Axioms are the synthesis of symbols and in this respect, all logic has an informal element of art.

However, art as an expression of truth is art as objectivity where "existence is identity." (Rand, For the New Intellectual) and "Percepts, not sensations, are the given, the self-evident." (Rand, Introduction to Objectivist Epistemology (second ed.))The axiom as the symbol can be observed across many branches and disciplines of “observation” and can be observed as the median point between representation and reality.

As a median point, the symbol and the axiom manifest a form of abstract/physical equilibrium. This importance of the symbol and the axiom can be further observed in mathematics. Haskell Curry argued that mathematics is at its core a disciplined system of symbols whose forms and function manifest further formula as "the science of formal systems". (Curry) Much can be inferred from this observation as these symbols were developed by Leonhard Euler in the 16th century (Mx) where before mathematics was simply an extension of common language (Kline).

As a “the science that draws necessary conclusions” (Peirce) a continuation on the importance of axiomatic symbolism was observed through Russell’s definition of “All Mathematics is Symbolic Logic” (The Principles of Mathematics). It can be inferred that the importance of axiomatic symbols stems back to the Pythagorean emphasis on the importance of form over matter (Stumpf)and that this emphasis on form may connect the mathematical Logicist’s position to the symmetrical, but not agreeable, perspective of the Mathematical Intuitionist whose view is that" Mathematics is the mental activity which consists in carrying out constructs one after the other" (Snapper) or the formalist perspective of a "the science of formal systems [symbols]". (Curry, Outlines of a Formalist Philosophy of Mathematics.)

From the nature of the symbol “Logic lay, it seemed, at the bottom of all the sciences.— For logical investigation explores the nature of all things. It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is this or that.——It takes its rise, not from an interest in the facts of nature, nor from a need to grasp causal connexions: but from an urge to understand the basis, or essence,, of everything empirical42e(Philo invest)

Logic is the deepest study of symmetry there is, for even the mathematicians require words to be understood. No language has yet to be expressed "only" in the form of numbers. “But how many kinds of sentence are there? Say assertion, question, and command?—There are countless kinds: countless different kinds of use of what we call "symbols", "words", "sentences". And this multiplicity is not something fixed, given once for all; but new types of language, new language-games, as we may say, come into existence, and others become obsolete and get forgotten. (We can get a rough picture of this from the changes in mathematics.)” (Wittgenstein, Philosophical Investigations)

## Symbols: Art as Logic, Logic as Art

- attofishpi
**Posts:**4138**Joined:**Tue Aug 16, 2011 8:10 am**Location:**Orion Spur-
**Contact:**

### Re: Symbols: Art as Logic, Logic as Art

It's 'get it?' art. The worst kind or best kind of art? I can't decide. Especially if you don't 'get it'.attofishpi wrote: ↑Fri Nov 10, 2017 3:11 am South America - Bra_zil

SIN_AI

Sun of God

Tree of Knowledge

UK: I_re_land

www.androcies.com

- attofishpi
**Posts:**4138**Joined:**Tue Aug 16, 2011 8:10 am**Location:**Orion Spur-
**Contact:**

- attofishpi
**Posts:**4138**Joined:**Tue Aug 16, 2011 8:10 am**Location:**Orion Spur-
**Contact:**

### Re: Symbols: Art as Logic, Logic as Art

To under_stand IT you need to comprehend the anomalies that the panetheistic 'God' has left behind, how unlikely these things are, such as:-

The perfection of the Alpha_bet A.I. You Owe. e=energy.

The perfection of the Alpha_bet A.I. You Owe. e=energy.

### Re: Symbols: Art as Logic, Logic as Art

Eodnhoj7Axioms:

are the synthesis of symbols and in this respect, all logic has an informal element of art.

However, art as an expression of truth is art as objectivity where "existence is identity." (Rand, For the New Intellectual) and "Percepts, not sensations, are the given, the self-evident." (Rand, Introduction to Objectivist Epistemology (second ed.))The axiom as the symbol can be observed across many branches and disciplines of “observation” and can be observed as the median point between representation and reality.

As a median point, the symbol and the axiom manifest a form of abstract/physical equilibrium. This importance of the symbol and the axiom can be further observed in mathematics. Haskell Curry argued that mathematics is at its core a disciplined system of symbols whose forms and function manifest further formula as "the science of formal systems". (Curry) Much can be inferred from this observation as these symbols were developed by Leonhard Euler in the 16th century (Mx) where before mathematics was simply an extension of common language (Kline).

As a “the science that draws necessary conclusions” (Peirce) a continuation on the importance of axiomatic symbolism was observed through Russell’s definition of “All Mathematics is Symbolic Logic” (The Principles of Mathematics). It can be inferred that the importance of axiomatic symbols stems back to the Pythagorean emphasis on the importance of form over matter (Stumpf)and that this emphasis on form may connect the mathematical Logicist’s position to the symmetrical, but not agreeable, perspective of the Mathematical Intuitionist whose view is that" Mathematics is the mental activity which consists in carrying out constructs one after the other" (Snapper) or the formalist perspective of a "the science of formal systems [symbols]". (Curry, Outlines of a Formalist Philosophy of Mathematics.)

