What Are Numbers? Philosophy of Mathematics (Elucidations) 

I think one major difference between numbers as abstract objects versus other universals like "blue" or "sweetness", is that "number" has formal, self-consistent definitions. There's no cultural or physiological variation in the way numbers are perceived or used in mathematics. I.e. "numbers are sets recursively containing the empty set (von neumann ordinals) or numbers are successors to nothing. These definitions seem a lot more useful and satisfying than calling numbers an example of another kind of object ("abstract" objects) that we cannot consistently define.

Quantity is recursive boundary conditions. Math is a subset of logic that deals exclusively with relationships of quantity. Logic is relationships that always replicate. Logic is a subset of science. Science is rigor. Numbers are individual instances of quantification.

Just remembered, you should re-upload Ray Brassier's Sellars talk (Nominalism, Naturalism & Materialism)

I took a graduate seminar on Kant with Sutherland years ago. He's excellent. He criticized my mediocre writings in the class very honestly and helpfully, in a way that I've always appreciated.

A thing that blows my mind is that we not only in practice, but also in theory can only use approximately 0 percent of all numbers out there. Most numbers are a number followed by a so called point and an infinite number of digits seemingly put out there at random. Imagine you change one digit in Pi. There will be an infinite amount of numbers between this number and Pi. They are called indescribable transcendentals and they are infinitely more numerous than the numbers we can communicate with math.

1:03 allow me to simplify this confusion. a number is a word in english. one ☝️ is a word in english. 🎉. I hope I answered all your questions. Let me know if there’s anything further I can help you with.

The comments section on every single video about philosophy is a sobering reminder of how much we overestimate our own abilities.

This was blissful to listen to, thank you for sharing your thoughts and knowledge with all of us and myself in particular.

Differences ... Maybe this is the start of brain ...

Numbers are symbols and names we make to do counting. Philosophy, abstract objects, knowledge of etc... are all nonsense terms that sound smart. Numbers are names. That is all.

Abstract concept is just an idea. A mental construct!

Extremely interesting. Have to say, I never before realized (40 years as a philosopher) just how profoundly formative mathematics has been on Philosophy. Thank you so much for this.

Well Ofcourse ... For most knowledges we need to work with the senses but this doesn't mean that the concept created in our mind isn't abstract. And with respect to numbers I know some East philosophers who worked a lot in answering all the questions about abstract objects and proving there are thought entitys In the world. It's time to pay more attention to them and see what they say.

Yes, treating adjectives as if they were nouns is confusing.

Platonic forms....mathematical objects exist as a universal proposition, P. P exists in mind, but P exists external to human mind as mind independent objects. P exists in the ultimate mind, hence God.

