So, what's science then?

Albert Einstein on Metaphysics and Philosophy

Remarks on Bertrand Russell’s Theory of Knowledge

In the evolution of philosophical thought through the centuries the following question has played a major role: what knowledge is pure thought able to supply independently of sense perception? Is there any such knowledge? If not, what precisely is the relation between our knowledge and the raw material furnished by sense impressions?

There has been an increasing skepticism concerning every attempt by means of pure thought to learn something about the ‘objective world’, about the world of ‘things’ in contrast to the world of ‘concepts and ideas’. During philosophy’s childhood it was rather generally believed that it is possible to find everything which can be known by means of mere reflection. It was an illusion which anyone can easily understand if, for a moment, he dismisses what he has learned from later philosophy and from natural science; he will not be surprised to find that Plato ascribed a higher reality to ‘ideas’ than to empirically experienceable things. Even in Spinoza and as late as in Hegel this prejudice was the vitalising force which seems still to have played the major role.

The more aristocratic illusion concerning the unlimited penetrative power of thought has as its counterpart the more plebeian illusion of naive realism, according to which things ‘are’ as they are perceived by us through our senses. This illusion dominates the daily life of men and of animals; it is also the point of departure in all of the sciences, especially of the natural sciences.

As Russell wrote;

‘We all start from naive realism, i.e., the doctrine that things are what they seem. We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow are not the greenness, hardness, and coldness that we know in our own experience, but something very different. The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself.’

Gradually the conviction gained recognition that all knowledge about things is exclusively a working-over of the raw material furnished by the senses. Galileo and Hume first upheld this principle with full clarity and decisiveness. Hume saw that concepts which we must regard as essential, such as, for example, causal connection, cannot be gained from material given to us by the senses. This insight led him to a skeptical attitude as concerns knowledge of any kind.

Man has an intense desire for assured knowledge. That is why Hume’s clear message seemed crushing: the sensory raw material, the only source of our knowledge,through habit may lead us to belief and expectation but not to the knowledge and still less to the understanding of lawful relations.
Then Kant took the stage with an idea which, though certainly untenable in the form in which he put it, signified a step towards the solution of Hume’s dilemma: whatever in knowledge is of empirical origin is never certain. If, therefore, we have definitely assured knowledge,it must be grounded in reason itself. This is held to be the case, for example, in the propositions of geometry and the principles of causality.

These and certain other types of knowledge are, so to speak, a part of the implements of thinking and therefore do not previously have to be gained from sense data (i.e. they are a priori knowledge).
Today everyone knows, of course, that the mentioned concepts contain nothing of the certainty, of the inherent necessity, which Kant had attributed to them. The following, however, appears to me to be correct in Kant’s statement of the problem: in thinking we use with a certain right, concepts to which there is no access from the materials of sensory experience, if the situation is viewed from the logical point of view. As a matter of fact, I am convinced that even much more is to be asserted: the concepts which arise in our thought and in our linguistic expressions are all- when viewed logically- the free creations of thought which cannot inductively be gained from sense experiences. This is not so easily noticed only because we have the habit of combining certain concepts and conceptual relations (propositions) so definitely with certain sense experiences that we do not become conscious of the gulf- logically unbridgeable- which separates the world of sensory experiences from the world of concepts and propositions. Thus, for example, the series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences. But there is no way in which this concept could be made to grow, as it were, directly out of sense experiences.

As soon as one is at home in Hume’s critique one is easily led to believe that all those concepts and propositions which cannot be deduced from the sensory raw material are, on account of their ‘metaphysical’ character, to be removed from thinking. For all thought acquires material content only through its relationship with that sensory material. This latter proposition I take to be entirely true; but I hold the prescription for thinking which is grounded on this proposition to be false. For this claim- if only carried through consistently- absolutely excludes thinking of any kind as ‘metaphysical’.
In order that thinking might not degenerate into ‘metaphysics’, or into empty talk, it is only necessary that enough propositions of the conceptual system be firmly enough connected with sensory experiences and that the conceptual system, in view of its task of ordering and surveying sense experience, should show as much unity and parsimony as possible. Beyond that, however, the ‘system’ is (as regards logic) a free play with symbols according to (logically) arbitrarily given rules of the game. All this applies as much (and in the same manner) to the thinking in daily life as to the more consciously and systematically constructed thinking in the sciences.

