So when you look at reality you see numbers and mathematical function symbols, not objects and their processes? F=ma refers to a state of affairs that isn't just more math. — Harry Hindu

When I look around, I do not see force, nor does "f=ma" refer to a state of affairs, it is a universal, which is a generalization. Force is a concept. And I do not think we can adequately differentiate between mathematical concepts and non-mathematical. Is "large" a mathematical concept? Are shapes mathematical?

When you look at the world what do you see?

Is it concepts all the way down?

Do objects and their behaviors symbolize mathematical concepts or do mathematical concepts symbolize objects and their behaviors?

When you look at the world what do you see?

Is it concepts all the way down? — Harry Hindu

No, I'm dualist, I apprehend both, with a fundamental incompatibility between the objects which I see, and the concepts which I understand.

Do objects and their behaviors symbolize mathematical concepts or do mathematical concepts symbolize objects and their behaviors? — Harry Hindu

It goes both ways. Some scientists try model the behaviour of natural things using concepts, but artificial things are representations of concepts. Fundamentally, symbols always represent something mental.

Sure, because the mathematical concepts refer to states of affairs that isn't just more math. What is a mathematical concept, if not words in a language? Are you saying that it's mathematical concepts all the way down? Are you an idealist? — Harry Hindu

The realist argument is that those numbers and symbols are about something which exists independent of us.

So you agree that language is necessary for math? — Harry Hindu

For us to do the math. Does that mean prime numbers only came to exist when mathematical language was created? I'm not so sure about that.

The universe isn't made of numbers and function symbols. It is composed of objects and their processes. The scribbles on paper refer to those objects and their processes. Are electrons numbers or objects or processes? Are tables and chairs composed of numbers or electrons? — Harry Hindu

I don't know what a fundamental particle is. I do know that its properties are described mathematically. Tegmark's point is that all physical properties are mathematical. I don't know whether that just means we have to understand them that way, or that there is real mathematical structure.

The challenge to the anti-realist here is to come up with a way of describing electrons that doesn't use math but is still faithful to the experimental results and predictions.

Do objects and their behaviors symbolize mathematical concepts or do mathematical concepts symbolize objects and their behaviors? — Harry Hindu

Sure, because the mathematical concepts refer to states of affairs that isn't just more math. — Harry Hindu

You’re working within the representative realist notion where ideas stand for, or represent, things.

Physicists went out to explore just those ‘objects and their processes’, confident that they existed independently of anything said about them. But that was just what was called into question by what they discovered. They discovered that the answer to the question 'is an electron a wave or particle' depended on how you asked the question, and that it was impossible to say that an electron 'really is' either of them.

It was the paradoxical nature of quantum theory that Einstein could not accept. He too was a staunch scientific realist, who believed that the world existed independently of all and any scientific theory. That's why he posed the question 'does the moon still exist when nobody is looking at it?' I think this was, in his mind, a rhetorical question, the implication being: of course it does. But the point is, he still had to ask the question.

This became the subject of the famous Bohr-Einstein debates, which went from around 1927 until Einstein's residency at Princeton.

For an in-depth discussion of the debate, it's protagonists and issues, check out the following:

Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science, David Lindley

Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality, Manjit Kumar.

But, be aware that Bohr himself says that the implications of quantum physics are 'shocking'. They're shocking precisely because they call into question our instinctive sense of the reality of the physical universe.

No, I'm dualist, I apprehend both, with a fundamental incompatibility between the objects which I see, and the concepts which I understand. — Metaphysician Undercover

I don't understand. You apprehend both what? What is incompatible?

It goes both ways. Some scientists try model the behaviour of natural things using concepts, but artificial things are representations of concepts. Fundamentally, symbols always represent something mental. — Metaphysician Undercover

It don't see how fundamentally, symbols always represent something mental when you just said that concepts can represent natural things, unless you're saying that natural things are mental, but then that would make you an idealist/pansychist, not a dualist.

Do tree rings represent the age if the tree independent of someone looking at the tree rings?

The realist argument is that those numbers and symbols are about something which exists independent of us. — Marchesk

Right. So is math the numbers and symbols, or the thing the the numbers and symbols are about, or the relationship between the numbers and symbols and what they are about?

