4th dimension is extension of 3rd dimension. A world within worlds

[river]

river said: ↑
What is the foundation of the abstract .

Logic.

What is the foundation of logic ?

 

[Write4U]

What is the foundation of logic ?

The Emergence of First-Order Logic
First published Sat Nov 17, 2018

For anybody schooled in modern logic, first-order logic can seem an entirely natural object of study, and its discovery inevitable. It is semantically complete; it is adequate to the axiomatization of all ordinary mathematics; and Lindström’s theorem shows that it is the maximal logic satisfying the compactness and Löwenheim-Skolem properties.

So it is not surprising that first-order logic has long been regarded as the “right” logic for investigations into the foundations of mathematics. It occupies the central place in modern textbooks of mathematical logic, with other systems relegated to the sidelines.

The history, however, is anything but straightforward, and is certainly not a matter of a sudden discovery by a single researcher. The emergence is bound up with technical discoveries, with differing conceptions of what constitutes logic, with different programs of mathematical research, and with philosophical and conceptual reflection. So if first-order logic is “natural”, it is natural only in retrospect. The story is intricate, and at points contested; the following entry can only provide an overview.

Discussions of various aspects of the development are provided by Goldfarb 1979, Moore 1988, Eklund 1996, Brady 2000, Ferreirós 2001, Sieg 2009, Mancosu, Zach & Badesa 2010, Schiemer & Reck 2013, the notes to Hilbert [LFL], and the encyclopedic handbook Gabbay & Woods 2009......more

https://plato.stanford.edu/entries/logic-firstorder-emergence/

 

[river]

The Emergence of First-Order Logic
First published Sat Nov 17, 2018 https://plato.stanford.edu/entries/logic-firstorder-emergence/

This about mathematical logic .

And Mathematical logic is not the pinnacle of logic . Just a form of logic .

 

[Write4U]

This about mathematical logic .

And Mathematical logic is not the pinnacle of logic . Just a form of logic .

Logic is logic, in any form. It is a process. Mathematics is one of the purest forms of logic.

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. ... Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory.
These areas share basic results on logic, particularly first-order logic, and definability.

en.wikipedia.org › wiki › Mathematical_logic

 

[river]

Logic is logic, in any form. It is a process. Mathematics is one of the purest forms of logic.
en.wikipedia.org › wiki › Mathematical_logic

Mathematics is " One of " . Forms of logic .

Define " Pure logic " .

 

[Write4U]

Mathematics is " One of " . Forms of logic

Yes, it does not rely on any form of assumptive truths.
All elements of basic (pure) mathematics are defined and definable in symbolic language.
Definition of symbolic logic

: a science of developing and representing logical principles by means of a formalized system consisting of primitive symbols, combinations of these symbols, axioms, and rules of inference

Define " Pure logic " .

Logical progression :
input (values) --> mathematical function(s) (processes) --> output (values)

Mathematics define the logic of the Universe.

Galileo, a contemporary of Descartes, also blurred the distinction between mathematical and philosophical method. An excerpt from his essay ‘Il Saggiatore’ (1623), or The Assayer, is often cited for advancing a revolutionary mathematisation of physics:

" Philosophy is written in this grand book – I mean the Universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.

In this quotation, it is philosophy that is written in the language of mathematics. It is no mere linguistic coincidence that Isaac Newton’s monumental development of calculus and modern physics was titled Philosophiæ Naturalis Principia Mathematica (1687), that is, Mathematical Principles of Natural Philosophy. The goal of philosophy is to understand the world and our place in it, and to determine the methods that are appropriate to that task. Physics, or natural philosophy, was part of that project, and Descartes, Galileo and Newton – and philosophers before and after – were keenly attentive to the role that mathematics had to play.

The turning point occurs around rule 14. According to Descartes, philosophy is a matter of discovering general truths by finding properties that are shared by disparate objects, in order to understand the features that they have in common. This requires comparing the degrees to which the properties occur. A property that admits degrees is, by definition, a magnitude.

The only way to be able to determine a magnitutude is to symbolize it "

And, from the time of the ancient Greeks, mathematics was understood to be neither more nor less than the science of magnitudes. (It was taken to encompass both the study of discrete magnitudes, that is, things that can be counted, as well as the study of continuous magnitudes, which are things that can be represented as lengths.)

Philosophy is therefore the study of things that can be represented in mathematical terms, and the philosophical method becomes virtually indistinguishable from the mathematical method.

https://aeon.co/essays/does-philosophy-still-need-mathematics-and-vice-versa

 

[river]

It does not rely on any form of assumptive truths.
All elements of basic (pure) mathematics are defined and definable in symbolic language.
Definition of symbolic logic

To the last statement ; disagree

The physical objects are not controlled by mathematics . Mathematics is controlled by real physical objects . Actions and effect , affect and cause in NO particular order .

 

[Write4U]

To the last statement ; disagree

The physical objects are not controlled by mathematics . Mathematics is controlled by real physical objects .

Please define a physical object without appealing to irreducible complexity, and how does it control the mathematics of its behavior?

 

[river]

river said: ↑
To the last statement ; disagree

The physical objects are not controlled by mathematics . Mathematics is controlled by real physical objects .

How?

Think , what is the Root of mathematics . Where does the concept of mathematics come from ?

 

[paddoboy]

Please define a physical object without appealing to irreducible complexity, and how does it control the mathematics of its behavior?

