On 28 Sep 2018, at 00:34, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:
- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.
- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.
Regards--
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-pt
Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:
f
- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.
Regards
On 28 Sep 2018, at 00:34, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:Yes, it was proved as a consequence of the Mechanist Hypothesis (well before Tegmark introduced it as an hypothesis).- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.What Tegmark missed is the first person indeterminacy, which makes the physical reality into a sort of statistics on *all* mathematical structures. The physical reality is not a mathematical structure among others, but a precise mathematical phenomenon, occurring in arithmetic.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If mechanism is false, both substantial physicalism and non substantial physicalism are wrong. Mechanism, in the cognitive science, makes the physical reality not Turing emulbale (“digital physics” is incoherent). Physics becomes reducible to machine’s psychology, or better, machine or number theology. Unfortunately a giant gap remain between physicists (who have the right question, but an inadequate metaphysics) and logician (who have the right tool but run away from theology and metaphysics).The main advantage in using Mechanism (properly) is that incompleteness justified all the modes of the self, and this makes possible to get a precise theory of quanta and qualia.In this list, we are a bit in advance on this, to be short. I can give references if asked. Actually I just gave them in some preceding posts.What some people missed, is that there has never been any evidence for Aristotelian Primary Matter. Materialism will be abandoned as a lasting supersitition.Bruno
On 28 Sep 2018, at 14:42, Philip Thrift <cloud...@gmail.com> wrote:
On Friday, September 28, 2018 at 2:44:18 AM UTC-5, Bruno Marchal wrote:On 28 Sep 2018, at 00:34, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:Yes, it was proved as a consequence of the Mechanist Hypothesis (well before Tegmark introduced it as an hypothesis).- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.What Tegmark missed is the first person indeterminacy, which makes the physical reality into a sort of statistics on *all* mathematical structures. The physical reality is not a mathematical structure among others, but a precise mathematical phenomenon, occurring in arithmetic.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If mechanism is false, both substantial physicalism and non substantial physicalism are wrong. Mechanism, in the cognitive science, makes the physical reality not Turing emulbale (“digital physics” is incoherent). Physics becomes reducible to machine’s psychology, or better, machine or number theology. Unfortunately a giant gap remain between physicists (who have the right question, but an inadequate metaphysics) and logician (who have the right tool but run away from theology and metaphysics).The main advantage in using Mechanism (properly) is that incompleteness justified all the modes of the self, and this makes possible to get a precise theory of quanta and qualia.In this list, we are a bit in advance on this, to be short. I can give references if asked. Actually I just gave them in some preceding posts.What some people missed, is that there has never been any evidence for Aristotelian Primary Matter. Materialism will be abandoned as a lasting supersitition.BrunoOn the other side it is held that numbers - universal numbers - actually exist (arithmeticalism) is superstition.
Even the texts in which the definition of the universal numbers appear are material:
They are seen as electronic dots on a screen in a PDF viewer, or ink glyphs on paper in a printout, etc. But there is nothing more than that .There is nothing outside matter.
(Materialism is not physicalism.)
- pt
If this is correct, other models also fall by the wayside. AGRegards
- pt
On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:f- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.You are begging the question.
Yet, I define matter by “the object of study of physics”, or the study of the observable mode, making strong materialism implying physicalism.Bruno
Thank you everybody for your responses.Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computerHere for example (4min video) Edelman:
On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:f- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.You are begging the question.In what way? The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG
On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:f- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.You are begging the question.In what way? The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG
On 28 Sep 2018, at 20:26, Philip Thrift <cloud...@gmail.com> wrote:
On Friday, September 28, 2018 at 11:00:58 AM UTC-5, Bruno Marchal wrote:Yet, I define matter by “the object of study of physics”, or the study of the observable mode, making strong materialism implying physicalism.BrunoI think (along with Philip Goff*) that physics is not complete in its study of matter.
Either a new physics is needed, of there is a theoretical gap between physics and brains.