For us to do the math. Does that mean prime numbers only came to exist when mathematical language was created? I'm not so sure about that. — Marchesk

Are you asking if the actual scribble, 19, came to exist when mathematical language was created or what it represents came to exist when mathematical language came to exist? What is the scribble, 19? What does it represent? Is not, "prime number" a word in a language?

don't know what a fundamental particle is. I do know that its properties are described mathematically. Tegmark's point is that all physical properties are mathematical. I don't know whether that just means we have to understand them that way, or that there is real mathematical structure.

The challenge to the anti-realist here is to come up with a way of describing electrons that doesn't use math but is still faithful to the experimental results and predictions. — Marchesk

To describe something is to use symbols to represent that thing. Does it really matter if we use math, English or Spanish? Claiming that all physical properties are mathematical is akin to claiming that physical properties is information, or that physical properties are measurable. Math makes use of measurements. That's what the numbers represent. Being that languge precedes math, therefore is more fundamental than math, then isn't it more accurate to just say that physical properties be represented using symbols?

You’re working within the representative realist notion where ideas stand for, or represent, things. — Wayfarer

Not just ideas, but everything. Effects stand for, or represent, their preceding causes. The scribbles in your post represent your idea yesterday that you intended to communicate to me.Your idea represents an actual state-of-affairs that exist independent of you and I talking about it. At least, that is what you are asserting. If that is not what you are asserting, then what are you talking and thinking about?

Physicists went out to explore just those ‘objects and their processes’, confident that they existed independently of anything said about them. But that was just what was called into question by what they discovered. They discovered that the answer to the question 'is an electron a wave or particle' depended on how you asked the question, and that it was impossible to say that an electron 'really is' either of them. — Wayfarer

But what about the physicists themselves? What are they composed of - waves or particles? You seem confident that these physicists and their discoveries exist independent of your observation of them. I assume that the physicists you are talking about aren't scribbles on a screen, but human beings, which are objects just like everything else that we observe. This idea that you're asserting that these physicists have contradicts the very thing that they are trying to show.

Whether or not an electron is a wave or particle is dependent upon the view you are taking and the causal sequence that lead to that particular observation. The observer is part of the very universe that the physicist is describing and part of the causal sequence that manifests as the effect in the mind.

I don't understand. You apprehend both what? What is incompatible? — Harry Hindu

You asked me:

When you look at the world what do you see?

Is it concepts all the way down? — Harry Hindu

It is not concepts all the way down, I am dualist, so I see (apprehend with my mind), that there are aspects of the sensible world which cannot be conceptualized. That is the incompatibility between the intelligible and the sensible, which gives the need for dualism.

It don't see how fundamentally, symbols always represent something mental when you just said that concepts can represent natural things, unless you're saying that natural things are mental, but then that would make you an idealist/pansychist, not a dualist. — Harry Hindu

A concept is not a symbol. So a symbol can represent a concept which can represent a natural thing. But a symbol cannot represent a natural thing directly because it is required that a mind establishes the relation required in order that something can be a symbol. Therefore, it is necessary that a mind acts as a medium, between the symbol and the thing, in order that the symbol can be a symbol. This is what it means to be a "symbol" to be related to soemthing by a mind.

Do tree rings represent the age if the tree independent of someone looking at the tree rings? — Harry Hindu

No, that's nonsensical. A symbol must be interpreted to represent anything, and what it represents is a function of the interpretation.

It is not concepts all the way down, I am dualist, so I see (apprehend with my mind), that there are aspects of the sensible world which cannot be conceptualized. That is the incompatibility between the intelligible and the sensible, which gives the need for dualism. — Metaphysician Undercover

This makes no sense. How can you apprehend something which cannot be conceptualized? Apprehend and conceptualize are synonyms. Both are akin to "grasping" something mentally.

A concept is not a symbol. So a symbol can represent a concept which can represent a natural thing. But a symbol cannot represent a natural thing directly because it is required that a mind establishes the relation required in order that something can be a symbol. Therefore, it is necessary that a mind acts as a medium, between the symbol and the thing, in order that the symbol can be a symbol. This is what it means to be a "symbol" to be related to soemthing by a mind. — Metaphysician Undercover

Are not concepts natural things?? You seem to be making a special case for human minds, as if human minds are seperate from nature, when minds are just another causal relationship, like everything else.

