Philosophy Now Forum

Or maybe both? I'm not sure myself.

PhilX

I'm not surprised if you can think it both.

Perhaps pure mathematics with its symbols and relationships was invented.

However its applications to the real world in the form of applied mathematics could be considered to have been discovered.

Maths is just one of the human languages used to discuss and describe the world. Of the range so languages, it is low on ambiguity and low on nuance, and expression. It fails to address qualities, but is all about quantities.

A_Seagull wrote:Perhaps pure mathematics with its symbols and relationships was invented.

However its applications to the real world in the form of applied mathematics could be considered to have been discovered.

For me, math has meaning in terms of how things relate to one another. E.g. the number one would have no meaning by itself, but two ones do because they form a group (two) which is immediately grasped by the mind as being more than one. An interesting question would be the number line where points on the line are matched up with numbers. The matchup would be in the mind and in the brain that sees the number line so that math can be invented and discovered.

Nowadays scientists say that the universe is math implying that math was discovered. I can also ask if it makes a difference what kind of math we're talking about?

PhilX

HC said about math:

"...is all about quantities."

What do you think about complex numbers?

PhilX

Why not discuss this in a broader sense? Maths are one form of formal language. We have programming languages and logical notations. So, why not change things up and ask if formal language is a discovery or invention? They have the same basis, do they not?

Dalek Prime wrote:Why not discuss this in a broader sense? Maths are one form of formal language. We have programming languages and logical notations. So, why not change things up and ask if formal language is a discovery or invention? They have the same basis, do they not?

If you want to Dalek, you can start a thread in the language or general philosophy section on this very subject.

PhilX

Philosophy Explorer wrote:

Dalek Prime wrote:Why not discuss this in a broader sense? Maths are one form of formal language. We have programming languages and logical notations. So, why not change things up and ask if formal language is a discovery or invention? They have the same basis, do they not?

If you want to Dalek, you can start a thread in the language or general philosophy section on this very subject.

PhilX

Why? You don't find it relevant? They are all formal languages, and it's the same query, so what's wrong with the suggestion? It's topical.

I'm with Hobbes and Dalek on math as a language used to describe phenomena. Like word-based language, math can describe reality or it can create fictitious and purely theoretical structures. Each language conveys a different aspect of reality - words convey reality's stories; math, its hard facts; pictures convey reality's activity and form, sounds convey the impact of that activity and form. Smells and tastes convey reactivity. Obviously there is significant overlap and none of it is objectively real, only naturally-selected glimpses of reality.

Stories are not real but understanding the stories behind the reality you encounter helps you survive. Math is not (or rather, was not) real but understanding the math provides empowerment and certainty/security. Like pictograms and body language, they are useful models. The mathematical relationships are real but the calculations of them merely efficacious.

Despite our sensory limitations, the imaginative scope of math and other languages allows us to extend on our senses by making projections that reduce the amount of trial-and-error needed to achieve goals.

Dalek Prime wrote:Why not discuss this in a broader sense? Maths are one form of formal language. We have programming languages and logical notations. So, why not change things up and ask if formal language is a discovery or invention? They have the same basis, do they not?

I do not consider it useful to consider mathematics and language as being of the same ilk.

Language consists primarily of labels which are linked to perceived objects and things. Whereas pure mathematics consists of symbols and relationships between those symbols.

Mathematics in its pure form can generate theorems through its internal logic, many of which can be considered as "interesting". For example a Mandelbrot set can be considered to be a theorem of mathematics and most people consider them to be interesting.

In contrast, if one considers language as a logical system with grammar denoting the relationships between the logical symbols (words) and also use the English dictionary among the 'axioms' of the system, then you can generate theorems of the form : "All unmarried men are bachelors", but that can hardly be categorised as "interesting".

A_Seagull wrote:

Dalek Prime wrote:Why not discuss this in a broader sense? Maths are one form of formal language. We have programming languages and logical notations. So, why not change things up and ask if formal language is a discovery or invention? They have the same basis, do they not?

I do not consider it useful to consider mathematics and language as being of the same ilk.

Language consists primarily of labels which are linked to perceived objects and things. Whereas pure mathematics consists of symbols and relationships between those symbols.

Mathematics in its pure form can generate theorems through its internal logic, many of which can be considered as "interesting". For example a Mandelbrot set can be considered to be a theorem of mathematics and most people consider them to be interesting.

In contrast, if one considers language as a logical system with grammar denoting the relationships between the logical symbols (words) and also use the English dictionary among the 'axioms' of the system, then you can generate theorems of the form : "All unmarried men are bachelors", but that can hardly be categorised as "interesting".

You may not consider it useful, as you say, to consider all the other formal languages together, but they undeniably are, including mathematics. I understand what you are saying about interest, which pure mathematics, being the most formal and general language system, can bring. But it's still of the same category, and so I can't accept the reason for treating them as separate.

Greta wrote:I'm with Hobbes and Dalek on math as a language used to describe phenomena. Like word-based language, math can describe reality or it can create fictitious and purely theoretical structures. Each language conveys a different aspect of reality - words convey reality's stories; math, its hard facts; pictures convey reality's activity and form, sounds convey the impact of that activity and form. Smells and tastes convey reactivity. Obviously there is significant overlap and none of it is objectively real, only naturally-selected glimpses of reality.

Stories are not real but understanding the stories behind the reality you encounter helps you survive. Math is not (or rather, was not) real but understanding the math provides empowerment and certainty/security. Like pictograms and body language, they are useful models. The mathematical relationships are real but the calculations of them merely efficacious.

Despite our sensory limitations, the imaginative scope of math and other languages allows us to extend on our senses by making projections that reduce the amount of trial-and-error needed to achieve goals.

You and Hobbes have stated this well and succinctly, and I'm in agreement.

Dalek Prime wrote:[You may not consider it useful, as you say, to consider all the other formal languages together, but they undeniably are, including mathematics. I understand what you are saying about interest, which pure mathematics, being the most formal and general language system, can bring. But it's still of the same category, and so I can't accept the reason for treating them as separate.

Ok then. I have shown how mathematics is dissimilar to a language.

Can you show how mathematics is similar to a language? (Just to say: "They undeniably are" hardly constitutes a rational philosophical argument.)

All knowledge is discovered, whether that discovery is of time (reasoned), or timeless (immeditate).

Knowledge
2c: the circumstance or condition of apprehending truth or fact through reasoning : cognition