On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:f- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.You are begging the question.In what way? The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AGIf that is the MUH, then that it is plainly ridiculous, indeed. To have a perceived universe, you need a measure on the computation/sigma-sentences. The physical emerges from an arithmetical phenomenon (assuming mechanism in cognitive science).The version of mathematicalism implied by mechanism does not lead any choice for the “physical reality”, it has to be a statistic on computations structured by the “observable” mode of self-reference. That indeed predicts quantum logic, and the many “histories” interpretation of arithmetic. Oracle are not impossible, but there are no evidence for them, and should be invoked in last resort (a bit like the “Alien” in cosmology).The empirical evidence is that there is no physical universe at all.Bruno
Please give me your thought on that.
On 29 Sep 2018, at 09:16, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:f- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.You are begging the question.In what way? The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AGIf that is the MUH, then that it is plainly ridiculous, indeed. To have a perceived universe, you need a measure on the computation/sigma-sentences. The physical emerges from an arithmetical phenomenon (assuming mechanism in cognitive science).The version of mathematicalism implied by mechanism does not lead any choice for the “physical reality”, it has to be a statistic on computations structured by the “observable” mode of self-reference. That indeed predicts quantum logic, and the many “histories” interpretation of arithmetic. Oracle are not impossible, but there are no evidence for them, and should be invoked in last resort (a bit like the “Alien” in cosmology).The empirical evidence is that there is no physical universe at all.BrunoThis double-talk nonsense IMO. I clearly gave a counter-example to the MUH,
falsifying it. Moreover, I explained clearly why I used "perceived". I just meant that plane waves can never be observed,
and since they are solutions to Maxwell's equations, the MUH is false.
Deal with that directly and stop with the double talk about the non-existence of the physical universe. That's not even an issue, since I am only dealing with what can be observed. AG
On 29 Sep 2018, at 09:16, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:f- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.You are begging the question.In what way? The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AGIf that is the MUH, then that it is plainly ridiculous, indeed. To have a perceived universe, you need a measure on the computation/sigma-sentences. The physical emerges from an arithmetical phenomenon (assuming mechanism in cognitive science).The version of mathematicalism implied by mechanism does not lead any choice for the “physical reality”, it has to be a statistic on computations structured by the “observable” mode of self-reference. That indeed predicts quantum logic, and the many “histories” interpretation of arithmetic. Oracle are not impossible, but there are no evidence for them, and should be invoked in last resort (a bit like the “Alien” in cosmology).The empirical evidence is that there is no physical universe at all.BrunoThis double-talk nonsense IMO. I clearly gave a counter-example to the MUH,You want make some mathematical object physical real. That assume some physical reality, which cannot be done.
To say that a mathematical object exist physically, does not make sense. It starts with a category error.
It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG
On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.
So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.
- pt
On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:Thank you everybody for your responses.Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computerHere for example (4min video) Edelman:The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AGA bacteria is already a computer (at least),
On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:A bacteria is already a computer (at least),Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:Thank you everybody for your responses.
Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computerHere for example (4min video) Edelman:
The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG
A bacteria is already a computer (at least), and a neurone is already a rather sophisticated society of bacteria and viruses, plausibly enough. So, a society of billions of neurons should not be compared to transistors. The substitution level is plausibly much lower than the level of neurons.
A bacteria is already a computer (at least),
Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
A bacteria is already a computer (at least),
Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
Not all computers are von Neumann computers.
Brent
Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.
One thing for sure; he doesn't know what the MUH is, and therefore cannot understand my simple falsification of the hypothesis. AG
On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
A bacteria is already a computer (at least),
Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
Not all computers are von Neumann computers.
Brent
Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.
Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.
Brent
- ptIs
On Saturday, September 29, 2018 at 9:28:34 PM UTC, Philip Thrift wrote:
On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:
On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
A bacteria is already a computer (at least),
Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
Not all computers are von Neumann computers.
Brent
Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.
Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.
