What LEM is not

[Magnus Anderson]

Equivocation.

You have yet to learn what that word means.

The entity represented by "Skepdick" is me. Where I live (my home address) is not (currently) where I am.
Which physical entity is being represented by "is". You are claiming that the concept of "is" has a physical location - like I do.

Where is it?

You don't have to know EXACTLY WHERE something exists and in WHAT EXACT SHAPE it exists in order to know that it does exist.

I don't know where Skepdick exists, and I don't even know anything about his physical makeup, but I can safely conclude that he does exist in one way or another ( even if he's merely a computer software, an AI of some sort, or a team of people pretending to be a single person for the sake of spreading propaganda on the Internet. )

Once again, you're making a demand that does not really have to be fulfilled.

Also, in your own nomenclature you are using "is" as a predicate...

2+2 is 5.
2+2 is 4.

So predicates are physical entities then?

The symbol "is" is a physical entity.

The concept attached to it, i.e. the set of rules governing what that symbol can represent, is also a physical entity.

[Skepdick]

Equivocation.

You have yet to learn what that word means.

You are yet to stop lying about that.

You don't have to know EXACTLY WHERE something exists and in WHAT EXACT SHAPE it exists in order to know that it does exist.

Contradiction. If something exists - it exists SOMEWHERE. e.g everything that exists has an idnetifiable location.

If you don't know WHERE it exists then HOW do you know it exists?

I don't know where Skepdick exists, and I don't even know anything about his physical makeup, but I can safely conclude that he does exist in one way or another ( even if he's merely a computer software, an AI of some sort, or a team of people pretending to be a single person for the sake of spreading propaganda on the Internet. )

And I exist. Here, on Earth and I have exact GPS coordinates. What are the GPS coordinates of a predicate?

Do predicates even have GPS coordinates? No - they don't.

So why are you conflating things WITH location and things WITHOUT location?

Once again, you're making a demand that does not really have to be fulfilled.

It needs to be fulfilled. For ALL physical entities.

If it has no identifiable location - then how do you know it's physical?

The symbol "is" is a physical entity.

Sure. And it exists on my screen (which has GPS coordinates). it exists on your screen (which has precise GPS coordinates).
It exists in the memory of the Philosophy Now server - which has GPS coordinates.

The concept attached to it, i.e. the set of rules governing what that symbol can represent, is also a physical entity.

What are the GPS coordinates of this concept; and the rules governing what the symbol represents?

You don't know? Fine.

Is the location knowable or not?

[Magnus Anderson]

You don't have to know EXACTLY WHERE something exists and in WHAT EXACT SHAPE it exists in order to know that it does exist.

Contradiction. If something exists - it exists SOMEWHERE. e.g everything that exists has an idnetifiable location.

Yes, if something exists, it exists somewhere. But you don't have to know where it exists in order to know that it exists.

I don't know WHERE and HOW you exist at this point in time but nonetheless I know that you DO exist. How is that possible?

If you don't know WHERE it exists then HOW do you know it exists?

How do you know that Magnus Anderson exists? You don't know where I exist and you don't know in what shape I exist. Yet, you know I exist, don't you? Or are you going to claim that you don't?

And I exist. Here, on Earth and I have exact GPS coordinates.

Tell us your GPS coordinates. Why should I talk to someone who does not exist? Prove to us that you do exist.

And even if you tell us your GPS coordinates, how can I know that what's located there is truly you?

I am seriously considering ending this pointless conversation with you.

Why should I talk to someone who does not exist?

Do predicates even have GPS coordinates? No - they don't.

Well, if they are concepts inside your brain, they certainly do have GPS coordintaes, don't they?

It needs to be fulfilled.

Says Skepdick. But Skepdick has proven too many times that he's extremely ignorant.

Sure. And it exists on my screen (which has GPS coordinates). it exists on your screen (which has precise GPS coordinates).
It exists in the memory of the Philosophy Now server - which has GPS coordinates.

Do you have thoughts? Do they exist? If they exist, can you tell us their GPS coordinates? If you can't, I will have to conclude that you have no thoughts. And you should conclude that as well, I am afraid, for you don't know the exact GPS coordinates of your thoughts.

You are a thoughtless individual. Why should I talk to you? You don't even disagree with me!

[godelian]

mathematical concepts are physical entities.

