Why does math work in our reality?

In summary, pure and applied mathematicians and physicists have tied our understanding of reality with mathematics. They believe that if it computes it is real. This will do for a while, till we pose a question beyond our understanding. The key to the "Unreasonable Effectiveness of Mathematics in the Natural Sciences" is having a large array of mathematical structures and choosing the one that best fits the specific application. Math works in our reality because it is a result of centuries of hard work and refinement to create a model of reality using symbols and logic. The universe can be seen as an aquarium where we are the marine species that got smarter, and mathematics is the tool we use to understand and explain it.
  • #71
emyt said:
If 2+2 = 5 because one gets pregnant and thus creating another human being, the equation would be 2+3 = 5; unless you don't consider the baby inside the womb to be a human being, but then why would you at the same time say that 2 humans plus another 2 humans equal 5?

Why would you? well that is the point. The kind of system you create will depend on what you want to do with it. If you want to describe procreation as part of your system, then 1+1=3, and 2+2=5, etc...

Your math depends on correspondence. There are mathematical systems that don't include the concept of zero. There are systems that are based on one, a few, more than a few.

And this is why you literally have to create new math to describe experiene which is quite alien to what you normally experience, for example, quantum reality. Because different things are important to you.

Saying, why, and what is important, is just part of defining your system.
 
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  • #72
JoeDawg said:
Why would you? well that is the point. The kind of system you create will depend on what you want to do with it. If you want to describe procreation as part of your system, then 1+1=3, and 2+2=5, etc...

Your math depends on correspondence. There are mathematical systems that don't include the concept of zero. There are systems that are based on one, a few, more than a few.

And this is why you literally have to create new math to describe experiene which is quite alien to what you normally experience, for example, quantum reality. Because different things are important to you.

Saying, why, and what is important, is just part of defining your system.

Actually I'm pretty sure it would look like this :

M⋃F → B(male union with female leads to baby or 1 union with 1 leads to 3)?
 
  • #73
Sorry! said:
Actually I'm pretty sure it would look like this :

M⋃F → B(male union with female leads to baby or 1 union with 1 leads to 3)?

Except when it doesn't.

You could also describe it:

1+1= 2 1/2

Or you could add up the cells in each body.

Or mathematically represent the genetic information.

Its all about what you consider relevant. Abstract reasoning allows you to make whatever distinctions you like. This is why math can be very precise. The only limit is your assumptions, and what you consider relevant, that is, what the math corresponds to.
 
  • #74
If, in your system, get 2+2=5 then what you are adding are not numbers! As a consequence of the properties of numbers, 2+2 always equal 4, and hence if 2+2=5 you are not dealing with numbers. This is not a flaw in the mathematical system, but in your ability to properly model the situation with mathematics. If this is a consequence in your system, then, clearly, the total amount of human beings cannot properly be computed by adding.
 
  • #75
Jarle said:
If, in your system, get 2+2=5 then what you are adding are not numbers!
They are numbers, they just don't correspond to the same 'things'. Which is the point.
This is not a flaw in the mathematical system, but in your ability to properly model the situation with mathematics.
Its not a flaw, its a different model.
If this is a consequence in your system, then, clearly, the total amount of human beings cannot properly be computed by adding.
And how do you confirm this?
 
  • #76
They are numbers, they just don't correspond to the same 'things'. Which is the point.

No. As a consequence of the definitional properties of numbers 2+2=4 is always correct. 2+2=5 is false statement when dealing with numbers, and thus is the statement is correct, they is not numbers.

This is not a flaw in the mathematical system, but in your ability to properly model the situation with mathematics.

Its not a flaw, its a different model.
Well, a model with dissatisfactory accuracy, which was the point...

If this is a consequence in your system, then, clearly, the total amount of human beings cannot properly be computed by adding.

And how do you confirm this?

Obviously by observing that 2+2=5 is a result in the system, which is untrue for numbers.
 
  • #77
Jarle said:
Obviously by observing that 2+2=5 is a result in the system, which is untrue for numbers.