No, that's nonsensical. A symbol must be interpreted to represent anything, and what it represents is a function of the interpretation — Metaphysician Undercover

What if it's interpreted wrong? Is it still a symbol? It seems more accurate, and less religious, to say effects represent/symbolize their causes.

This makes no sense. How can you apprehend something which cannot be conceptualized? Apprehend and conceptualize are synonyms. Both are akin to "grasping" something mentally. — Harry Hindu

You're clearly not trying, if it makes no sense to you. Have you ever "grasped" the idea that you do not understand something? That's what I mean. When someone speaks a foreign language for instance, you might apprehend that you do not understand what the person is saying.

Are not concepts natural things?? You seem to be making a special case for human minds, as if human minds are seperate from nature, when minds are just another causal relationship, like everything else. — Harry Hindu

In the ontology which I respect, concepts are artificial. Do you not respect the difference between natural and artificial? "Artificial" is commonly defined as produced by human act or effort rather than originating naturally.

What if it's interpreted wrong? Is it still a symbol? It seems more accurate, and less religious, to say effects represent/symbolize their causes. — Harry Hindu

I don't see any principle, other than 'what was intended by the author', whereby we'd distinguish a wrong interpretation from a right interpretation of a symbol. Therefore your claim that a natural effect symbolizes its cause (without an appeal to intention), is just as likely to be incorrect as correct. So it's a worthless assertion.

You're clearly not trying, if it makes no sense to you. Have you ever "grasped" the idea that you do not understand something? That's what I mean. When someone speaks a foreign language for instance, you might apprehend that you do not understand what the person is saying. — Metaphysician Undercover

Or you're clearly not trying if it makes no sense to me. Someone speaking a different language to me clearly does not understand that I don't understand that language. Speaking and writing requires an understanding of your audiences understanding of the words you are using. It requires two or more following the same protocols to communicate. How you might communicate with a child or a person just learning English will be different than how you communicate with an adult that speaks English fluently.

So you're saying that your dualism isn't one of mind vs. body, rather one of understanding vs mis-understanding? I still don't get it.

In the ontology which I respect, concepts are artificial. Do you not respect the difference between natural and artificial? "Artificial" is commonly defined as produced by human act or effort rather than originating naturally. — Metaphysician Undercover

And humans and their actions are outcomes of natural processes. The only reason you'd want to distinguish between what humans do and what everything else does is because you believe in the antiquated idea that humans are specially created or created separate from nature.

I don't see any principle, other than 'what was intended by the author', whereby we'd distinguish a wrong interpretation from a right interpretation of a symbol. Therefore your claim that a natural effect symbolizes its cause (without an appeal to intention), is just as likely to be incorrect as correct. So it's a worthless assertion. — Metaphysician Undercover

I haven't excluded intent. As a matter of fact I told Wayfarer that their posts symbolize their idea and their intent to communicate it, which are causes for there being scribbles on the screen that we can observe. Tree rings symbolize the age of the tree because of how the tree grows throughout the year, not anything to do with the intent of some human. Humans come along and observe the tree rings and their intent is to understand what the tree rings are. The human attempts to grasp what is already there and the processes that produced the tree rings. This is how the human comes to understand what the tree rings are, which is what they mean. This is what humans do, we attempt to understand what exists by explaining the causal processes involved in producing what we observe.

Or you're clearly not trying if it makes no sense to me. Someone speaking a different language to me clearly does not understand that I don't understand that language. Speaking and writing requires an understanding of your audiences understanding of the words you are using. It requires two or more following the same protocols to communicate. How you might communicate with a child or a person just learning English will be different than how you communicate with an adult that speaks English fluently. — Harry Hindu

The question you asked me was how can I apprehend that there is something which I cannot conceptualize. The example was, when someone speaks a foreign language to me, I can apprehend that the person is speaking to me but I cannot conceptualize what the person is saying. Therefore it is an example of what I said, there are aspects of what I am hearing, which I cannot conceptualize.

So you're saying that your dualism isn't one of mind vs. body, rather one of understanding vs mis-understanding? I still don't get it. — Harry Hindu

Don't fret, it's not a big deal if you do not understand dualism. But if you want to, I suggest studying some classical philosophy to get a grasp of the concepts.