By his clear critique Hume did not only advance philosophy in a decisive way but also- though through no fault of his- created a danger for philosophy in that, following his critique, a fateful ‘fear of metaphysics’ arose which has come to be a malady of contemporary empiricist philosophising; this malady is the counterpart to that earlier philosophising in the clouds, which thought it could neglect and dispense with what was given by the senses. … It finally turns out that one can, after all, not get along without metaphysics.

(Albert Einstein, Ideas and Opinions, 1944)

Thanks for sharing that, it’s a pretty good read. After reading it, I copied it into a doc and printed a copy, it’ll make a good companion for my doggy walks today.

You know, on a simple level I touch on this age old dilemma,
heck, I dare say, I stab right to the heart of it with my little Appreciation for:

The Physical Reality ~ Human Mindscape divide,
with it’s accompanying deeper appreciation for me, myself, you, yourself, being a biological product of Earth’s evolutionary processes.

That within your body you have countless direct connections and memories to previous worlds of reality, that your consciousness can never touch.

Still, our “unconscious” is a vibrant happening world of activity and interaction.

*Not revelation for science, but important for us humans and how we think about things and ourselves.

:+1:t2:

I was just rereading and this smacked me, it’s almost like the “infinitude” thing. Words more intent on reassuring then explaining.

1 Like

Reread it again and take note of the words “known expressed function of spacetime”

Spacetime

Mathematical model combining space and time

Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur. Wikipedia

I don’t think I have ever used the term “infinitude”.

Wow! Then writers must warp spacetime.

No, gravity warps spacetime. It is a known universal function (constant).

Earlier you said this:

“It” is referring to logic. “Logic is the essence of spacetime” is a category error, or something.

This one:

I’d call that a deepity. Apparently profound but expresses something trivial. A function is something that has an input and an output and shows the relationship. You’ve shown that graphic a few times. So, logic does that, okay. That it’s not a property of the mind is an additional fact. I don’t get what you mean.

1 Like

No category error.
Logic is the 1. relationships between rigorously defined concepts and of mathematical proof of statements.

Mathematical logic

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.

Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert’s program to prove the consistency of foundational theories.

Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory.

Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.
Mathematical logic - Wikipedia

Nothing in there about spacetime. Try it from other direction. What is spacetime?

1 Like

I was being sarcastic because you were talking about words … "words “known expressed function of spacetime”. It’s how you wrote it that triggered my sarcasm.

Spacetime is the emergence (BB) of a geometric object consisting of 3 dimensions permitting the self-formation of quanta (values) and physical interactions via mathematical permissions and restrictions.

The fabric of space-time is a conceptual model combining the three dimensions of space with the fourth dimension of time. According to the best of current physical theories, space-time explains the unusual relativistic effects that arise from traveling near the speed of light as well as the motion of massive objects in the universe.

WHO DISCOVERED SPACE-TIME?

The famous physicist Albert Einstein helped develop the idea of space-time as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton’s laws of physics described the motion of massive objects, while James Clerk Maxwell’s electromagnetic models explained the properties of light, according to NASA.

Related: Newton’s Laws of Motion

But experiments conducted at the end of the 19th century suggested that there was something special about light. Measurements showed that light always traveled at the same speed, no matter what.

And in 1898, the French physicist and mathematician Henri Poincaré speculated that the velocity of light might be an unsurpassable limit. Around that same time, other researchers were considering the possibility that objects changed in size and mass, depending on their speed

SOL imposes a mathematical order to all physical actions, such as limits and permissions of physical interactions and wave functions.

Can anything travel faster than light?

Think again. For centuries, physicists thought there was no limit to how fast an object could travel. But Einstein showed that the universe does, in fact, have a speed limit: the speed of light in a vacuum (that is, empty space). Nothing can travel faster than 300,000 kilometers per second (186,000 miles per second).

And there is your mathematical limit of allowable interactions (and it is not 186,000 miles per second that is the controlling factor, it is the “limit” imposing “order” that is the determining factor).
Without inherent universal mathematical permissions and restrictions on physical actions and interactions, there is only chaos.

It’s right there in your words, it’s a model. And what’s mathematical permissions"?

A function that is mathematically permitted

Domain and Range

In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions.

Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above.

We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Domain and Range | Algebra and Trigonometry

Nature does not need to think about that. An action or function is mathematically permissible or restricted. In a gravitational field an object cannot fall up, it is mathematically (physically) not permitted. It always falls down because it is not only permitted to fall down, but the mathematics of the function control the rate of descent.

Galileo’s inclined plane experiment clearly shows the mathematics of the function.