Before the 19th century, mathematicians thought like that:

https://en.wikipedia.org/wiki/Philosophy_of_mathematics

Relationship with physical reality

Before the 19th century, the basic mathematical concepts, such as points, lines, natural numbers, real numbers (used for measurements), etc. were abstractions from the physical world, and it was commonly considered that it was sufficient for defining them.

After strong debates, axiomatic approach became eventually a de facto norm in mathematics. This mean that mathematical theories must be based on axioms (basic assumptions that are considered as true) and a fixed set of inference rules; the theory consists of the results (theorems) that can be deduced (proved) from the axiom by using inference rules, and inference rules only. The entities (mathematical objects) involved in the axioms are considered as defined by the axioms, and nothing else is supposed on their nature.

Mathematical objects are not physical entities. That view has been abandoned almost two centuries ago.

[Skepdick]

Mathematical objects are not physical entities. That view has been abandoned almost two centuries ago.

Yeah, but computational objects are physical entities. Everything else is encoding.

Any manipulation of symbolic encodings (syntax) is computation.

You can represent anything you want with the symbol X, but it's utterly meaningless to discuss anything about X without also considering what operations we want to perform on it.

Operational semantics is meaningful.
Denotational semantics is Mathematical delusion.

https://en.wikipedia.org/wiki/Operational_semantics

[Magnus Anderson]

Mathematical objects are not physical entities. That view has been abandoned almost two centuries ago.

It does not matter what anyone thinks, such as what happens to be popular among a particular group of people at a particular point in time, what matters is what is actually true.

Humans do not always develop in the positive direction, i.e. towards the better. They do not always move forward. They sometimes move backward. Moreover, they often do both at the same time, i.e. they make a number of steps forward and a number of steps backward. It's not as simple as, "Oh, look what we can do with this! Obviously, this is better in every way than what we had before!"

"2 + 2 = 4" literally means "If you take a basket that contains two apples and add to it two apples, you will end up having four apples".

You can empirically verify that claim. You can take a basket with two apples, add to it two more apples and then count how many apples there are in it. In fact, you can do the whole experiment in your head.

But you don't have to do any of that because there is an easier way ( for people who know how to think, that is. )

This easier way consists in analyzing the relationships between the concepts involved.

Whoever said "2 + 2 = 4" meant something by "2", "+", "=" and "4". In other words, he attached certain concepts to these symbols. He also worked with a set of rules that determine how combining different symbols determines the meaning of the resulting compound symbol. All of these are stored somewhere in his mind. Therefore, they are physical entities.

But of course, you don't have to open his brain and look for these physical entities yourself. If you know that he used a standard language, you can simply look into the dictionary of that language. If you know that he didn't use a standard language, but a language of his own, perhaps a variation of some standard language, you can look into his own dictionary ( assuming he wrote one. ) And there are many other ways to indirectly perceive the meaning of statements. You don't have to directly perceive concepts in order to perceive them.

[Skepdick]

"2 + 2 = 4" literally means "If you take a basket that contains two apples and add to it two apples, you will end up having four apples".

What does 2-5=-3 then in terms of aples?

[Magnus Anderson]

"2 + 2 = 4" literally means "If you take a basket that contains two apples and add to it two apples, you will end up having four apples".

What does 2-5=-3 then in terms of aples?

What are "aples"? And why don't you tell us your GPS coordinates? Why should I talk to someone who does not exist?

"2 - 5 = -3" means that, for every sufficiently large positive number "x", if you have a basket with "x + 2" apples, and you remove 5 apples from it, you will end up with "x - 3" apples.

Put another way, it means that, if you have a basket with 2 apples, and you have to give someone 5 apples, you will have to give all of your apples and borrow 3 more, ending with exactly 0 apples in your basket and a debt of 3 apples.

[Skepdick]

blah blah blah

That was an elaborate conflation between the existence of an abstract property (such as location); the value of an abstract property (such as explicit GPS coordinates of a person which signify a location on Earth); and the existence of an physical enties which posess the abstract property of "location". Such as planets, which have a location but no GPS coordinates.

It was an even more elaborate equivocation of "exists" - mixing up the existence of abstractions (such as propositions) with the existence of concrete entities (such as humans).

Just as I thought you weren't that dumb you've convinced to give you way less credit.

If you claim that something physicaly exists then somebody, somewhere, somewhen must have physically located that something. Where? What is the location of physical numbers?

If you can't physically locate something (that exists) then how do you know it's physical?

