The specification of a prime number (i.e., a description of how to identify it) is:

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

The Fibonacci numbers are characterized by the fact that every number after the first two is the sum of the two preceding numbers with the first two numbers being 1 and 1.

The sequence starts as ->

1, 1, 2, 3, 5, 8, 13, 21, 55, 89, 144

The donkey sequence (defined by me) is the sequence of numbers where a number N in the sequence is equal to the sum of twice the number preceding N plus 3

1, 3, 9, 21, 45, 93,

These number sequences are based on specifications (descriptions created by men) of how to identify valid numbers in the sequence.

Are these sequences objects?

]]>Thanks for your comments, Ed. I am researching the various philosophical positions on whether numbers exist and hope to publish something about it here. The second part of my comments on morality will appear soon.

]]>> The number three is now, was always and always will be a prime number.

The number three and “prime number” are concepts. Both are based on mathematical rules (concepts) created by men. Attempting to think of them as something more implies something similar to the “forms” that Plato proposed.

> But, like physical objects, mathematical/logical objects persist.

What is a mathematical object? Can I weigh it, measure it, pick it up?

See this blog on whether numbers exist:

http://scienceblogs.com/evolutionblog/2012/10/02/do-mathematical-objects-exist/

Mathematical objects exist in a fictional world created by mathematicians. For example, in the context of modern abstract algebra I know what it means to ask if finite, simple groups exist. But if you ask whether finite, simple groups existed prior to the establishment of modern abstract algebra, then I don’t know what you mean. It’s like asking if Sherlock Holmes existed prior to the writings of Arthur Conan Doyle.

The general view of mathematics I am defending is known as fictionalism. Its main rival is Platonism, which holds that mathematical objects exist independently of anyone’s ideas about them.

My reply to someone who insists that mathematical objects exist in some non-spatiotemporal realm that we come to understand through mathematical research is just to stare at him blankly. I don’t understand what he’s trying to convince me of. The existence of physical objects makes sense to me. The existence of abstract objects that cannot possibly be reduced to some physical phenomenon does not make sense to me. The concept of existence does not seem helpful here.

A comment at the end of the blog on numbers:

What we colloquially know as Numbers are, just like you said, just symbols for an abstract idea.

Likewise, words (collections of symbols) don’t really exist. They just represent the abstract and quite complicated biochemistry in our brains that make us “recognize” a real physical object.

EG. If i write “You can sit down in that chair”, you cant really do that, because in this case the chair is just some symbols on a webpage or piece of paper. However you instantly recognize the physical object even without me pointing to a real chair.

[END OF QUOTES from blog]

See https://jakubmarian.com/are-mathematical-objects-real/

The point is—if our mathematics is not objective but rather a construct of one particular species, it doesn’t make much sense to say that mathematical objects as we define them exist in any objective sense.

> Whenever we think of them they appear to us just as they did before, somewhat as a tree does when we open our eyes after closing them.

The symbol “thirst” has a meaning in the English language. The meaning Is described in a dictionary We can close our eyes (or even sleep for a while) after which the symbol still has a meaning. Is thirst an object or simply a concept?

The number 3 is a symbol that has a meaning defined by mathematical axioms.

Although the term “mathematical object” is used extensively, the use of “mathematical concept” would be more appropriate for a philosophical discussion.

> Mathematical/logical entities seem to exist independently of us as well, although they do so differently from physical objects.

Do they? Do they exist independent of the human brain? We may write a string of symbols on paper, but that string has no meaning except when interpreted by a human brain. The symbols themselves are not mathematical objects. The symbol “+” is the symbol interpreted as the addition operation, not the operation itself.

> Do we construct it? I find it more reasonable to believe that, like physical objects, mathematical/logical objects exist independently of us.

If I stop thinking about the sum of 2+2, does it continue to exist? Where? In my memory? Is a memory or a thought an object?

Throughout the history of mathematics and logic, axioms have changed. Do the old “objects” based on obsolete (and usually faulty) axiomatic systems still exist?

For example: After the discovery of paradoxes in naive set theory, such as Russell’s paradox, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms are the best-known. A mathematical system is based on a set of axioms that have been created by humans.