Sigh.

And where does the definition of 'numbers' come from?
 
  • #78
JoeDawg said:
Sigh.

And where does the definition of 'numbers' come from?

Try peanos axioms for example. And ZFC defines numbers based on the concept of sets. This is a rigorous construction of the natural numbers.
 
  • #79
Math works in our reality because we define our physical concepts in mathematical terms. Mathematics is an extremely effective tool for describing physical theories for exactly this reason. Because physical laws seem to follow certain laws, we are naturally encouraged to apply our mathematical concepts too it, and with great accuracy.
 
  • #80
Jarle said:
Try peanos axioms for example.

And what is an axiom?

Its an assumption.

Why would we choose one axiom over another?

Because some axioms have a broader scope, they describe a wider range of experience.

Math is about generalizations, we draw these generalizations from observing consistency in the world, the greater the scope of the axiom, the more we can use it, and the more we do use it.

1+1=3 is useful, if you are talking about sex. But its not useful when you are discussing apples. 1+1=2 is useful for apples, as well as a large range of things we as humans consider relevant.
 
  • #81
JoeDawg said:
And what is an axiom?

Its an assumption.

Why would we choose one axiom over another?

Because some axioms have a broader scope, they describe a wider range of experience.

Math is about generalizations, we draw these generalizations from observing consistency in the world, the greater the scope of the axiom, the more we can use it, and the more we do use it.

1+1=3 is useful, if you are talking about sex. But its not useful when you are discussing apples. 1+1=2 is useful for apples, as well as a large range of things we as humans consider relevant.

An axiom is not an assumption as in the context of "taking it for granted". The concept of an axiom is a definition. When we are postulating an axiom, then we are defining whatever we are talking about. We are not talking about something we think we know something about, and then saying something we might think is true, and then take it for granted. An axiom is an assumption made in order to explore the consequences, and this is a critical point.

Math is about making generalizations, but it does not base itself upon empirical evidence, although it is inspired by it. Mathematics is (luckily) based upon rigorous definitions, which make silly statements like 1+1=3 meaningless if you are talking about numbers.
 
  • #82
Jarle said:
although it is inspired by it.
Inspired? What does that even mean?
which make silly statements like 1+1=3 meaningless if you are talking about numbers.
I think I see the problem here, you've decided that certain axioms of math have some sort of Platonic existence. But what 'numbers' are, is whatever they are defined to be. Now, some definitions are more useful... empirically, and those are the ones we keep, use, modify, and refine. However, it is via observation that we decide which axioms are useful, and which are meaningless. You can't generalize from nothing, first you have to have instances, and then you develop rules based on those instances... this is how logic and math work. Oh, and your patronizing tone is actually quite amusing. I don't disagree with most of what you said, I just don't think it means what you think it does.
 
  • #83
Hehe, I think we have lost track of objectivity here. This debate has obviously come to a halt, I guess we have to agree to disagree. I won`t discuss anything but arguments.

However, I will say this: It doesn`t matter how we are choosing our axioms here, what is important is that we follow those we have chosen. In any reasonable definition of numbers, (read: axioms), 2+2=4.

I am patronizing?

Sigh.

And where does the definition of 'numbers' come from?

:smile:
 
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  • #84
Jarle said:
In any reasonable definition of numbers, (read: axioms), 2+2=4.

And reasonable means... whatever Jarle agrees with.

Like I said... patronizing.
 
  • #85
JoeDawg said:
And reasonable means... whatever Jarle agrees with.

Like I said... patronizing.

You aren`t really discussing, are you?
 
  • #86
JoeDawg said:
And reasonable means... whatever Jarle agrees with.

Actually Jarle has been taking the more reasonable line here. Yes the idea of numbers may be a generalisation from experience, but it is also a maximally general one. As far as we can know. From the prime test, which is the self-consistency of the algebraic structures we find we can spin from the number system.

The "1+1=3 when we are talking about making babies" is a childish debating point. It is a description using numbers to talk about some specific kind of biological event. It is not a self-consistent consequence of the numbers themselves.