From the nature of the symbol “Logic lay, it seemed, at the bottom of all the sciences.— For logical investigation explores the nature of all things. It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is this or that.——It takes its rise, not from an interest in the facts of nature, nor from a need to grasp causal connexions: but from an urge to understand the basis, or essence,, of everything empirical42e(Philo invest)

Logic is the deepest study of symmetry there is, for even the mathematicians require words to be understood. No language has yet to be expressed "only" in the form of numbers. “But how many kinds of sentence are there? Say assertion, question, and command?—There are countless kinds: countless different kinds of use of what we call "symbols", "words", "sentences". And this multiplicity is not something fixed, given once for all; but new types of language, new language-games, as we may say, come into existence, and others become obsolete and get forgotten. (We can get a rough picture of this from the changes in mathematics.)” (Wittgenstein, Philosophical Investigations)

Just a note: If you reference some philosopher, the reference should to the point of the idea, here, art as logic. There is so much of this, perhaps all of this, that says nothing about art. Are you talking about form, as a formalist would? Is Clive Bell in there somewhere? Peirce? Are you making some pragmatist (or pragmaticist, as he put it) statement about the nature of art and how logic is intrinsically pragmatic. Dewey says this, but his argument is nowhere in this. And Ayn Rand?? She is an authority on.....what? Objectivism? She was a crank.

I know, this is confrontational, and apologies for that. But: what IS this about?

are the synthesis of symbols and in this respect, all logic has an informal element of art.

However, art as an expression of truth is art as objectivity where "existence is identity." (Rand, For the New Intellectual) and "Percepts, not sensations, are the given, the self-evident." (Rand, Introduction to Objectivist Epistemology (second ed.))The axiom as the symbol can be observed across many branches and disciplines of “observation” and can be observed as the median point between representation and reality.

As a median point, the symbol and the axiom manifest a form of abstract/physical equilibrium. This importance of the symbol and the axiom can be further observed in mathematics. Haskell Curry argued that mathematics is at its core a disciplined system of symbols whose forms and function manifest further formula as "the science of formal systems". (Curry) Much can be inferred from this observation as these symbols were developed by Leonhard Euler in the 16th century (Mx) where before mathematics was simply an extension of common language (Kline).

As a “the science that draws necessary conclusions” (Peirce) a continuation on the importance of axiomatic symbolism was observed through Russell’s definition of “All Mathematics is Symbolic Logic” (The Principles of Mathematics). It can be inferred that the importance of axiomatic symbols stems back to the Pythagorean emphasis on the importance of form over matter (Stumpf)and that this emphasis on form may connect the mathematical Logicist’s position to the symmetrical, but not agreeable, perspective of the Mathematical Intuitionist whose view is that" Mathematics is the mental activity which consists in carrying out constructs one after the other" (Snapper) or the formalist perspective of a "the science of formal systems [symbols]". (Curry, Outlines of a Formalist Philosophy of Mathematics.)

From the nature of the symbol “Logic lay, it seemed, at the bottom of all the sciences.— For logical investigation explores the nature of all things. It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is this or that.——It takes its rise, not from an interest in the facts of nature, nor from a need to grasp causal connexions: but from an urge to understand the basis, or essence,, of everything empirical42e(Philo invest)

Logic is the deepest study of symmetry there is, for even the mathematicians require words to be understood. No language has yet to be expressed "only" in the form of numbers. “But how many kinds of sentence are there? Say assertion, question, and command?—There are countless kinds: countless different kinds of use of what we call "symbols", "words", "sentences". And this multiplicity is not something fixed, given once for all; but new types of language, new language-games, as we may say, come into existence, and others become obsolete and get forgotten. (We can get a rough picture of this from the changes in mathematics.)” (Wittgenstein, Philosophical Investigations)

Just a note: If you reference some philosopher, the reference should to the point of the idea, here, art as logic. There is so much of this, perhaps all of this, that says nothing about art. Are you talking about form, as a formalist would? Is Clive Bell in there somewhere? Peirce? Are you making some pragmatist (or pragmaticist, as he put it) statement about the nature of art and how logic is intrinsically pragmatic. Dewey says this, but his argument is nowhere in this. And Ayn Rand?? She is an authority on.....what? Objectivism? She was a crank.

I know, this is confrontational, and apologies for that. But: what IS this about?

### Re: Symbols: Art as Logic, Logic as Art

We synthesize art, through forms which extend as medial points to further forms, which in turn justify them as symbols. Hence the synthesis of axioms, as symbols, observes truth not only as subjective or objective but both and what we understand of truth is inseperable from "observation as synthesis through the axiom".odysseus wrote: ↑Sun Feb 11, 2018 10:50 pm Eodnhoj7Axioms:

are the synthesis of symbols and in this respect, all logic has an informal element of art.