[Skepdick]

"2 - 5 = -3" means that, for every sufficiently large positive number "x", if you have a basket with "x + 2" apples, and you remove 5 apples from it, you will end up with "x - 3" apples.

Sorry, where do you see an "x" in "2-5=3", and how many apples is "x-3" apples?

[Magnus Anderson]

That was an elaborate conflation between the existence of an abstract property (such as location); the value of an abstract property (such as explicit GPS coordinates of a person which signify a location on Earth); and the existence of an physical enties which posess the abstract property of "location". Such as planets, which have a location but no GPS coordinates.

You didn't answer a single question that you were asked.

Tell me, why should I bother answering yours -- and on my thread?

It was an even more elaborate equivocation of "exists" - mixing up the existence of abstractions (such as propositions) with the existence of concrete entities (such as humans).

What does the word "equivocation" means? Explain it to us in your own words, i.e. don't link to Wikipedia and other sources.

If you claim that something physicaly exists then somebody, somewhere, somewhen must have physically located that something. Where? What is the location of physical numbers?

What are your GPS coordinates?

If you can't physically locate something (that exists) then how do you know it's physical?

So you don't physically exist?

[Magnus Anderson]

Sorry, where do you see an "x" in "2-5=3"

Do you have to see it? You are not capable of reading between the lines? Everything must be spelled out for you? Is that why you endorse the simple-minded philosophy of formalism?

And "2 - 5" isn't "3". It's "-3". Put some effort in your posts.

how many apples is "x-3" apples?

So you don't understand how universal quantification works?

"For every sufficiently large positive number x, if you have a basket with x + 2 apples, and you remove 5 more apples from it, you will end up having x - 3 apples in it."

So in the case that "x" is 10, you will have "10 + 2" apples in your basket, which is 12 apples, and if you remove 5 from it, you will end up with "10 - 3" apples, which is 7 apples. Obviously true for that particular case.

In the strict sense of the word, "-3" isn't really a number. Only positive whole numbers and infinite whole numbers ( i.e. whole numbers larger than every integer ) are numbers. "-3" is closer to being a partial number, a pseudo-number or a proto-number. It's almost a number but not quite. It does not have all of the necessary components. You have to add a sufficiently large number to it in order to make it a proper number. In the same exact way you have to multiply a fraction ( such as 3/5 ) by an adequate positive whole number ( such as 5 ) in order to turn it into a proper number ( such as 3. )

[godelian]

"2 + 2 = 4" literally means "If you take a basket that contains two apples and add to it two apples, you will end up having four apples".

Physicalism has turned out to be unsustainable:

https://en.m.wikipedia.org/wiki/Philoso ... athematics

During the 19th century, there were an active research for giving more precise definitions to the basic concepts resulting of abstraction from the real world; for example Peano arithmetic for natural numbers, the formal definitions of limit, series (infinite sums that may have a finite value), and continuity by Cauchy and Weierstrass, the definition of real numbers by Cauchy and Dedekind. These formal definitions allowed to prove counterintuitive results, which are a part of the origin of the foundational crisis of mathematics. For example, Weierstrass function is a function that is everywhere continuous and nowhere differentiable. Since the existence of such a monster seemed impossible, people had two choices: either they accept such unrealistic facts, which implies that mathematics does not need to reflect the physical reality; or they change the logical rules for excluding such monsters.

In the meanwhile we know that only a very small part of the abstract, Platonic world of mathematics can occasionally be mapped directly onto physical observables.

Still, this larger abstract, Platonic world is very interconnected.

The explanation for Platonic phenomena that do have a mapping to physical reality is deeply interconnected with the explanation for the ones that don't.

Physicalism fails because it cannot deal with the abstract, Platonic phenomena that do not have a counterpart in the physical universe but which are essential to explain the ones that do.

For example, the 18th century is replete with philosophers and mathematicians who rejected calculus because infinitesimals were not physically "real" as they do not map to anything in physical reality:

https://en.m.wikipedia.org/wiki/Calculus

In early calculus, the use of infinitesimal quantities was thought unrigorous and was fiercely criticized by several authors, most notably Michel Rolle and Bishop Berkeley. Berkeley famously described infinitesimals as the ghosts of departed quantities in his book The Analyst in 1734. Working out a rigorous foundation for calculus occupied mathematicians for much of the century following Newton and Leibniz, and is still to some extent an active area of research today.[34]

Several mathematicians, including Maclaurin, tried to prove the soundness of using infinitesimals, but it would not be until 150 years later when, due to the work of Cauchy and Weierstrass, a way was finally found to avoid mere "notions" of infinitely small quantities.