Fingers...first experience of quantity

What is a number? A Mathematical Breakthrough God is the designer of our universe, and He is eternal. The proof is in the math. Here is that proof: Infinity = 1/x(delta) + 1. This equation says a number, any number is a set-in space that change with space. In physics this equation reads: Gravity is matter changing with space. It combines Relativity or fractured space with Quantum mechanics or spatial expansion. How dose God fit into this equation? This equation is God's mathematical name. God's name in this equation reads: God's Mind Is Man Changed With God. Breakdown: God's mind is infinite. In math this measure out as the set of infinity In math (1/x) represents a fraction of a whole. Any child is a fraction of a parent and man according to the Bible is God's child. Therefore, man is a fraction of God Change in math is represented by the Greek letter (delta) and it denotes a difference of some kind. Plus (+) in math means: “with” the addition of There is only one God. In mathematics the number “1” represents a single entity. Spelled out: God's Mind (Infinity) is (=) Man (1/x) Changed (delta) With (+) God (1). Scientific Method Step 1 Observation: Math can deliver unbreakable truths such as 2+2 will always = 4 Step 2 Question: Do math and Divinity share a common truth? Step 3 Hypothesis: If God exist, He should be found in the house of mathematics. Step 4 Prediction: God's Mind Is Man Change With God is an equation Step 5 Test: Any number (Infinity) is (=) a set-in space (1/x) that change (x^2) with (+) space (1)) Note: "X" describes any set, (1) describes any kind of space physical or otherwise This equation tells us why 2 feet is not the same as 2 inches. Both distances are measured out as 2 units of space but there is a change or difference between both units. They are each sets in a space of distance, but they represent changes in their measurement of distance. Step 6 Iterate: New look at what makes up reality. Reality consists of 3 domains of space. a. Fractured space or matter b. spatial expansion a.k.a time and energy c. Complete or unbroken space/information Step 7 Conclusion: We now know Infinity is real therefore the value in enumeration demand God exists otherwise the domain for enumeration would be incomplete. We know the domain for enumeration is complete because we can count. God must be able to count too all the way to Infinity because His mathematical name tells us what is any number. Cantor's Mistake George Cantor known as the father of set theory was wrong. There are no sets of numbers larger than Infinity. Cantor's mistake was he did not see that "change" is a subset within Infinity. Cantors one on one correspondence between sets of numbers is wrong. Cantor used only one description of a number from one set to match out or with a number from a different number set. Example. Cantor said the whole number set was smaller than the integer number set. This is how he made his measurement. Take the integers 2.1 and match it with the whole number 1. Then match 2.11 with the whole number 2. Then match 2.111 with the whole number 3 and so forth. In this view we would run out of whole numbers when we get to the integer 3.1. This is Cantor's big mistake! A correct set correspondence method Here is a better way to measure these two number sets. Match 2.1 with say 2. In the next sequence match for 2.1 we could match this integer with 4/2 or 5-3 or the square root of 100 divided by the square root of 25. The point being we can match any description for the number 2 to continue this [integer- whole] number matching sequence forever. In this way we could then match the integer 3.1 with 9/3 or 7- 4. Again, if Cantor had understood that change describes what any number looks like he would have known there can be no numbers larger than Infinity. Now that we have the knowledge of what is a number. My question is why now? Throughout all of man's conceptual use and beneficial outcomes from using numbers why is it we did not see the anatomy of a number until today? How is it possible that we have been unable to see that numbers do more than describe our physical reality, but they also describe our existence outside our perceived notion of reality. Numbers like truths don't lie. Yes, we are creatures of the cosmos and whatever makes up the cosmos is in many ways our inheritance. Learning is a part of our cosmos and we do know great discovery comes about over time. There is not always a discovery that changes the world, yet this equation is fundamental to all of existence and it comes from the creator of this existence. So, again why has this knowledge been away from us so long? Here is my thinking. Mind you my thought in asking then trying to understand this event is not based in math or science but in faith. We have been blessed, but I also believe we should be concerned for what is coming. Very highly speculative: Infinite gravity suggest we may be living inside a black hole that is internally expanding. 1/x(delta) may explain why inflation happened. The case maybe that inside a black hole space is cracked and stretched due to the compression and pulling of space by the difference in layer spatial collapsing. Outside space coexisting with points of space already consumed into an infinitesimal boundary create symmetry and this symmetry get to spread evenly as matter. Our universe becomes virtual and expanding. Zero in this context equals the difference in symmetry. A zero field is in this case a field of opposites. One field is collapsing while its opposite is expanding. This speculation does not rule out God. If it is how our universe happen and is evolving it is best understood as a tool used to do the work needed to fashion existence and life. We should not be afraid of knowing God's working regardless as to how He choose to do those works. Whether it be evolution or any other methodology in His works the truth is we are here to learn and practice those learnings. If doubt remain then please answer this question. What is a number? Google it if you need help. Infinity says a number is both qualitatively and quantitatively a set-in space that change with space. Isn't this what we do when we count or measure anything at all. Yes, this is exactly what we do when we measure or count anything. In counting we take a memory or a something we name and put that something into an order of some kind in the space of our mind. We can arrange that something into least to greatest or whatever meets our satisfaction but the fact that we put anything into an ordered sequence is in effect making a change happen. So, there we have it. A set in the space of our mind changes with the mind. At one moment the set is 1 and at the next moment it is 2 then 3, 4, 5 and so on. Conclusion why would God give us his love scientifically and mathematically if he did not want us to know HIM? Fighting over whether Creationism or Evolution is the right answer as to why we are here is the wrong picture both have a place with God. william.mabon@yahoo.com