BrentBacterial computing: a form of natural computing and its applicationsBacteria make computers look like pocket calculatorsBacteria Can Now Be Programmed Like a Computer- pt
What is a computer -- what is it -- that bacteria can be seen as being like? Why bother to define it. Nothing obvious here except sloppy use of analogies. AG
On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
A bacteria is already a computer (at least),
Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
Not all computers are von Neumann computers.
Brent
Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.
Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.
Brent
Physicist Paul Benioff make interesting idea https://arxiv.org/abs/quant-ph/0201093
that mathematics and laws of physics coemerged somehow randomly.
To say that a mathematical object exist physically, does not make sense. It starts with a category error.I don't think you know what the MUH is. I have falsified it. AG
- pt
On 29 Sep 2018, at 12:41, Philip Thrift <cloud...@gmail.com> wrote:
On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.
So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.- pt
(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AG
- pt
On 29 Sep 2018, at 13:34, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:Thank you everybody for your responses.Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computerHere for example (4min video) Edelman:The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AGA bacteria is already a computer (at least),Really? Then you should be able to identify the entities that store binary information.
And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
- pt
On 29 Sep 2018, at 13:16, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.Bruno wrote 1 & 2. AGSo then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.According to Wiki, and what I've heard from its adherents, the MUH posits that ALL mathematical object or entities exist in nature. But plane waves do not exist in nature.There is no nature that you can invoke. Once mechanism is assumed, a term like nature needs to be (re-defined, or explained, without physicalist assumption, implicit or explicit.(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AGI agree with your conclusion, but you assume some nature or matter, which cannot work in the mechanist context.
On 29 Sep 2018, at 20:59, Brent Meeker <meek...@verizon.net> wrote:
On 9/29/2018 12:16 AM, Bruno Marchal wrote:
On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:Thank you everybody for your responses.
Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computerHere for example (4min video) Edelman:
The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG
A bacteria is already a computer (at least), and a neurone is already a rather sophisticated society of bacteria and viruses, plausibly enough. So, a society of billions of neurons should not be compared to transistors. The substitution level is plausibly much lower than the level of neurons.
It has been estimated that simulating a single neuron requires a micro-controller like an AVR, which contains 80,000 transistors.
<blicjehabnofhiib.png>
On 29 Sep 2018, at 13:34, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:Thank you everybody for your responses.Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computerHere for example (4min video) Edelman:The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AGA bacteria is already a computer (at least),Really? Then you should be able to identify the entities that store binary information.By computer I mean a number u such that phi_u(<x,y>) = phi_x(y), for some enumeration phi_i of the partial computable function. No need of binary information. But it needs digitally coded information, and that is given by the genome (the sequence of adenine, thymine, cytosine, guanine (French spelling, sorry).
On 29 Sep 2018, at 22:52, Brent Meeker <meek...@verizon.net> wrote:
On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
A bacteria is already a computer (at least),
Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG
Not all computers are von Neumann computers.
Brent
Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.
Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.
- pt
On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:On 29 Sep 2018, at 13:16, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.Bruno wrote 1 & 2. AGSo then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.According to Wiki, and what I've heard from its adherents, the MUH posits that ALL mathematical object or entities exist in nature. But plane waves do not exist in nature.There is no nature that you can invoke. Once mechanism is assumed, a term like nature needs to be (re-defined, or explained, without physicalist assumption, implicit or explicit.(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AGI agree with your conclusion, but you assume some nature or matter, which cannot work in the mechanist context.I didn't assume anything, except that plane waves will never be observed (regardless of your model of external reality) unless you agree to instantaneous action at a distance, and on steroids (!), since as time evolves, the amplitude of a plane wave changes instantaneously in all infinite directions. So I am just asserting that Tegmark's MUH has been falsified since plane waves mathematically exist, but are never reified by whatever is out there -- matter, or nothing but restrictions on motion giving rise the illusion of matter or something solid existing. Incidentally, I don't think the Wiki article refutes Tegmark as you claim; rather it just describes it. AG
On 30 Sep 2018, at 11:53, agrays...@gmail.com wrote:
On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:On 29 Sep 2018, at 13:16, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.Bruno wrote 1 & 2. AGSo then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.According to Wiki, and what I've heard from its adherents, the MUH posits that ALL mathematical object or entities exist in nature. But plane waves do not exist in nature.There is no nature that you can invoke. Once mechanism is assumed, a term like nature needs to be (re-defined, or explained, without physicalist assumption, implicit or explicit.(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AGI agree with your conclusion, but you assume some nature or matter, which cannot work in the mechanist context.I didn't assume anything, except that plane waves will never be observed (regardless of your model of external reality)
unless you agree to instantaneous action at a distance, and on steroids (!), since as time evolves, the amplitude of a plane wave changes instantaneously in all infinite directions. So I am just asserting that Tegmark's MUH has been falsified since plane waves mathematically exist,
but are never reified by whatever is out there -- matter, or nothing but restrictions on motion giving rise the illusion of matter or something solid existing.