I certainly believe that we model reality. And also that our concept of number can be challenged. Axioms are always questionable.

But it becomes just silly to not understand that axioms are generalisations that can then have matchingly crisp or definite consequences. So you can't just try to assign your own private meanings to the objects of that system of morphisms as JoeDawg wants. The actual model consists of both its axioms and its consequences.

As ever, you have to keep your eye on the dichotomies at the centre of these things. o:) That is why maths moved on to category theory in its search for its fundamental ground. Structure-preserving change, patterns or symmetries that can persist.
 
  • #87
apeiron said:
The "1+1=3 when we are talking about making babies" is a childish debating point. It is a description using numbers to talk about some specific kind of biological event. It is not a self-consistent consequence of the numbers themselves.
I was never advocating that is was a replacement for 1+1=2, nor that we should throw out mathematics.

The point was simply that we derive our math from experience. The reason it is self-consistent is because we have specifically created it to be so, and moved from using numbers that only really work in specific cases, like with babies, to number systems that cover a wider amount of instances and with great precision. 1+1=3 may be descriptive, but only in a limited sense. 1+1=2 is also limited, however, integers are not as precise as decimals. And fractions also function differently. We have found ways to convert from one to the other, but each has problems and limitations.

And as we add more to math we specifically seek ways to make it consistent with what we already have. Its only self-consistent because that's the standard by which it is judged useful, and usefulness is about correspondence to reality.
 
  • #88
If you dislike the babies argument, consider a universe where Bose-Einstein condensates were more common than in ours. In that universe, the development of mathematics may have favored axioms that result in the theorem 1+1=1 versus the more exotic 1+1=2 branch (if anthropomorphic consciousness is even possible in such a universe).
 
  • #89
JoeDawg said:
I was never advocating that is was a replacement for 1+1=2, nor that we should throw out mathematics.

The point was simply that we derive our math from experience. The reason it is self-consistent is because we have specifically created it to be so, and moved from using numbers that only really work in specific cases, like with babies, to number systems that cover a wider amount of instances and with great precision. 1+1=3 may be descriptive, but only in a limited sense. 1+1=2 is also limited, however, integers are not as precise as decimals. And fractions also function differently. We have found ways to convert from one to the other, but each has problems and limitations.

And as we add more to math we specifically seek ways to make it consistent with what we already have. Its only self-consistent because that's the standard by which it is judged useful, and usefulness is about correspondence to reality.

Though I have been trying to stay out of this until I understand the philosophical points you are making my gut still objects to the idea that reality and mathematics are somehow disjoint. It seems to me that pure sensation has no intrinsic structure. So to say that you are generalizing from something without structure seems impossible. Controlled observation can only give us clues to the structure of reality. But reality is not something we directly experience or observe. Though a fusion of thought and observation we lift the veil of sense experience.
 
  • #90
slider142 said:
If you dislike the babies argument, consider a universe where Bose-Einstein condensates were more common than in ours.

If your reality were a Bose-Einstein condensate, where would the notion of a this one, as distinct from that one, derive? It would seem you would only feel like saying 1=1 at best? Experience would not yield a 1 plus a 1.
 
  • #91
JoeDawg said:
The reason it is self-consistent is because we have specifically created it to be so, and moved from using numbers that only really work in specific cases, like with babies, to number systems that cover a wider amount of instances and with great precision.

So you are arguing against yourself here. It seems there was some innate and inevitable trend to be discovered. A path that leads from the vaguely useful to the crisply useful, from the particular to the universal.

Of course, human civilisation did not actually start with a mathematics based on babies and then progress to something better.

Psychologically, the first and most natural dichotomy was probably the distinction between the one and the many. Or figure and ground, event and context, signal and noise. The idea of symmetry and then the symmetry breaking.

And anthropologically, if we want to focus on utility, the origins of maths probably had most to do with the cycles of the days and the seasons. Cycles of death and renewal. So more geometry than algebra. Though perhaps they did notch off sticks to count off cycles of the moon.

