Once a concept is defined within an existing framework of mathematics, in a sense all that logically flows from it is potential, awakened by diligent investigations and discovery. — jgill

The way I put it is that numbers are real, but they're not existent in the sense that phenomenal objects are existent, — Wayfarer

Yes, mathematical potential exists because our forms of mathematics exists - linear equations, set theory etc. So the question is, where is this potential? Is it merely inside our skulls or does it exist independently of the human brain? Is it universal?

I disagree with him entirely-

The problem, though, is that this world is essentially full of junk. The vast majority of it is simply useless, and of no interest to anyone whatsoever. — Streetlight

There is no junk, there is only mathematical truth. An example is chess: Chess is a concept built on a few simple ideas and rules. Once these ideas exist chess exists, potentially, in its entirety. But this entirety contains good chess and 'bad' chess. All possible games of chess from genius to silliness. They exist because chess as a concept exists. If math exists all math exists potentially. Is there a difference between an actual Platonic realm (containing good math) and a potential Platonic realm (containing 'junk')?

the idea of natural numbers (1, 2, 3...). Rovelli basically asks: why does anyone think natural numbers are natural at all? We certainly find it useful to count solidly individuated items, but he notes that what what actually counts as 'an object' is a very slippery affair: "How many clouds are there in the sky? How many mountains in the Alps? How many coves along the coast of England?". — Streetlight

Very woolly thinking here. Numbers exist as an abstraction, there is no need to have 2 or 3 actual things to have numbers:
/ = 1
// = 2
/// = 3 etc.
If all mathematics exists then it is natural for our experience to awaken (induction) particular aspects of mathematics. eg. If there are sheep their multiplicity might awaken numbers in our intuition. If we lived without a need for numbers their existence might not have been awakened by our experience. But numbers would exist anyhow.

As for the Platonic realm - does it mean that the number 3 exists in some concrete reality or does it mean that in the depths of mathematical reality there is a potential for '3' to exist - depending on what events bring it into existence? That is, is there a mathematical potential, above our specific forms of math, that makes these forms of math possible? If we say mathematics 'exists' we have to be very clear on what we mean by 'exist'.

The concept of chess can exist without a single game of chess being played in 'real' terms. In this situation, does chess exist if it exists as a concept but no games are ever played? What is the difference between a game of chess that is played and one that is merely possible, because the concept of chess exists? I think the Platonic realm does exist in the sense that it makes all kinds of math possible but not necessarily realized. I don't think he is getting very far by making a distinction between math that we have become aware of and math that might have been if the world had been different.

Maybe the Platonic realm is God's Mind, which contains all possible forms of math in the way the rules of chess makes all chess games possible.

It is the difference between a synonym and a metaphor. A synonym does not necessarily exhibit the nature of its cause but a metaphor or analogy more closely manifests the nature of the thing it represents.

Total possible universes = every possible arrangement of Plank spaces and Plank times?

I agree entirely. The loss of good language will be our undoing.

For my filthy (crypto) lucre ...
1 The world is all that is the case.
1.1 The world is the totality of facts, not of things.

[ ... ]

1.13 The facts in logical space are the world.
1.2 The world divides into facts.
— WItty, TLP (1921)
An analoguous approximation of the metaphysical to the physical: (contra Aristotlean e.g. "only continuum, no vacuum, geocentric" dogmas) classical atomism ~ RQM; logical atomism ~ information entropy; etc. Definitional questions of "matter" and "energy" are, btw, methodologically vacuous. — 180 Proof

The problem is with the word 'divide'. The connections between things are as important as the things themselves and when things are severed apart they lose meaning. This is why reductive science is inadequate and destroys meaning.

n is known and its factors, p and q are unknown. p or q are to be found.

n is the modulus. If pq = n the algorithm is designed to find p or q.

Mod n finds the remainder on division.

eg 114 = 14 (mod 100) because 14 is the remainder on division by 100.
14 o'clock = 2 o'clock (mod 12), on a 12 hour clock. Modular arithmetic is sometimes called clock arithmetic.

Search for Pollard's Rho Algorithm

Yes, so we need to qualify words like 'energy' and 'matter' and keep them in context.

Interestingly Pollard's Rho method uses this kind of iteration and waits for circularity to factor integers-


$x = 3$

$f(x) = x^2 + 1 (mod n)$

$f(x) = x_{1}$

$f(x_{1}) = x_{2}$

$f(x_{2}) = x_{3}$ etc

Isn't "energy" material in principle? — Gregory

It depends on how you define matter. For me, usually, matter is everything from the hydrogen atom up: things that are constructed. There is an expression "material particle" but this only means it is a constituent of a material object, it does not mean it is a material thing. If everything is matter nothing is, if you get my drift...

Matter does not exist as a substance in the way our (crude) senses convince us. The substance of matter is energy and matter - when we mean a physical object - is only a pattern in a field of energy. The physical universe is not really there in the way we naively imagine. All that is there, in terms of substance, is energy. Material patterns can dissolve away leaving only energy; the table can decay and be absorbed into the soil; the atom can dissolve into energy; even the black hole evaporates. All that is there is energy and temporal patterns.

I think self and ego are not the same. The self is one's individuality, the ego is self-ish or self-centered. Love looks out and loves what is not self: one loves poetry, art, nature, another being... these are not self. Ego looks inward and loves the self. Love and ego are opposites. Too much inward looking ego becomes pathological; the megalomaniac, the tyrant etc.

Is it already too late? — Xtrix

The narrative we are being given is that we have a global warming problem and we have to fix that and move on to 2050 and beyond. This narrative is false. We have a constellation of problems and all of them are hitting at the same time and we have to solve them at the same time (as in right now). So yes, it is not likely we will solve all this stuff in time.

1. Fish stocks have collapsed. 1 bn. people in South Asia depend of fish for their livelihood.
2. Agricultural soil is now so depleted there are only 60 harvests left
3. Natural resources are getting scarce
4. Urbanization
5. Pollution
6. etc.

Can we solve all this stuff now before it gets to 1.5 degrees excess warming?

If not there's Catabolic Capitalism.

↪Wayfarer I like that quote of Ed Feser a lot. — RogueAI

Yes. Reductive science takes things apart and studies the parts but in doing so it has broken all connections. But connections between parts are as important as the parts themselves. It is these connections that make the whole and meaning is in the whole, not the parts.

Yes, 99.999% of what we do is plagiarism!

I think the question ought to be, what is rational thinking, because by introducing reason you have at least some common ground to start with. Otherwise it's so broad as to not be meaningful, 'thinking' in the loose sense being simply all of the spontaneous activities of any mind. — