What is mathematics?

[Spectrum]

Spectrum wrote:
What Kant asserted is there is no real thing-in-itself to be perceived by perceivers. There is no absolute reality which is absolutely independent of the perceiver awaiting to be perceived.
What Kant proposed was two aspects of reality, i.e. the 'inner sense reality' and 'outer sense reality' where both are not absolutely independent of the perceiver [one who cognize].

What is mind-blowing is according to Kant the inner and outer reality emerges spontaneously continuously and thus has a semblance of "permanent" nature. In reality, nothing is permanent as 'change is the only constant.'

Here is a demonstration re the Einstein Mask;

I think Kant is a predecessor of phenomenology.

In a way, but note,

Phenomenology came into its own with Husserl, much as epistemology came into its own with Descartes, and ontology or metaphysics came into its own with Aristotle on the heels of Plato. Yet phenomenology has been practiced, with or without the name, for many centuries. When Hindu and Buddhist philosophers reflected on states of consciousness achieved in a variety of meditative states, they were practicing phenomenology. When Descartes, Hume, and Kant characterized states of perception, thought, and imagination, they were practicing phenomenology. When Brentano classified varieties of mental phenomena (defined by the directedness of consciousness), he was practicing phenomenology. When William James appraised kinds of mental activity in the stream of consciousness (including their embodiment and their dependence on habit), he too was practicing phenomenology. And when recent analytic philosophers of mind have addressed issues of consciousness and intentionality, they have often been practicing phenomenology. Still, the discipline of phenomenology, its roots tracing back through the centuries, came to full flower in Husserl.

I find your thoughts to be true – to my mind – but then again that is only my - 'spontaneous emergent reality'. Additionally I agree – “That's philosophy at its best”. Please stop saying – never mind.

I stated 'never mind' to absolve myself from having to justify and explain in details my view on a rigorous basis.
If you agree to some degree on what I have presented it would be better if you can spent some time on Kant to get the full picture. Note I spent 3+ years full time researching Kant.

[Burning ghost]

Woodart -

Decide on what question you are asking and it is easier to look toward an answer. What is "mathematics" can be taken as an ontological question or an epistemic question.

This discussion seems to have moved beyond mathematics and is now asking what is epistemic and what is ontological.

Husserl regarded "phenomenology" to have had two major players in philosophical history. The first being Plato and the second being Descartes.

I was sort of following this thread but I am unsure where it is now. Mathematics is very much part of human nature, because we are able to discovered it when all knowledge is lost and all books are burned. We will possess the ability to formulate Pi and work out the area of a circle. We will still be able to apply the idea of infinity to equations and discover rules that express the reality of electronic circuits.

Kant made an obvious statement. We know math because we can apply it to perception and come to understand nature. If I know something I know it by way of experience or abstraction. I get the gist of what you are looking at and it ends in the dichotomy of mind and body. This is where Husserl decided to simply focus on experience without regard for ideas of "reality". Meaning an illusion is still a real experience.

I think a lot of the difficulties arise for us in this area due to language and the obvious limitations of the concepts we can play with.

It probably does make sense looking at Kant first of all because in my experience on forums I have found so many people unable to grasp what Kant meant by "noumenon" and "phenomenon". Only once you've grasped the mistaken belief in "the thing in itself" can you move to Husserl and phenomenology proper.

That said the problem is Kant is not someone you can simply browse overnight and come to understand. It may be really worth your while focusing on how he frames the concept of "noumenon", he even made attempts to rewrite his views after receiving critique.

So where are we in this thread? Any place to go? Has the question in the OP been addressed or not? What are the seemingly resolvable questions you think you have to pose for us to mull over?

[Woodart]

So, what is mathematics? I have put out a few ideas which I have not got as much feedback as I would like. Let me summarize and ask for specific comments and/or refutation.

1- Meaning or cognition precedes language.
2- Language can be spoken, sign and/or written and can be art.
3- Math is a language type, but comes after spoken language.
4- Philosophy developed concurrent with spoken language.
5- Philosophy asks questions and therefore is the first science.
6- Math can ask questions too and therefore a science.
7- Time is a type of math – woman understood time first because of menstruation.
8- Women were the first astronomers because of the relationship of menstruation and cycles of the moon.
9- Math is involved in every science.
10- Math via programing is actively involved in the search for artificial intelligence.
11- philosophy defines each science by asking questions – stating hypothesis – defining methodologies
13- Cognition is a sixth sense.
14- We have more than six senses.
15- Math is a more complex language than the spoken word.
16- Math exist in the universe before humans – for example - the Fibonacci spiral and Golden Ratio
17- Humans discovered math in the world and created their own math.
18- We know about infinity through mathematics, but we do not know infinity in an experiential sense.
19- Logic developed concurrently with spoken language in order to give words coherence.
20- The logic skill we developed in the spoken word allowed mathematical language to develop.
21- The universe begged us to develop math language.
22- Math is a subset of logic skill. Logic developed first before math skill.
23- Logic evolved in spoken language first and developed simultaneously with philosophy.
24- This list is an example of spoken language, logic, philosophy, science and math.

Please tell me what you think about any and/or all of these ideas? Some of the current thoughts are off topic – somewhat – please relate your thinking to math.

[Burning ghost]

I can only seriously address point 15 for now. In what respect is mathematical language more complex than spoken language?

[Woodart]

Burning ghost wrote:
I can only seriously address point 15 for now. In what respect is mathematical language more complex than spoken language?

Math starts out simple enough – I think counting was first – 1, 2, 3, etc. Then a simple equation – 1+1=2. Then it becomes progressively more complex – when we reach geometry or algebra – math exceeds the spoken word in expression. Math still uses the spoken word to express itself – but now the spoken word has a hard time keeping up as a succinct expression. When we reach calculus and computer programing – the spoken word cannot do what math is doing. The spoken word can always describe what math is doing – but – it cannot perform the function that math can do. Math goes beyond the spoken word. The logic of math is always conceived in the spoken word – they are always tied together. However, math can manipulate concepts and solve problems that the spoken work is not capable of. Therefore, math is a more complex language than the spoken word.

It is possible when, and if, we reach artificial intelligence in computers – the spoken word will not be necessary for the AI. AI may not see a need for the spoken word as we know it. I think this is a warm and fuzzy idea. If this is so – it will clearly demonstration complexity beyond the spoken word. What do you think?

[Burning ghost]

You baffle me.

I'll just leave yo to think about reducing phenomenon to a simplistic model being some how more complex than being able to express it emotionally with words that include adjectives such as "warm", "yellowish", "phenomenal", "cognitive" and "young".

In geometry we can call horizontal X and vertical Y. We use a starting point called 0,0. From there we assume an infinite plane. Is that complex? In algebra we merely assume balance. That is all. We work off the abstract principle that 1=1 and 3=3. All the symbols we use in mathematics are based on this extremely simple premise.

Computers "talk". They use "languages". We write the languages for them and they carry out the actions according to the language commands we issue. They don't "think" and have no "intelligence".

[Woodart]

Burning ghost wrote:
You baffle me.

I'll just leave yo to think about reducing phenomenon to a simplistic model being some how more complex than being able to express it emotionally with words that include adjectives such as "warm", "yellowish", "phenomenal", "cognitive" and "young".

I think what you are saying here is that emotions – shades of yellow and cognition are more complex than math. I would say these ideas are different. They can be very complex. However, shades of yellow can be grasped by most people – and – the other ideas you mentioned. There are some ideas that defy understanding by most that are not mathematical. Most non-mathematical ideas can be broken down and discussed by most. In most advanced math – very few people – really understand what is going on. If we ask 100 people what a calculus equation means – maybe 10% can answer correctly. If we ask the same 100 people your concepts – perhaps 90% can answer correctly.

Burning ghost wrote:
In geometry we can call horizontal X and vertical Y. We use a starting point called 0,0. From there we assume an infinite plane. Is that complex? In algebra we merely assume balance. That is all. We work off the abstract principle that 1=1 and 3=3. All the symbols we use in mathematics are based on this extremely simple premise.

Math does have “extremely simple” elements, but the combination can become very complex. Take the following for example:

The Heart of Fermat's Last Theorem - Numberphile

Professor wins $700k for solving 300-year-old math equation

The Most Beautiful Equation in Math

10 Mathematical Equations That Changed The World

Burning ghost wrote:
Computers "talk". They use "languages". We write the languages for them and they carry out the actions according to the language commands we issue. They don't "think" and have no "intelligence".

I think IBM will disagree with you. It has already invested 10 billion dollars in Watson. Google has invested over 6 billion in artificial intelligence. These companies are not known for wasting their money. AI research is proceeding at frantic pace and some of our best minds are working on it – all over the globe.

[Burning ghost]

Can mathematics describe a sunset? No.

Can I explain the idea of infinity and fractions in a simple understandable terms? Can I explain algebra in simple terms? Yes, I can.

That is my argument against mathematical language being more complex than spoken language.

[Woodart]

Burning ghost wrote:
Can mathematics describe a sunset? No.

I agree – however, no one ever said that is math’s purpose. Spoken language and math language have different functions.

Burning ghost wrote:
Can I explain the idea of infinity and fractions in a simple understandable terms? Can I explain algebra in simple terms? Yes, I can.

That is my argument against mathematical language being more complex than spoken language.

Many math ideas can be explained simply. However, many math ideas defy understanding – even by great mathematicians – to say nothing about the common man. Can you explain Fermat's Last Theorem in a hundred words or less and be understood by most? I don’t think so – watch the first video on it again.

Therefore, math is shown to be more complex than spoken language – empirically.

[Sy Borg]

Can mathematics describe a sunset? No.

Can I explain the idea of infinity and fractions in a simple understandable terms? Can I explain algebra in simple terms? Yes, I can.

That is my argument against mathematical language being more complex than spoken language.

A sunset can most certainly be described in mathematical languages. Every photo you see online is constructed with code, and an image provides a much more precise description, evoking more of how the sunset appeared than words could manage. So none of us could use words to capture this image:

pbs.twimg.com/profile_images/2681159895 ... ee583.jpeg

Spoken and metamathematical languages are interrogative and communication tools, variably suited to different tasks. If I was to say to you "¥]nÑÔUW¡n¤^ÈøGUàýÞÎ\aYkrÊ5w:)ÅøI鿐ºž‡cŸüUܲœ¯ÍΏö°", you would be as nonplussed as if the instructions given to a computer to render a sunset were given as an English description rather than code. Likewise, there's not much point describing the scene to most of us in Chinese or Norwegian languages either.

Maths is a much more precise language than spoken languages, hence its use in engineering. You don't want to drive on a bridge constructed without use of mathematical descriptions of how to build it, only regular lingual descriptions of what needs to be done.

[Burning ghost]

Greta -

No, that just doesn't hold up. I was not asking for a visual reconstruction I was asking for a description.

Either way I would not say "precision" means more "complexity". There are a number of extremely complex ways I can describe a sunset to someone, yet math can only reproduce the image into a stream of numbers that are quite meaningless. This is not an unknown argument. I am pretty sure Dennett tries to argue the same thing, and fails in my view. By this I mean having all the information of what blue is without experiencing blue is meaningless. I cannot learn how to see blue by reading books about the colour blue. The thrust of my point is mathematics cannot give me anything like an emotional description of something in the way vague and ambiguous words can. There is no room for movement in mathematics, it is a limited language precisely because it describes an abstract infinite world.

Can mathematics describe how the professor who solved Fermat's Last Theorem felt when he solved it? He was happy at first and then quite devastated because he realized he'd never achieve anything of the like again (quite strange to see him speaking talking about it in obvious distress - probably not in youtube video above.)

Woodart -

There is also point (7) ... I cannot grasp from what nook of your mind you conjured such a bizarre idea from? It looks like a double whammy of nonsense. Mathis a type of time? Women new about time first because of menstruation?

Pursuing Ai is useful. The reality of a sentient machine is very likely to remain a myth. Silicon just ain't all that. Quantum computing is the only possible avenue to get close to the complexity of the human brain, then there is the very obvious problem of creating a body for the machine mind to live it (this would arguably be essential for any sentient machine as it is for any biological creature). If a computer could be sentient without a body then I would argue that we'd have to call it something very, very different and that sentient would be a false representation.

There are too many questions about consciousness still to be answered for me to guess that computers can be made sentient. The proof is in the pudding. I am far more interested in the integration of humans with computers.

[Sy Borg]

Greta -

No, that just doesn't hold up. I was not asking for a visual reconstruction I was asking for a description.

What is a visual reconstruction but a description, just a very precise one? This is how dolphins and bats communicate - they effectively overhear the images that another constructs in sound. Further, a lucid description of the scene in Chinese or Portuguese would be no more use to me than a string of numbers.

Either way I would not say "precision" means more "complexity". There are a number of extremely complex ways I can describe a sunset to someone, yet math can only reproduce the image into a stream of numbers that are quite meaningless.

As would Chinese because maths is the language of machines, not humans.