Counting became important in ancient agricultural civilisations with hierarchical ownership. Counting boards and tally sticks to keep track of the goats and sheafs of wheat. But I don't think even the Summerians recorded 1 goat + 1 goat as making 3. Or derive from that the further truth that if I have 3 goats and give you 1, then that must leave me also with only 1.

Again, mathematical systems must follow a certain path - the dichotomy defined by category theory. You must have the fully broken symmetry of the local and the global, the one and the many, the object and the morphism. Yes this is derived from experience - and also appears to be a truth about reality. Which is why maths works.

The mistake you keep making is then to just focus on one half of the dichotomy, of the broken symmetry. The number 1 does not stand alone. It is defined only in relation to its context. Which is why 1 has a stabilised meaning and cannot float free as something that could be defined anyway we choose.

Of course there is then a further epistemological wrinkle to all this. Out there in reality, symmetries are not truly "broken". Instead the breaking apart is merely approached in the limit. However in maths, as a modelling choice, we do treat symmetries as properly broken. So we treat the number 1 as not the limit of the act of separating the one from the many, but as actually - axiomatically - a thing which is separate, isolate, discrete. So maths is in fact unreal in this crucial regard. It appears to say something about reality which cannot in fact be.
 
  • #92
wofsy said:
It seems to me that pure sensation has no intrinsic structure.
In as far as its a function of biology, I would say it does, but I'm not sure what you mean here. The human mind instintively separates experiences into events and objects.
So to say that you are generalizing from something without structure seems impossible. Controlled observation can only give us clues to the structure of reality. But reality is not something we directly experience or observe. Though a fusion of thought and observation we lift the veil of sense experience.
Well, I would say reality is what we experience, both with regards to thinking and observation. The source of reality is the mystery.
 
  • #93
apeiron said:
It seems there was some innate and inevitable trend to be discovered. A path that leads from the vaguely useful to the crisply useful, from the particular to the universal.
Utility is relative. Consistency in experience gives us the foundation. The direction and scope are up to us. Narrowing the scope when needed just gives you a better picture of what you want to see... like a fractal.
Of course, human civilisation did not actually start with a mathematics based on babies and then progress to something better.
It would have been more basic than that, but the arbitrariness of the example is also important to my point. I think many people want there to be some ultimate math, like a ToE, but math is what it is used for.
And anthropologically, if we want to focus on utility, the origins of maths probably had most to do with the cycles of the days and the seasons. Cycles of death and renewal. So more geometry than algebra. Though perhaps they did notch off sticks to count off cycles of the moon.
The ancient Egyptians invented geometry to deal with the problem created by the Nile flooding the land. It was good for the land, but it made it difficult to allot farmland. The flooding destroyed all landmarks. Geometry solved this problem. It was also useful with regards to astronomy, and the building of tombs. But no perfect circles exist.
Again, mathematical systems must follow a certain path - the dichotomy defined by category theory.
One doesn't need math to have categories or dichotomies. Math just formalizes what our minds and bodies already do.
The mistake you keep making is then to just focus on one half of the dichotomy, of the broken symmetry. The number 1 does not stand alone. It is defined only in relation to its context. Which is why 1 has a stabilised meaning and cannot float free as something that could be defined anyway we choose.
I agree there has to be context, which is why I used procreation as context. It's simplistic and not broadly useful, but it makes the point. Without context all math is just squiggles on a page.
Of course there is then a further epistemological wrinkle to all this. Out there in reality, symmetries are not truly "broken". Instead the breaking apart is merely approached in the limit. However in maths, as a modelling choice, we do treat symmetries as properly broken. So we treat the number 1 as not the limit of the act of separating the one from the many, but as actually - axiomatically - a thing which is separate, isolate, discrete. So maths is in fact unreal in this crucial regard. It appears to say something about reality which cannot in fact be.
The map is not the territory.
 
  • #94
JoeDawg said:
In as far as its a function of biology, I would say it does, but I'm not sure what you mean here. The human mind instintively separates experiences into events and objects.