And humans and their actions are outcomes of natural processes. The only reason you'd want to distinguish between what humans do and what everything else does is because you believe in the antiquated idea that humans are specially created or created separate from nature. — Harry Hindu

No, my reason for separating intentionally constructed things (artificial) from natural things, is to help me understand reality. Clearly we haven't yet obtained a firm grasp on reality, so I don't know why you would think that this is an antiquated approach.

Tree rings symbolize the age of the tree because of how the tree grows throughout the year, not anything to do with the intent of some human. — Harry Hindu

Obviously, the intent to determine the age of the tree is implied in this description. Otherwise you simply have a growing tree with the form that it grows into, nothing symbolized by that tree without the intent to determine something about it. Therefore you have not separated this relationship from intent, as you claim.

Humans come along and observe the tree rings and their intent is to understand what the tree rings are. The human attempts to grasp what is already there and the processes that produced the tree rings. This is how the human comes to understand what the tree rings are, which is what they mean. This is what humans do, we attempt to understand what exists by explaining the causal processes involved in producing what we observe. — Harry Hindu

Right, you seem to understand here. The relationship between the tree rings and the age of the tree is something determined by human beings through their intent to understand. It is a form of measurement. Do you agree? And do you see that measurement is an act of comparison carried out by human beings, relating one thing to another, rings to a time scale in this case? This comparison, act of relating one to the other, does not occur without those human beings.

Are you asking if the actual scribble, 19, came to exist when mathematical language was created or what it represents came to exist when mathematical language came to exist? What is the scribble, 19? What does it represent? Is not, "prime number" a word in a language? — Harry Hindu

Obviously I'm not talking about the symbol. It's the number it references, not whatever we use to denote it. 19 is just a symbol. It represents a quantity which is also prime.

Right. So is math the numbers and symbols, or the thing the the numbers and symbols are about, or the relationship between the numbers and symbols and what they are about? — Harry Hindu

Math is about the mathematical objects the symbols represent. Numbers, sets, proofs, functions, graphs, whatever. Realism is asking whether any of those objects are real, not the symbols. The symbols we came up with to represent the objects.

To describe something is to use symbols to represent that thing. Does it really matter if we use math, English or Spanish? — Harry Hindu

It matters for this debate. If we can't use a non-abstract language to describe the world, then the realists about abstract arguments have a good argument for something abstract being part of the world.

I'm way late to your most excellent post. I think Bertrand Russell is exactly right about mathematics and ignorance. There are elements in Platonism which are very appealing to some, in particular me. The thing is, or one of the problems it faces, is that we have to posit almost an infinite amount of mental objects to account for what we see in the world. The general line of thinking here is not so much that for example, all "trees" fall under our concept or Platonic notion of Tree and likewise for "apples" and "horses" and many of the classical objects of thought. The issue is, what do we do about new objects? What do we say about, say, laptops or plastic or anything else that did not exist previously? Are we going to have to postulate ideas for all these objects?

Maybe I'm misunderstanding you final point, but, even though I agree that we need some kind of Platonism to make sense of manifest reality, I'm not convinced that most of these objects can fall under the scope of science, in any deep theoretically illuminating type of inquiry.

The thing is, or one of the problems it faces, is that we have to posit almost an infinite amount of mental objects to account for what we see in the world. The general line of thinking here is not so much that for example, all "trees" fall under our concept or Platonic notion of Tree and likewise for "apples" and "horses" and many of the classical objects of thought. The issue is, what do we do about new objects? What do we say about, say, laptops or plastic or anything else that did not exist previously? Are we going to have to postulate ideas for all these objects? — Manuel

Thanks for your interest, and a very good point. There's an essay I often cite, 'What's Wrong with Ockham', by Joshua Hothschild, which unfortunately is no longer published online (although downloadable here.). It's a critical review of the baleful consequences of the nominalism of Ockham (and others) on the Western intellectual tradition. Aquinas is presented as the exemplar of scholastic realism, i.e. defending the notion of forms. Ockham made a similar criticism of scholastic realism to yours, saying that it implied 'a highly populated domain of discourse'. But Hothschild points out that:

...among all the kinds of forms which can be signified by terms, according to Aquinas, there is no one uniform way in which they exist. The existence of the form “sight,” by which the eye sees, may be some positive presence in the nature of things (which biologists can describe in terms of the qualities of a healthy eye that gives it the power to see), but the existence of the form blindness in the blind eye need be nothing more than the nonexistence of sight ‒ the form of blindness is a privation of the form of sight and so not really an additional form at all. In general, distinguishing and qualifying the different ways there can “be” a form present in a thing goes a long way toward alleviating the apparent profligacy of the realist account of words signifying forms.