Incidentally, I don't think the Wiki article refutes Tegmark as you claim; rather it just describes it.
On 30 Sep 2018, at 11:58, agrays...@gmail.com wrote:
On Sunday, September 30, 2018 at 9:40:07 AM UTC, Bruno Marchal wrote:On 29 Sep 2018, at 13:34, agrays...@gmail.com wrote:
On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:
On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:Thank you everybody for your responses.Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computerHere for example (4min video) Edelman:The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AGA bacteria is already a computer (at least),Really? Then you should be able to identify the entities that store binary information.By computer I mean a number u such that phi_u(<x,y>) = phi_x(y), for some enumeration phi_i of the partial computable function. No need of binary information. But it needs digitally coded information, and that is given by the genome (the sequence of adenine, thymine, cytosine, guanine (French spelling, sorry).So now a computer isn't some device that executes programs, but a number? Please elaborate on your mathematics. I have no idea what it is supposed to mean. AG
Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:
- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.
Regards
[Re:] forcing theory in set theories with classes.Bruno
On 30 Sep 2018, at 08:03, Philip Thrift <cloud...@gmail.com> wrote:What is a computer?A computer is a device that executes programs.If we can synthesize bacteria that execute programs (which we can do), then these bacteria are computers.OK. You might add “… that can execute all programs”. In any programming language. All universal number (mathematical computer, universal Turing machine, …) can imitate any other universal numbers. Either by Rogers compilation theorem, or by the usual interpretation theorems.Bruno
0.1. PTLOS configurations
A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, ο, and capital Greek letter Σ are variables that take on concrete (particular) values — is defined:
PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that is transformed via a compiler/assembler τ into an output object ο that executes in a computing substrate Σ.
6.5. A programming language including experiential modalities (experiential modal logic, experiential modal operators or qualifiers) is needed to extend the picture we have of matter [Goff] to include consciousness.
(Modal logic historically covers modalities such as possibility/necessity, belief, time, morality, knowability [ML1], but also self-reference [SR1],[SR2],[SR3].)
Selves: An Essay in Revisionary Metaphysics
Galen Strawson
[Selves]
The Subject of Experience
Galen Strawson
[SubjExp]
On 9/30/2018 7:58 AM, Philip Thrift wrote:
On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal wrote:
On 30 Sep 2018, at 08:03, Philip Thrift <cloud...@gmail.com> wrote:
What is a computer?
A computer is a device that executes programs.
If we can synthesize bacteria that execute programs (which we can do), then these bacteria are computers.
OK. You might add “… that can execute all programs”. In any programming language. All universal number (mathematical computer, universal Turing machine, …) can imitate any other universal numbers. Either by Rogers compilation theorem, or by the usual interpretation theorems.
Bruno
I now have a next version of
Real computationalism
= my "pragmatic" definition of computing.
0.1. PTLOS configurations
A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, ο, and capital Greek letter Σ are variables that take on concrete (particular) values — is defined:
PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that is transformed via a compiler/assembler τ into an output object ο that executes in a computing substrate Σ.
(Turing-completeness is included.)