Well, I would say reality is what we experience, both with regards to thinking and observation. The source of reality is the mystery.

biology is an explanation of experience - there may be other explanations - these are not what experience is - if you are saying that all ideas generalize experience then from this point of view you are just making a statement about biological theory.

Different people attach different intellectual constructs to experience of the outside world. Does this mean that they have different instincts? Does this mean that there are multiple realities?

The Impressionist era artists, particularly, Monet and Cezanne, tried to eliminate intellectual constructs from their images. They rejected the idea that such things as perspective and the theory of light actually are part of experience. They viewed these things as intellectual overlays. Their goal was to record experience at the moment of sensation just before the division into objects occurs. This is what Cezanne meant when he said that when he paints he tries to learn from nature. This is what I meant by unstructured experience. This is why their pictures often appear flat and are not supported by a geometrical skeleton as in classical art. At that time, people believed that pure experience was individual and even racial. from your point of view, they would say that there are as many realities as there are individuals. And I get the impression that this is what you are saying.

To me, whether experience is instinctively organized or not - and I am not sure how anyone knows this - that does not mean that experience is not separable into is cognitive constructs and sensory elements. To me the intellectual constructs are those things which are not experienced and the sensory data is what is given - that which is directly experienced.
 
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  • #95
Well I think it is because our world is about relations between things. Why object that has mass of 1 kg has twice smaller mass then object of 2 kg? If you say it has four times smaller mass, what would you say comparing it to object that has mass of 4 kg? Nature of course does not care about numbers, they are symbols made by us in our modest attempt to explain our existence through relations between entities.
 
  • #96
wofsy said:
biology is an explanation of experience - there may be other explanations - these are not what experience is - if you are saying that all ideas generalize experience then from this point of view you are just making a statement about biological theory.
It seems to be the case that Ideas are distinct from Experiences.
And it also seems to be the case that certain Ideas are linked to certain Experiences.
Experiences however, seem to have more detail and specificity. Ideas seem more vague.

If you want to accept the radical empiricism of Berkeley and state that matter doesn't exist and such... yes, that is another 'explanation'... but accepting the conceit of the common understanding of modern science and physicalism, yes, all ideas generalize experience.
Different people attach different intellectual constructs to experience of the outside world. Does this mean that they have different instincts? Does this mean that there are multiple realities?
Defining reality can be confusing. Often people equate reality with existence, which is fine, but it ignores the fact that experience sometimes contradicts existence. At which point you have two 'realities'. Dreams are a good example of this. Last night I flew through an alien city... does the alien city exist the way my computer does... well no, but it does, or did, exist.

So yes, in that sense everyone has their own 'reality' following them around. And those realities all seem to come from the same source... existence.

As to instincts... there are biological instincts and learned instincts, so yes different people can have different instincts. An example of the latter instinct would be something you are trained to do, and therefore do automatically without thinking.
At that time, people believed that pure experience was individual and even racial. from your point of view, they would say that there are as many realities as there are individuals. And I get the impression that this is what you are saying.
In terms of experience sure, but not ontologically. Its true we can't know for certain whether 'its all just a dream', but this is where being reasonable comes in. I see no reason to doubt that there is a common source for experience.
To me, whether experience is instinctively organized or not - and I am not sure how anyone knows this - that does not mean that experience is not separable into is cognitive constructs and sensory elements. To me the intellectual constructs are those things which are not experienced and the sensory data is what is given - that which is directly experienced.
Problem there is 'true sensory experience' is not self-reflective. Think of how animals and babies seem to live in the moment. Any analysis of experience, and certainly taking the time to paint it on canvas, would entail cognitive constructs. Even talking or thinking about an experience... puts it within a constructed framework. Meaning is cognitive. Experience just is, and then it's gone.
 
  • #97
wofsy said:
To me the intellectual constructs are those things which are not experienced and the sensory data is what is given - that which is directly experienced.