No the math isn’t a force. It doesn’t control anything. Every post you make has the language the negates your proposition. “Model, assumption, premise, meaningful”. “What’s permitted” <> “permission”.

And if it’s not permitted, we invent new math, that will permit new conceptions and functions.

1 Like

No, if something is not mathematically permitted it cannot happen. It has nothing to do with human mathematical symbolism or modeling.

Example: trying to put a square peg in a round hole, it can’t be done. It is mathematically (physically) not permitted.

Ask a simple question. What does Human mathematics symbolize?

Mathematical notation

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way.

For example, Albert Einstein’s equation E=mc^{2} is the quantitative representation in mathematical notation of the mass–energy equivalence.

Mathematical notation was first introduced by François Viète at the end of the 16th century and largely expanded during the 17th and 18th centuries by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler.
Mathematical notation - Wikipedia

My entire point, it symbolizes. Using logic, math <> spacetime.

In physical theories prior to that of special relativity, mass and energy were viewed as distinct entities.

So before Einstein the math permitted that, now it doesn’t.

It appears you will never see the language in the same way I do. You say it’s not about symbolism, then provide a definition that says it’s symbols.

What I’d like, is that you stop turning every thread into an “it’s all math” thread, or microtubles, or whatever.

Did Humans Invent Mathematics, or Is It a Fundamental Part of Existence?

PHYSICS24 November 2021
BySAM BARON, THE CONVERSATION

(FlashMovie/Getty Images)

Many people think that mathematics is a human invention. To this way of thinking, mathematics is like a language: it may describe real things in the world, but it doesn’t ‘exist’ outside the minds of the people who use it.

But the Pythagorean school of thought in ancient Greece held a different view. Its proponents believed reality is fundamentally mathematical.

More than 2,000 years later, philosophers and physicists are starting to take this idea seriously.

As I argue in a new paper, mathematics is an essential component of nature that gives structure to the physical world.

Honeybees and hexagons

Bees in hives produce hexagonal honeycomb. Why?

According to the ‘honeycomb conjecture’ in mathematics, hexagons are the most efficient shape for tiling the plane. If you want to fully cover a surface using tiles of a uniform shape and size, while keeping the total length of the perimeter to a minimum, hexagons are the shape to use.

[Charles Darwin reasoned](Secret of bees' honeycomb revealed › News in Science (ABC Science)) that bees have evolved to use this shape because it produces the largest cells to store honey for the smallest input of energy to produce wax.

The honeycomb conjecture was first proposed in ancient times, but was only proved in 1999 by mathematician Thomas Hales.

more… Did Humans Invent Mathematics, or Is It a Fundamental Part of Existence? : ScienceAlert

You are so enamored with evolution via natural selection, how is it that you miss the natural selection of mathematically efficient patterns. Bees don’t know mathematics, but they know how to build honeycombs using the MOST EFFICIENT mathematical structure.

How would they know the Fibonacci Sequence?

Scientists Crack the Mathematical Mystery of Stingless Bees’ Spiral Honeycombs

The waxy architectural wonders seem to grow like crystals


Mathematically speaking, the honeycombs grow like crystals.

The same mathematical model that explains how crystals grow can also explain how tropical stingless bees build honeycombs in spiraling, multi-terraced shapes, according to a study published on Wednesday in the [Journal of the Royal Society Interface]
(https://royalsocietypublishing.org/doi/10.1098/rsif.2020.0187).

Bees from the genus Tetragonula specialize in sophisticated feats of architecture built from hexagonal beeswax cells. Each individual cell is both the landing spot for an egg and a building block for structures that can grow up to 20 levels high, Brandon Specktor reports for Live Science. Stingless bees’ hives can come in several shapes, including stacks of circles in a bulls-eye, a spiral, a double spiral, and a group of disorderly terraces.

So bees use not only hexagonal honeycombs but also arrange them in spirals in accordance to the Fibonacci Sequence, a further efficient use of small areas.

They don’t. They have some instinct that combines with others to create the pattern.

It’s an interesting topic, but it’s not this topic. Your article is about the question. Your posts are about how sure you are that you’re right. That’s not inquiry.

And how did that instinct evolve? Natural selection of the most efficient patterns allowing for most efficient storage in a limited area. The bees stumbled on this pattern and the increased efficiency allowed the bees to store more honey and increase the population without requiring larger facilities.
That is just one type of evolution via natural selection.

Nature selects for mathematical efficiency. Human mathematics are based on that principle.

I am describing what I believe science to be. How is that not on-topic?