But I want to meet therein the "consciousness challenge" of Philip Golff and Gaylen Strawson in the PLTOS framework (the output object would be a conscious agent):
6.5. A programming language including experiential modalities (experiential modal logic, experiential modal operators or qualifiers) is needed to extend the picture we have of matter [Goff] to include consciousness.
(Modal logic historically covers modalities such as possibility/necessity, belief, time, morality, knowability [ML1], but also self-reference [SR1],[SR2],[SR3].)
Are you trying to define consciousness into existence by assuming modal operators for it? Or are you just trying to provide a language for talking about it? Where is the subconscious in this theory?
Brent
On 30 Sep 2018, at 13:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:On Thursday, September 27, 2018 at 8:02:36 PM UTC-5, kujawski...@gmail.com wrote:Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:- applicability of mathematic, to natural sciences- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.What are your thoughts.RegardsI think it is best to assume pragmatic stance with respect to this.
The idea the physical universe is ultimately mathematics is a huge category mixing that suffers from problems.
Physics is an empirical subject that tests the workings of a theory by performing observations and measurements. Mathematics is a subject concerned with abstract structures and objects and their logical relationships. Physical objects move through space or are an aspect of geometrodynamics in relativity and they obey conservation rules. As such mathematics is used to describe physical systems and to compute things. This is different than saying the two subjects are equivalent. Mathematics is not an empirical subject, though with computers some areas of math have started to take one a sort of synthetic empiricism. Physics is also not something that is determined entirely by logical relationships and just pure theory. We have some issues of course with quantum gravitation and whether that can ever be empirically brought to tests.
Quantum mechanics is close to being a sort of physical logic. Quantum mechanics is close to being a case of MUH, though I would not go so far as to actually make that pronouncement. For those who take the trouble to learn about the bosonic string, say by reading Polchinski's vol 1 String Theory will see this is really pure quantum mechanics according to a more complete understanding of the complex plane. This may go further with modular forms. Vol 2 of Polchinski's book works with supersymmetry. This might be ultimately a deeper description of quantum mechanics. Maybe quantum mechanics is just a modular system of automorphisms over the Fischer-Griess Monster Group that maintains a conservation of this as the fundamental vacuum state. So this all sounds highly mathematical, but I would still hesitate to say physics is mathematics.
The relationship between physics and mathematics is maybe unknowable.
I think of Garrison Keillor with his Guy Noir skits that start with, "One man on the tenth floor of the Acme Building searches for answers to life's persistent questions; Guy Noir private eye."LC
On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:
On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:[Re:] forcing theory in set theories with classes.BrunoDo you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)(I have a basic idea of a type-theoretic parallel to this.)The set-theoretic multiverse
Joel David Hamkins@JDHamkinsProfessor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,
> I think (along with Philip Goff*) that physics is not complete in its study of matter.
>It has been estimated that simulating a single neuron requires a micro-controller like an AVR, which contains 80,000 transistors.
I don't see how Bruno answered your question when he misstated and doesn't understand the MUH. Yet you thank him and not me. AG
On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:
On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:
On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:[Re:] forcing theory in set theories with classes.BrunoDo you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)(I have a basic idea of a type-theoretic parallel to this.)The set-theoretic multiverse
Joel David Hamkins@JDHamkinsProfessor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AG
On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:
On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:
On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:[Re:] forcing theory in set theories with classes.BrunoDo you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)(I have a basic idea of a type-theoretic parallel to this.)The set-theoretic multiverse
Joel David Hamkins@JDHamkinsProfessor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AGGood question.The answer is not simple technically. The point is that using only the theory Q (Robinson Arithmetic) or SK (the combinators), I can define the universal (Turing, Church) machine, and the concept of infinity will be a tool used by them in their mathematics.I do not ban anything from mathematics, nor from physics. I ban only infinity from the ontological terms. I ban only infinity in the metaphysics/theology. (Even God is not ontological, like in Proclus or Plotinus theology).Have you understand the post on Church’s thesis. You might tell me as this will help me to see how to proceed to make you grasp all this.Bruno
On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:
On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:
On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:[Re:] forcing theory in set theories with classes.BrunoDo you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)(I have a basic idea of a type-theoretic parallel to this.)The set-theoretic multiverse
Joel David Hamkins@JDHamkinsProfessor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AGGood question.The answer is not simple technically. The point is that using only the theory Q (Robinson Arithmetic) or SK (the combinators), I can define the universal (Turing, Church) machine, and the concept of infinity will be a tool used by them in their mathematics.I do not ban anything from mathematics, nor from physics. I ban only infinity from the ontological terms. I ban only infinity in the metaphysics/theology. (Even God is not ontological, like in Proclus or Plotinus theology).Have you understand the post on Church’s thesis. You might tell me as this will help me to see how to proceed to make you grasp all this.Bruno
Computable real analysis (one can teach computable calculus instead of "conventional" calculus) is essentially finitist:One can formulate the Axiom of Infinity [ https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski ], described in https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC ]. What results is an "ontology" of bigger and bigger finite sets of numbers with gaps in them.