The idea that experience is given - the ineffability of qualia - is not something that would be supported by psychology and neuroscience. Experience is also constructed.

The terms I prefer to use here are "ideas" and "impressions" as it helps preserve the constuctedness of both aspects of awareness. One is not being favoured over the other in term of veridity (or lack of it).

Now what is the nature of the actual divide (I mean dichotomy) that you are sensing here? The instinctive separation you want to make?

It is between the general and the particular, the model and the measurements. Or as in Grossberg's neural nets, the long term and the short term memories.

So in all these ways of saying the same thing, we have something that acts as the longer lived context - the idea that constrains. And then we also have the moment to moment impressions, the fleeting train of events, that constructs some particular state of experience.

And the two scales of mental activity are in interaction. They are not separate processes but instead separate levels of process.

So ideas are the established habits of memory, anticipation and thought which serve to give shape to impressions. They make sense and organise each moment. Awareness is created top-down.

But equally, impressions over time build up the ideas. The brain learns by generalising from what it thinks happened (the experiences it constructed) and so builds broader, sturdier, habits of interpretation/perception.

So all this activity is subjective. There is no direct objective access to reality. But, being a systematic approach, the subjective collection of ideas~impressions does come to model reality very well for our purposes.

And then maths/science/philosophy are activities that try to repeat this basic cognitive formula on a still broader social scale. Societies have purposes and evolved models of reality that serves them.
 
  • #98
apeiron said:
The idea that experience is given - the ineffability of qualia - is not something that would be supported by psychology and neuroscience. Experience is also constructed.

While this is arguably true, its also more complex than that...
Experiences and Ideas exist on the level of consciousness. They are, in a sense, immediate.
Neuroscience and psychology work on the level of explanation.
So you can indeed describe experience as unconstructed. Its only after experience has been assessed and compared that we get the sciences, and then we work backwards for an explanation. It is then that we can view experience as constructed.

Which is not to say that neuroscience and psychology don't offer good explanations, but they are heavily dependent on that 'ineffable qualia', which is our primary mode of being.

Ideas are more obviously constructed, since they involve internal (mental) processes, not external sources.
 
  • #99
JoeDawg said:
So you can indeed describe experience as unconstructed. Its only after experience has been assessed and compared that we get the sciences, and then we work backwards for an explanation. It is then that we can view experience as constructed.

I understand what you mean but this is what I call the introspectionist fallacy.

In fact paying attention to your experiences is a highly artificial and learned skill. Animals and babies can't do it. And it takes a lot of practice and scaffolding for even modern Western adults.

You can argue that there are degrees of construction. So the naked sensation of redness is perhaps less obviously mediated than your perception that a ship on the horizon is a large object a long way away.

Yet still the very act of stopping and contemplating "redness" is a highly constructed - and constructing - action. Your brain has to suppress attention to much else to manage to make it seem like the redness of something red is filling your awareness.

Or to use a better example, think of the tricks that an impressionist painter goes through to see the distant hills as purple not brown or green. Cut out a little square in white card and hold it up to physically block out the contextual information that is fooling your appreciation of the pure actual colour.

Yes, some things may be less mediated, less apparently constructed. But in the end, all experience is the result of some act of mediation, some constructive effort and not about naked witnessing.
 
  • #100
apeiron said:
In fact paying attention to your experiences is a highly artificial and learned skill.
Well, sure. But that is not really what I'm referring to.
Animals and babies can't do it.
And this would be the example of 'experience'. Quite a lot of our adult life is constructed, but that's because we build ideas around 'sensations'. This is why differentiating between ideas and experience is important. Pleasure and pain, for instance, are immediate. They don't even need to be localized in time or space, within our minds, although quite often they are... and in that case part of the experience is constructed.
Yet still the very act of stopping and contemplating "redness" is a highly constructed
Contemplating yes, but experiencing no. Obviously if you are calling it red, you're attaching an idea to it. But there are lots of times, when we see something for the first time, we don't place it... within a framework, at least not immediately.