Infinitesimals do not have a counterpart in physical reality but they are perfectly real in the abstract, Platonic universe of mathematics.

Calculus is just one field in mathematics that suffered from unproductive objections inspired by misguided physicalism.

For at least two centuries, it has been the consensus in mathematics not to listen or to take into account objections based on physicalism. Mathematics is simply not about the physical universe. Physicalism is considered an impediment to progress, of which the arguments have always turned out to be utterly wrong and spectacularly unproductive.

[Gary Childress]

ChatGPT might be a better reference than Wikipedia, not sure. But it seems to take a more objective approach and is a little less polemic overall.

You said:
Is physicalism in mathematics unproductive or false?

ChatGPT said:
ChatGPT
Physicalism in mathematics is the idea that mathematical entities, concepts, and truths are grounded in or reducible to physical reality. This perspective stands in contrast to views like mathematical Platonism, which posits that mathematical objects exist in an abstract realm, independent of the physical world.

Whether physicalism in mathematics is "unproductive" or "false" can be explored from a few angles:

1. Philosophical Critique: Is Physicalism in Mathematics "False"?
Abstract Nature of Mathematical Entities: Many argue that mathematics seems to deal with idealized entities—like numbers, points, or functions—that do not have direct counterparts in physical reality. For example, the concept of an infinite series or irrational numbers can’t be fully instantiated in the physical world but are crucial to mathematical reasoning.
Indispensability Argument: Some philosophers argue that mathematical objects, while not physically observable, are indispensable to our best scientific theories. They claim that the success of these theories implies that mathematical objects “exist” in some sense, even if they aren’t physical.
Argument from Objectivity and Necessity: Mathematical truths often seem objective and necessary (e.g., 2+2=4), which raises questions about how physicalism could account for these properties. Physical processes, governed by contingency and variability, don’t seem capable of grounding such unchanging truths.

2. Productivity: Does Physicalism Constrain Mathematical Practice?
Limitations on Pure Mathematics: Physicalism might struggle to account for large areas of pure mathematics, especially those that appear "detached" from any physical interpretation. Fields like higher-dimensional geometry, complex analysis, or category theory are often developed without any reference to physical reality and are sometimes only later found to have applications.
Creativity and Innovation: Mathematics has historically been driven by abstract reasoning that transcends physical constraints. A physicalist view might impose restrictions on mathematical creativity by binding it to what can be physically instantiated or empirically verified. This could limit the exploration of concepts that, while abstract, later prove critical for advancements in physics or technology.

3. Potential Justifications for Physicalism
Empirical and Applied Successes: Physicalists might argue that mathematics is justified by its successful application in the physical sciences, suggesting that mathematical concepts are simply effective models of reality rather than independently existing truths. They may posit that physicalism keeps mathematics "grounded" in observable phenomena.
Mathematics as a Cognitive Construct: Another physicalist stance might propose that mathematical ideas are constructs of human cognition, shaped by our interactions with the physical world. This viewpoint could explain why mathematics seems so effective in describing natural phenomena without requiring that mathematical entities exist outside of physical reality.

In Summary
Physicalism in mathematics can be seen as both potentially restrictive and philosophically contentious. For many, it seems "unproductive" for areas of mathematics that don’t have immediate physical interpretations, though it might offer a pragmatic framework for applied mathematics. Whether it’s "false" depends largely on one's metaphysical stance on the nature of mathematical existence, objectivity, and necessity. Many mathematicians and philosophers lean toward viewing mathematical truths as either abstract or conceptual rather than strictly physical, though physicalist interpretations remain a topic of active debate.

[Skepdick]

Do you have to see it? You are not capable of reading between the lines? Everything must be spelled out for you? Is that why you endorse the simple-minded philosophy of formalism?

No, I don't have to see it. But it has to be there..

Since I am the one who wrote the expression "2-5=-3" in the first place - I know exactly what was; and especially what wasn't between the lines.

Since you found an "x" I didn't put there you can rest assured you were halucinating.

So you don't understand how universal quantification works?

I understand it just fine. The problem is this basket of yours with "x-2" apples. Where x=1.