On 2 Oct 2018, at 10:14, agrays...@gmail.com wrote:
On Tuesday, October 2, 2018 at 7:20:10 AM UTC, Bruno Marchal wrote:On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:
On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:
On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:[Re:] forcing theory in set theories with classes.BrunoDo you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)(I have a basic idea of a type-theoretic parallel to this.)The set-theoretic multiverse
Joel David Hamkins@JDHamkinsProfessor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AGGood question.The answer is not simple technically. The point is that using only the theory Q (Robinson Arithmetic) or SK (the combinators), I can define the universal (Turing, Church) machine, and the concept of infinity will be a tool used by them in their mathematics.I do not ban anything from mathematics, nor from physics. I ban only infinity from the ontological terms. I ban only infinity in the metaphysics/theology. (Even God is not ontological, like in Proclus or Plotinus theology).Have you understand the post on Church’s thesis. You might tell me as this will help me to see how to proceed to make you grasp all this.BrunoYou only ban infinity from ontological terms? I have no idea what this means.
I do know you start with the natural numbers, presumably an infinite set and existing in some Platonic realm.
So I have no idea about your aversion or denial of infinity.
As for the Church's thesis, I have set aside a copy of Chrome with several relevant topics which I see as prerequisites to that understanding including, for example, Cantor's theorem, but have yet to get into it seriously due to personal issues and computer problems in Russia and Ukraine (the latter now solved). But when I do, I'll get back to you. AG
Physicists take a theory T and replace it with a program P that then is used to match with data D.
The theory T is completely dispensable. Only P matters, because it is only P that us used to say whether a theory T matches D in the results sections of papers.
PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that is transformed via a compiler/assembler τ into an output object ο that executes in a computing substrate Σ.
Suppose Σ = UniversalNumbers
That is, the computing substrate is the actual Universal Numbers (arithmetic reality).
What would be the programs and languages (π,λ) that could be defined?
- pt
What would be the programs and languages (π,λ) that could be defined?
You need a universal machinery. Very elementary arithmetic (like Peano without induction) determines such a universal machinery (the phi_i), then, you get all the universal number u (such that phi_u(x,y) = phi_x(y), and each u defines its own universal machinerery: phi_u(0, _), phi_u(0, _), phi_u(1, _), phi_u(2, _), …
All universal “thing” mimic all universal “thing”, but they have special statistical relation, and different personal beliefs. They determine (in the arithmetical reality) the “consciousness flux”, which determine the (unique!) physical reality, which is a sort of multiverse/multi-dreams.
What would be the programs and languages (π,λ) that could be defined?
All of them, but with their different relative measure. They are mathematically determined by the G* logic (self-referential truth).
Brent
"reality contains all mathematical objects"Ironically, Tegmark doesn't believe that at all. He says infinite mathematical entities are "ruining physics".The only thing to conclude is that Mad Max published his mathematical universe hypothesis as a joke!