Impressionist painters are trying to simulate raw experience... on canvas. Not something I think you can really do successfully, but they try.
Yes, some things may be less mediated, less apparently constructed. But in the end, all experience is the result of some act of mediation, some constructive effort and not about naked witnessing.
Like I said, the fact biology 'constructs' a sensation in the mind is, I think, quite a different thing. Biology is an explanation. We as adults may reflect on sensations, almost immediately, and certainly our brains seem to want to categorize everything. But before we learn to do this, and on occasion when something intense or unexpected happens, we do have a kind of raw experience. And that is the sort of thing I am talking about. Adrenaline junkies crave this, and so do people who meditate.

A person's first orgasm, for instance, can completely shatter their reality. It's only after, when they organize thoughts around it, that it becomes 'constructed'.
 
  • #101
You are arguing here from personal prejudice rather than psychological or neurological fact. Which makes for an unproductive conversation as usual.

To ground your ideas, why not simply tell me at which point as a photon strikes a retinal receptor you feel that there is this supposed transition from raw input to mediated experience - constructed in the sense that the processing has begun in earnest.

Or if you prefer to focus on pain, then again, where after the finger is pricked with a pin does the percept swim into view. We know the neurology of the pain pathway. Where is the location where the magic of qualiahood achieved and there is an experience ready to be contemplated?

Yes, agreed there are degrees of mediation. And Sperling's iconic memory experiments would be a good line of evidence for you to be arguing here I would have thought.

But I fear you will never get the essential point that I am arguing. Which is that all experience is processing - mental construction - and ideas and impressions are then two extremes of this one process. They are not two different kinds of thing.

But if you insist on being dualist, taking the position that qualia are primal - naked conscious facts - then you will have to accept all the mystical and unscientific baggage with comes with such a philosophy.
 
  • #102
If experience is constructed then it must have been constructed from something. that something was either not experienced or it was non-constructed experience. If it is not constructed, then it is given.

Experience has two fundamentally different ingredients - that which is unchanging, such as the idea of space and that which is changing such as the perception of a color. One is certain the other unpredictable.

An attempt to isolate these two through e.g. through introspection does not invalidate the difference just because the attempt is contrived.
 
  • #103
Apeiron I don't know why you are getting insulting with me again. I feel like you are telling me that I am so stupid and biased that I don't have the right to be part of this discussion.

If that it true why not just ignore my posts?

I choose to be part of this discussion whether you like it or not.

I don't think you don't understand the basic fact of philosophy. That is that empirical theories of experience do not explain it they merely describe data that in the past has been detected in some experiment. You have no proof that these same outcomes will occur in the next experiment. These are merely constructs. The existential nature of experience - the true subject of philosophy (as opposed to science) - does not deal with empirical constructs. Your references to experiments and photons and whatever illustrate this that you do not agree with this. You think it is all mystical. The fact that you refute me by referring to neurological and psychological "fact" shows you believe this. A fact for you is some testable result of an experiment.

I think that you confuse philosophy with the theory of knowledge. Empiricists and positivists and others argue that statements about experience can only refer to testable results and can mean nothing more than the outcomes that they predict. This is a theory of meaning not a theory of the existential nature of experience.

If i say 'This is a piece of chalk', you say well what does that mean? What testable results does that imply? If I say experience is given, you say what experiments can I do that give that statement meaning?

I personally think that the idea that all meaning is really a collection of testable empirical outcomes is a definition that ignores the fundamental existential nature of experience. While it is valid for Science it begs the questions of Philosophy.
 
  • #104
to the OP (I haven't read this thread, I've participated in a couple like it):

Because we designed it to.
 
  • #105
wofsy said:
Apeiron I don't know why you are getting insulting with me again. I feel like you are telling me that I am so stupid and biased that I don't have the right to be part of this discussion.

Ha, no I was insulting JoeDawg this time round o:). Sorry if that wasn't clear in the quoting.

wofsy said:
The existential nature of experience - the true subject of philosophy (as opposed to science) - does not deal with empirical constructs.