I think there's an irresistible tendency to conceive of the forms as shapes - that the form of a cat is a feline shape, and so on. And many school book examples of the forms are given as triangles and circles, which reinforces that tendendy. Nevertheless I think it's a mistaken apprehension of what the forms are, although understanding what they are, is obviously one of the key issues!

There's another useful essay, Meaning and the Problem of Universals, Kelly Ross. It's a revisionist interpretation of the meaning of the forms, where he remarks:

Universals represent all real possibilities. Thus, what Plato would have called the Form of the Bed, really just means that beds are possible. What would have seemed like a reductio ad absurdum of Plato's theory, that if there is the Form of the Bed, there must also be the Form of the Television also (which is thus not an artifact and an invented object at all, but something that the inventor has just "remembered"), now must mean that the universal represents the possibility of the television, which is a possibility based on various necessities of physics (conditioned necessities) and facts (perfect necessities) of history.

That's interesting and it seems to follow from the general argument. But then the concept of form seems to become extremely elastic, as in we'd have to speak of the Form, and not forms in the plural. It seems to dissolve our notion of an object as a particular entity, as in a television and a book are different objects.

But then do we do away with objects all-together? The problem for me is that I can't think of form in the abstract absent initial instantiation. And I am no nominalist, I tend to side with Scotus, Peirce and Haack, existence and real are different, I believe universals to be necessary to make the world intelligible. So if we think of form in the abstract, I'm not left with any positive notion that I can use, outside its application.

The idea of the forms has always been very elusive. I'm intending to do more reading on the topic.

If you find something interesting let me know. I don't have a clue either.

Here's an index of the Dialogues in which the forms are discussed.

The key dialogue is Plato's Parmenides.

On a very general note, this lecture, Lloyd Gerson on Platonism vs Naturalism, is well worth listening to. The standout passage for me is around 38:00 with discussion of Aristotle's doctrine of universals, but take the time to listen to the whole thing when you have an hour or so.

Will watch it for sure. Thanks for sharing.

Math is about the mathematical objects the symbols represent. Numbers, sets, proofs, functions, graphs, whatever. Realism is asking whether any of those objects are real, not the symbols. The symbols we came up with to represent the objects. — Marchesk

But numbers are just symbols. Where in reality is there a number that the symbol points to? Quantities are always OF something, not something that can exist on its own. Math is merely a comparison of measurements.

Obviously I'm not talking about the symbol. It's the number it references, not whatever we use to denote it. 19 is just a symbol. It represents a quantity which is also prime. — Marchesk

Where is the number/quantity 19 in relation to the symbol 19?

Quantities are always OF something, not something that can exist on its own. — Harry Hindu

The issue is in mathematical physics, that discoveries are made BECAUSE of the maths, not made first by observation, and then described mathematically. A case in point was Dirac's discovery of anti-matter. According to the equations he developed or discovered that described electrons, there ought to be positive counterparts to the negatively-charged electrons. At the time no such things were known but lo and behold some years later they were discovered ¹. There are many other such examples in the history of physics, which is why Eugene Wigner felt compelled to write the essay On the Unreasonable Effectiveness of Mathematics in the Natural Sciences.

Where is the number/quantity 19 in relation to the symbol 19? — Harry Hindu

A number is a symbol denoting a count. And the count is nowhere but in the mind of the counter, it is a purely intellectual act. Yet all who can count will agree that 19=19 so it is not the property of a single observer.

But numbers are just symbols. Where in reality is there a number that the symbol points to? Quantities are always OF something, not something that can exist on its own. Math is merely a comparison of measurements. — Harry Hindu

If that's true, then it should be possible to do physics without numbers.

Where is the number/quantity 19 in relation to the symbol 19? — Harry Hindu

In the world somehow? I don't know, but the symbol 19 is arbitrary. There are other symbols that also denote 19, such as its binary representation or the word nineteen. A mathematical object is not its symbol, since the symbol can be anything we want it to be.