Further, numbers are far from meaningless. Consider the emotional/qualitative difference implied between being told to do two or two hundred sit ups.

This is not an unknown argument. I am pretty sure Dennett tries to argue the same thing, and fails in my view. By this I mean having all the information of what blue is without experiencing blue is meaningless. I cannot learn how to see blue by reading books about the colour blue. The thrust of my point is mathematics cannot give me anything like an emotional description of something in the way vague and ambiguous words can. There is no room for movement in mathematics, it is a limited language precisely because it describes an abstract infinite world.

Mary's room. I am not saying that mathematics (or spoken languages) is actual reality, confusing the map for the territory.

Spoken languages and maths are different ways of expressing different things in different contexts. Try describing to an engineer with words how you want a bridge to be built. Try using numbers to comfort a lost child.

[Burning ghost]

Greta -

Try describing to an engineer with words how you want a bridge to be built.

Very easy to do.

What is a visual reconstruction but a description, just a very precise one? This is how dolphins and bats communicate - they effectively overhear the images that another constructs in sound. Further, a lucid description of the scene in Chinese or Portuguese would be no more use to me than a string of numbers.

It is not a description. Bats "see" things they don't "hear" them. You are mistaking different forms of sense for different forms of cognitive mapping (of which there is none known beyond basic intuitions of time and space). Here you very much are confusing "the map for the territory".

Next you'll be telling me women were the first to discover time because of menstruation maybe?

Present something that backs up the claim that Woodart is making, the claim that math as a language is more complex than the spoken/written/signed word (Chinese is included in this category btw).

Woodart -

IBM are looking at augmented intelligence not artificial intelligence. They are not trying to create conscoius computers (because they cannot)

[Sy Borg]

Greta -

Try describing to an engineer with words how you want a bridge to be built.

Very easy to do.

If we could adequately describe bridges with words then we wouldn't need numbers to construct them. You'd just describe the bridge to the builders.

Make it it big. How big? Big enough to span the river.
How wide? Wide enough for x lanes of traffic plus walkways.
How much room to leave on the sides? Enough.
How much concrete is needed? Enough to go from A to B.

Far from adequate.

What is a visual reconstruction but a description, just a very precise one? This is how dolphins and bats communicate - they effectively overhear the images that another constructs in sound. Further, a lucid description of the scene in Chinese or Portuguese would be no more use to me than a string of numbers.

It is not a description. Bats "see" things they don't "hear" them. You are mistaking different forms of sense for different forms of cognitive mapping (of which there is none known beyond basic intuitions of time and space). Here you very much are confusing "the map for the territory".

I can see why you'd think that but, in the case of animals with echolocation, data sensed is automatically shared. When one animal sends its ultrasonic signal, any nearby animal will share its perception. Thus, there is a communicated description between animals by way of shared imagery. It's akin to speaking by putting pictures directly in another's mind.

Bat echolocation calls facilitate social communication rspb.royalsocietypublishing.org/content ... .2012.1995

Our study demonstrates that social information encoded in bat echolocation calls plays a crucial and hitherto underestimated role for eavesdropping conspecifics and thus facilitates social communication in a highly mobile nocturnal mammal.

Next you'll be telling me women were the first to discover time because of menstruation maybe?

Thanks for that little unprovoked burst of unpleasantness. I thought you were better than that.

Present something that backs up the claim that Woodart is making, the claim that math as a language is more complex than the spoken/written/signed word (Chinese is included in this category btw).

What we have at present is one who reckons math is more complex, one who reckons spoken languages are more complex.

There is no competition. Spoken languages have their applications and mathematical protocols have theirs. Each is used to transfer information between humans. Certainly greater detail can be achieved more effectively with math than with language, provided someone or something can understand. Consider NASA sending data to the ISS for the construction of special tools on a 3D printer. Then consider NASA trying to describe the parameters of instruments to the crew in spoken language.

[Fan of Science]

The reason mathematicians use the symbols they do is simply for convenience. The symbols allow for statements to be made without having to use a lengthy verbal description. However, there is nothing stated with mathematical symbols that could not also be stated through the use of a verbal description. A backwards E just means "there exists." An upside down A just means "for all." The symbols are basically just short-hand. It's not as if the concepts cannot be described purely in words. It would just result in lengthy written descriptions.

Whether this makes mathematical "language" more or less complex than the use of ordinary words is most likely dependent on how one defines complexity.