I would be surprised if everyone agreed this was what philosophy was about. But maybe that is because my interests are clearly meta-physics and epistemology. Get these right and the rest follows I believe - even ethics and aesthetics.

As to my use of scientific facts, I follow Rosen's modelling relations approach. It is all about the interaction between ideas and impressions, models and measurements. So the "facts" inform the opinion, just as much as the opinon informs (or prejudices) the facts. You tend to see what you believe, and that is a meta-fact that our attempts to understand the world must deal with systematically.

This makes me impatient both with those who haven't worked sufficiently on forming their opinions (doing the philosophy) and noting the facts (doing the science).

wofsy said:
I personally think that the idea that all meaning is really a collection of testable empirical outcomes is a definition that ignores the fundamental existential nature of experience. While it is valid for Science it begs the questions of Philosophy.

I was a psychology/biology student in the 1970s so felt all the frustrations of science's failure to tackle the issue of mind. And science is still generally failing to do its job here. It is the proper scientific (and mathematical) generalisation of the idea of mind which is my major life project. And I just don't see any real division between the philosophical and scientific aspects of this quest.
 
<h2>1. Why is math considered to be the language of the universe?</h2><p>Math is considered to be the language of the universe because it is a universal and consistent system that can be used to describe and explain natural phenomena. It is based on logical and precise rules that can be applied to any situation, making it a powerful tool for understanding the world around us.</p><h2>2. How is it possible that mathematical concepts and theories can accurately describe the physical world?</h2><p>The accuracy of mathematical concepts and theories in describing the physical world is due to the fact that mathematics is based on abstract concepts and principles that can be applied to any situation. This allows for the development of theories and equations that can accurately model and predict the behavior of natural phenomena.</p><h2>3. Is math a human invention or does it exist independently in the universe?</h2><p>This is a philosophical question that has been debated by scientists and mathematicians for centuries. Some argue that math is a human invention, created to help us understand and manipulate the world around us. Others believe that math exists independently in the universe and humans have simply discovered and described it.</p><h2>4. How does the human brain process and understand mathematical concepts?</h2><p>The human brain is capable of processing and understanding mathematical concepts due to its ability to recognize patterns and make logical connections. This is why math education often involves visual aids and real-life examples, as our brains are better able to understand and remember information when it is presented in a familiar and relatable way.</p><h2>5. Can math ever be proven wrong or is it infallible?</h2><p>Math is based on axioms and logical rules that are considered to be true and cannot be proven wrong. However, mathematical models and theories can be updated and refined as new evidence and discoveries are made. This is why the scientific method involves continually testing and revising theories, including those based on mathematical principles.</p>

1. Why is math considered to be the language of the universe?

Math is considered to be the language of the universe because it is a universal and consistent system that can be used to describe and explain natural phenomena. It is based on logical and precise rules that can be applied to any situation, making it a powerful tool for understanding the world around us.

2. How is it possible that mathematical concepts and theories can accurately describe the physical world?

The accuracy of mathematical concepts and theories in describing the physical world is due to the fact that mathematics is based on abstract concepts and principles that can be applied to any situation. This allows for the development of theories and equations that can accurately model and predict the behavior of natural phenomena.

3. Is math a human invention or does it exist independently in the universe?

This is a philosophical question that has been debated by scientists and mathematicians for centuries. Some argue that math is a human invention, created to help us understand and manipulate the world around us. Others believe that math exists independently in the universe and humans have simply discovered and described it.

4. How does the human brain process and understand mathematical concepts?

The human brain is capable of processing and understanding mathematical concepts due to its ability to recognize patterns and make logical connections. This is why math education often involves visual aids and real-life examples, as our brains are better able to understand and remember information when it is presented in a familiar and relatable way.

5. Can math ever be proven wrong or is it infallible?

Math is based on axioms and logical rules that are considered to be true and cannot be proven wrong. However, mathematical models and theories can be updated and refined as new evidence and discoveries are made. This is why the scientific method involves continually testing and revising theories, including those based on mathematical principles.

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