hubble of mathematics: it shows that it is *very* big, and that there is an infinity of surprises awaiting us.

Bruno

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