Anyway, the mass of an electron is the same value before our evolutionary ancestors could count. We understand that value numerically.

@Wayfarer I've already touched upon the gist of this post in recent posts addressed to you in other threads but you might've missed them so I reiterate my thoughts here again for your consideration.

When we speak of real, the gold standard seems to be real in a physical sense - touchable, visible, audible, tasteable, in short detectable by some physical method i.e. real is defined in terms of the physical. My last conversation with you in this thread ended on that note. If it's all the same to you, I wish to explore this a bit more.

To my reckoning, there are two distinct worlds we humans and probably some non-human animals experience and they are: 1. the physical world and 2. the mental world. The former is the world we can bodily bump into like chairs, tables, rocks, etc. and the latter is populated by what are basically abstractions.

It's evidently clear that what all of us are aiming for is an agreement between the physical and the mental - when the two are in sync, we feel good and when they're not, it's disconcerting. My theory is that the reason why we seek a convergence between the two worlds is that it's absolutely necessary for our well-being and survival. If we have the wrong mental impression of the physical, it has unpleasant, even fatal, consequences. Just ask the person who mistook a venomous snake for a coil of rope.


Since, as can be inferred from the previous paragraph, making a mistake in matters physical can lead to injury and death, the physical becomes our top priority and, on any given day, we'd rather side with the physical than the mental. In other words, given an inconsistency concerning the physical and mental world, e.g. that unicorns and demons aren't physical, we're, in the case of the former, disappointed and, in the case of the latter, relieved. These responses reveal the privileged status the physical world enjoys over the mental world. Our conception of real as physical is reflected in this.

Yet, if we ask for a reason as to why the physical should be treated in such a special manner, a reason other than concern for our own welfare as physical bodies, we find none. Too, if well-being is a priority and if that's the reason, it seems to be so, why our idea of the real is grounded in the physical, then what do you make of this short clip,




of people who die inside which, the way I see it, is mental death. We do, on many occasions, go through mental death and such experiences are, by all standards, equivalent to physical injury and death - the pain and suffering of dying inside is at par with the pain and suffering of physical injury and death.

In conclusion, the mental world, since it too has its own version of injury and death just like the physical world, shouldn't be treated as less real than the physical world. It must be mentioned though that most cases of dying inside happen when our mental impressions are shot to pieces by physical facts i.e. when our mental world fails to line up with our physical world. Despite this it can't be denied that there's something nonphysical about mental injury and death (dying inside); after all, why does our body not respond in the way it does to physical assaults.

To wind up, the mental world has all the features of the physical world even though they differ qualitatively. If so, we're not justified in treating them differently and if that's the case, mental objects in the mental world are as real as physical objects in the physical world.

Sorry for the long post, What say you?

If that's true, then it should be possible to do physics without numbers. — Marchesk

Would it be possible to do meaningful math without the numbers referring to things that are not mathematical? When Farmer Joe counts the chickens in the pen and there is one less than there was yesterday, is he counting numbers, or counting chickens? Are chickens math or organisms?

Anyway, the mass of an electron is the same value before our evolutionary ancestors could count. We understand that value numerically. — Marchesk

What is the mass of an electron? Wouldnt you be providing an arbitrary measurement? Does an object weigh 19 pounds or 8.6 kg?

If that's true, then it should be possible to do physics without numbers. — Marchesk

https://books.google.com/books/about/Science_Without_Numbers.html?id=Exc1DQAAQBAJ — bongo fury

Thanks for the book reference. Without having read it, what does the author replace numbers with? If it's something else that's abstract (some kind of operators that can quantify over particulars), then nothing is gained, because then you have to account for that abstraction.

My question would be that if you ditched numbers, how can talk about the properties of electrons, such as their mass and charge, since the value is the same for all electrons? Another way to ask the question is what are physical properties if they're not mathematical (que Tegmark)?

Does an object weigh 19 pounds or 8.6 kg? — Harry Hindu

Those are just different units for the same value.

Would it be possible to do meamingful math without the numbers referring to things that are not mathematical? — Harry Hindu

Yes, math is done in abstraction all the time. It's not like there are prime chickens.