However, art as an expression of truth is art as objectivity where "existence is identity." (Rand, For the New Intellectual) and "Percepts, not sensations, are the given, the self-evident." (Rand, Introduction to Objectivist Epistemology (second ed.))The axiom as the symbol can be observed across many branches and disciplines of “observation” and can be observed as the median point between representation and reality.

As a median point, the symbol and the axiom manifest a form of abstract/physical equilibrium. This importance of the symbol and the axiom can be further observed in mathematics. Haskell Curry argued that mathematics is at its core a disciplined system of symbols whose forms and function manifest further formula as "the science of formal systems". (Curry) Much can be inferred from this observation as these symbols were developed by Leonhard Euler in the 16th century (Mx) where before mathematics was simply an extension of common language (Kline).

As a “the science that draws necessary conclusions” (Peirce) a continuation on the importance of axiomatic symbolism was observed through Russell’s definition of “All Mathematics is Symbolic Logic” (The Principles of Mathematics). It can be inferred that the importance of axiomatic symbols stems back to the Pythagorean emphasis on the importance of form over matter (Stumpf)and that this emphasis on form may connect the mathematical Logicist’s position to the symmetrical, but not agreeable, perspective of the Mathematical Intuitionist whose view is that" Mathematics is the mental activity which consists in carrying out constructs one after the other" (Snapper) or the formalist perspective of a "the science of formal systems [symbols]". (Curry, Outlines of a Formalist Philosophy of Mathematics.)

From the nature of the symbol “Logic lay, it seemed, at the bottom of all the sciences.— For logical investigation explores the nature of all things. It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is this or that.——It takes its rise, not from an interest in the facts of nature, nor from a need to grasp causal connexions: but from an urge to understand the basis, or essence,, of everything empirical42e(Philo invest)

Logic is the deepest study of symmetry there is, for even the mathematicians require words to be understood. No language has yet to be expressed "only" in the form of numbers. “But how many kinds of sentence are there? Say assertion, question, and command?—There are countless kinds: countless different kinds of use of what we call "symbols", "words", "sentences". And this multiplicity is not something fixed, given once for all; but new types of language, new language-games, as we may say, come into existence, and others become obsolete and get forgotten. (We can get a rough picture of this from the changes in mathematics.)” (Wittgenstein, Philosophical Investigations)

Just a note: If you reference some philosopher, the reference should to the point of the idea, here, art as logic. There is so much of this, perhaps all of this, that says nothing about art. Are you talking about form, as a formalist would? Is Clive Bell in there somewhere? Peirce? Are you making some pragmatist (or pragmaticist, as he put it) statement about the nature of art and how logic is intrinsically pragmatic. Dewey says this, but his argument is nowhere in this. And Ayn Rand?? She is an authority on.....what? Objectivism? She was a crank.

I know, this is confrontational, and apologies for that. But: what IS this about?

I don't like apologies, never apologize to me again.

The synthesis of form leads to function with function leading to further form, hence the only manner we can understand truth in a linear manner is through the extension of medial points to further points. In these respects, axioms are the synthesis of truths which in turn form reality through the exhibition of the will through perspective.

Take for example the extension of the argument about the symbolism of mathematics. What we understand of number and space, quantitatively, is dependent on a qualitative symbolism which we synthesize as medial points. The symbol of "1", may very from culture to culture, which in turn subjectively determines the manner in which that culture views "1".

So for instance the western version of "1" observes a linear structure which subconsciously leads us to premise our logic and methodology on a form of linear progression as "unity through direction".

In a separate example, eastern cultures (specifically the Chinese for example), use a degree of curvature which intuitively observes a degree of circularity (as all curvature is a degree of the circle). We can see this reflect through the eastern reasoning processes of "circularity" and "wholism" which in turn form their respective cultures.

So in simpler terms, we synthesize axioms through forms which act as medial points to further axioms which in turn form perspectives which form the world. Observing a universal principle of "1", through the symbolism of the line or curve, creates a subjective interpretation of it which in turn forms the culture, individual perspectives, etc.

Hence how "math", through its inherent form, was observed and formulated into a language in itself inevitably led to the scientific processes we observe today and how we interpret reality. Would relativity exist if we perceived space as strictly straight lines. Would the Minkowski Space, used to premise Einstein's Relativity, exist without Euclidian lines forming the frame of the diagram?

Observing a constant, such as a line, through different manners in turn forms axioms which determines principles, and the problem occurs in the respect that the axioms in themselves are dependent upon a subjective symbolism. Are our foundations dependent upon Euler's symbolism, which he quite literally made up? What if I replaced "1" with a Pythagorean Monad: "⨀"?

Would we be building pyramids instead of satellite dishes? (figuratively speaking).

Art is an expression of perspective with perspective being a form of measurement equivalent to causality, which in turn may observe "measurement" as "cause" where "man as measurer" is "man as cause".