**Morality – Objective or Relative?**

Philosophers have long debated the rational basis for moral judgments, but in fact, most of our moral judgments are not made rationally.

A person’s temperament is strongly determined by inheritance (genetics) but can be somewhat influenced by nurture (environment). Humans, except for a very small percentage, are naturally empathetic. Most culture and religions have some form of the Golden Rule (ethic of reciprocity) which seems to be a rational direction for morality. However, less rational moral strictures have originated from religions, personal biases of authorities, groups with common characteristics and others.

https://www.iep.utm.edu/moral-re/

Relativistic views of morality first found expression in 5th century B.C.E. Greece, but they remained largely dormant until the 19th and 20th centuries. During this time, a number of factors converged to make moral relativism appear plausible. These included a new appreciation of cultural diversity prompted by anthropological discoveries; the declining importance of religion in modernized societies; an increasingly critical attitude toward colonialism and its assumption of moral superiority over the colonized societies; and growing skepticism toward any form of moral objectivism, given the difficulty of proving value judgments the way one proves factual claims.

A common, albeit negative, reason for embracing moral relativism is simply the perceived untenability of moral objectivism: every attempt to establish a single, objectively valid and universally binding set of moral principles runs up against formidable objections. A more positive argument sometimes advanced in defense of moral relativism is that it promotes tolerance since it encourages us to understand other cultures on their own terms.

Rorty & Rawls

Rorty, Richard. *Objectivity, Relativism, and Truth: Volume 1: Philosophical Papers*.

On my view, the frequent remark that Rawls’ rational choosers look remarkably like twentieth-century American liberals is perfectly just, but not a criticism of Rawls. It is merely a frank recognition of the ethnocentrism which is essential to serious, nonfantastical thought. I defend this view in “The Priority of Democracy to Philosophy” and “Postmodernist Bourgeois Liberalism” in Part III of this volume.

The tenets of the Satanic Temple

These include the concepts of the Golden Rule and Rawls (e.g., John Rawls first principle: Each person is to be granted an equal right to the most extensive basic liberty compatible with a similar liberty for everyone else.)

https://thesatanictemple.com/

There are seven fundamental tenets.

1. One should strive to act with compassion and empathy towards all creatures in accordance with reason.

2. The struggle for justice is an ongoing and necessary pursuit that should prevail over laws and institutions.

3. One’s body is inviolable, subject to one’s own will alone.

4. The freedoms of others should be respected, including the freedom to offend.

5. To willfully and unjustly encroach upon the freedoms of another is to forgo one’s own.

6. Beliefs should conform to our best scientific understanding of the world. We should take care never to distort scientific facts to fit our beliefs.

7. People are fallible. If we make a mistake, we should do our best to rectify it and remediate any harm that may have been caused.

Every tenet is a guiding principle designed to inspire nobility in action and thought.

The spirit of compassion, wisdom, and justice should always prevail over the written or spoken word

Having said that; when I read your comments, I kept flashing back to a youtube video I saw about savants.

When two specific parts of the brain cross activate it is called “synaethesia”. The young man in the video can see numbers in his head as colors, textures, forms and landscapes. He interprets these different shapes, patterns etc. as if they appear as numbers (they don’t explain how he arrived at their association with the numbers). There is the question, if he does not mentally calculate these mathematical equations then how do they appear? Do numbers, colors, shapes meld into a singularity as in our dreams which make no sense to our waking reality but do in the dreaming mind? If so then are these integrations only limited by our physical structure but at one time, say before we were born, did they exist as a blanket of consiousness that is made independent only by our compartmentalized body structure?

If we go down this singularity path of maybe an ultimate universal consciousness, then morality too has structure in a form yet unrecogized by us mentally except through emotions which are composed of chemical reactions. These reactions often get described by color or texture. We feel blue; there was a black hole in him or her; they made my skin crawl; it gave me goose bumps. Perhaps these colors and textures of morality exist but we just haven’t fine tuned ourselves to be aware of them because they too come naturally and without effort.

Just a crazy idea I had.

Enjoy- https://youtu.be/PPySn3slfXI

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