An old Aussie expression Write4U, debating this with river, is akin to pushing shit up hill.
In defining maths, I like the simple definition as being the language of physics, but a more encompassing definition is in https://en.wikipedia.org/wiki/Mathematics
and defined as
"Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions."
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Note the highlighted bit. "Ëstablishing Truth"
This is the reason why river in general, dismisses the importance of maths, as it also defines and supports science/physics and the scientific method, and at the same time refuting his completely ridiculous scenarios and fairy tales.

 

[river]

An old Aussie expression Write4U, debating this with river, is akin to pushing shit up hill.
In defining maths, I like the simple definition as being the language of physics, but a more encompassing definition is in https://en.wikipedia.org/wiki/Mathematics
and defined as
"Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions."
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Note the highlighted bit. "Ëstablishing Truth"
This is the reason why river in general, dismisses the importance of maths, as it also defines and supports science/physics and the scientific method, and at the same time refuting his completely ridiculous scenarios and fairy tales.

Mathematics basic mathematics was based on accounting . Real physical objects .

 

[Write4U]

Think , what is the Root of mathematics . Where does the concept of mathematics come from ?

The "concept" of mathematics existed long before humans came on the scene.

The Universe functioned flawlessly 14 billion years ago as it does today, thanks to its mathematical underpinnings.

Human symbolic mathematics are a result of observation of natural dynamical phenomena and invented the symbolic language to describe these values and functional mechanisms, which allows us to practise the science of physics (physical values and potentials) to begin with.

Humans did not invent mathematics, humans invented symbolic languages to describe observed universal mathematics of self-ordering patterns from Planck scale and up.

p.s. Note how often bad human mathematics have been written from incorrect interpretation of natural phenomena. At no time did the Universe present a false picture, we just did not see it correctly, at that time.

The geometry and energy potential of this Universe is the essential truth of all things, regardless of the existence of humans and it is able to evolve all dense physical patterns which can be observed, experienced, and described by human mathematical symbolic language as "reality".

"Something" from "Nothing" physical is more logical than "Irreducible Complexity from Nothing"...

 

[river]

The "concept" of mathematics existed long before humans came on the scene.

The Universe functioned flawlessly 14 billion years ago as it does today, thanks to its mathematical underpinnings.

Human symbolic mathematics are a result of observation of natural dynamical phenomena and invented the symbolic language to describe these values and functional mechanisms, which allows us to practise the science of physics (physical values and potentials) to begin with.

Humans did not invent mathematics, humans invented symbolic languages to describe observed universal mathematics of self-ordering patterns from Planck scale and up.

p.s. Note how often bad human mathematics have been written from incorrect interpretation of natural phenomena. At no time did the Universe present a false picture, we just did not see it correctly, at that time.

The geometry and energy potential of this Universe is the essential truth of all things, regardless of the existence of humans and it is able to evolve all dense physical patterns which can be observed, experienced, and described by human mathematical symbolic language as "reality".

"Something" from "Nothing" is more logical than "Irreducible Complexity from Nothing"...

Highlighted

What is observed , experienced is always changing

Further

Neither exist in the first place . To your last statement . Anything with nothing included in the theory is based on non-sense . We should know this by now .

 

[Write4U]

Mathematics basic mathematics was based on accounting . Real physical objects .

When did that "accounting" start and who started it and what symbols were used to describe the relative values of the "accounted" properties?

 

[river]

When did that "accounting" start and who started it and what symbols were used to describe the relative values of the "accounted" properties?

I think it was in ancient Sumar . You had your own mark .

 

[Write4U]

Neither exist in the first place .

So, you're going with the "Something from Nothing" proposition?

What is observed, experienced is always changing

Sure, but the change is always in accordance with some universal mathematical imperative, and we can observe, measure, and mathematically symbolize these changes in "value", from one state (pattern) into another state (pattern).

 

[river]

↑

Neither exist in the first place .

So, you're going with the "Something from Nothing" proposition?

No I'm going with something from something .

 

[Write4U]

I think it was in ancient Sumar . You had your own mark .

And how did these original inventors of "accounting" keep accounts of everything in the Universe?

You are looking at this from a purely subjective human perspective. What about an accounting of the rest of the Universe, before man came on the scene? Before man emerged, there was no defined order to the universe?

You cannot argue that there was no Universal Order before man invented mathematics? Ask a Cosmologist.
They will tell you they are "discovering" the mathematics of the universe, and only "invent" the human symbolic representations of the universal mathematical values and functions being processed.

 

[Write4U]

↑
No I'm going with something from something .

That is not a logical argument, IMO.

 

[paddoboy]

↑
No I'm going with something from something .

You appear to be going with confusion.

So, you're going with the "Something from Nothing" proposition?

Space/time/universe is either eternal/infinite, or had a beginning, which is accepted at the BB. The spacetime evolved from an unknown state at the BB. As Lawrence Krauss pushes [and which I find reasonably plausible] is that perhaps the quantum foam from whence the BB and spacetime evolved is the most realistic definition of nothing that is possible. I mean its pretty damn close to "nothing" that we generally define, and as such far more likely and logical then any ID creation event. The quantum foam is that which is eternal if we accept that definition of nothing.
I mean I find nothing pretty hard to imagine, no space, no time, no quantum foam, no nothing!!!

Sure, but the change is always in accordance with some universal mathematical imperative, and we can observe, measure, and mathematically symbolize these changes in "value", from one state (pattern) into another state (pattern).

Not bad.