If our universe does not have infinitely-computing objects but there are other universes that do, that would seem strange.Why would our universe be left out? :)
BTW, on "non-relations [which] are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia)", that is what I try to address inwhere there is information processing (which is all mathematical processing) and something else: experience processing.- pt
I am generally sympathetic to Tegmark's mathematical multiverse idea, but I have two comments/criticisms to it:
1) I am not sure whether Tegmark is aware of the so-called "instantiation" relation. In philosophy, the instantiation relation is the relation between a general and a particular object, where the particular object is an instance of the general object. In other words, the general object is a property of the particular object. Example: general triangle (or triangle "in general") is the property of any particular triangle, and any particular triangle is an instance of general triangle. Another example: number 2 is a general relation that is instantiated in the particular relation between any two objects. I am not sure whether Tegmark realizes the difference between general objects and their instances, because he said something like: when we probe matter we only find numbers (and hence reality is just mathematics). But numbers cannot be found in our world; you cannot find number 2 sitting on a tree or in the atomic nucleus. You can only find instances of number 2, as relations between particular objects. Mathematical objects are usually thought to be general objects, but in that case there is more in reality than mathematical objects: there are general objects and their instances. And in our physical world there are no general objects, only their instances. If we want to say that there are mathematical objects in our physical world, we should include among mathematical objects also non-general objects, that is, objects that have no instances. (By the way, there is a hierarchy of generality: more general objects are instantiated in less general objects and those are ultimately instantiated in non-general objects. Non-general objects are often called "concrete", while general objects are also called "abstract".)
2) While I agree with Tegmark that reality contains all mathematical objects (both general and non-general), I think there is also a non-mathematical aspect of reality. That's because mathematical objects are relations or structures of relations, but relations cannot exist without objects between which they hold. While it is true that relations can hold between other relations, there should also be objects that are non-relations, which ultimately make sense of all relations. These non-relations are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia) - because (1) they have an unanalyzable/unstructured nature, and (2) they stand in relations to other objects (relations or non-relations) that we call "correlates of consciousness".
On 10/21/2018 7:11 AM, Tomas Pales wrote:
I am generally sympathetic to Tegmark's mathematical multiverse idea, but I have two comments/criticisms to it:
1) I am not sure whether Tegmark is aware of the so-called "instantiation" relation. In philosophy, the instantiation relation is the relation between a general and a particular object, where the particular object is an instance of the general object. In other words, the general object is a property of the particular object. Example: general triangle (or triangle "in general") is the property of any particular triangle, and any particular triangle is an instance of general triangle. Another example: number 2 is a general relation that is instantiated in the particular relation between any two objects. I am not sure whether Tegmark realizes the difference between general objects and their instances, because he said something like: when we probe matter we only find numbers (and hence reality is just mathematics). But numbers cannot be found in our world; you cannot find number 2 sitting on a tree or in the atomic nucleus. You can only find instances of number 2, as relations between particular objects. Mathematical objects are usually thought to be general objects, but in that case there is more in reality than mathematical objects: there are general objects and their instances. And in our physical world there are no general objects, only their instances. If we want to say that there are mathematical objects in our physical world, we should include among mathematical objects also non-general objects, that is, objects that have no instances. (By the way, there is a hierarchy of generality: more general objects are instantiated in less general objects and those are ultimately instantiated in non-general objects. Non-general objects are often called "concrete", while general objects are also called "abstract".)
This appears not to be a well-order hierarchy. The thing I am sitting on is an instance of a chair, and it's concrete. But it's also an instance of a matter, i.e. a collection of particles of the Standard Model (which may or may not be the most general category). It's also an instance of things I own.
2) While I agree with Tegmark that reality contains all mathematical objects (both general and non-general), I think there is also a non-mathematical aspect of reality. That's because mathematical objects are relations or structures of relations, but relations cannot exist without objects between which they hold. While it is true that relations can hold between other relations, there should also be objects that are non-relations, which ultimately make sense of all relations. These non-relations are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia) - because (1) they have an unanalyzable/unstructured nature, and (2) they stand in relations to other objects (relations or non-relations) that we call "correlates of consciousness".
Can you clarify with some examples?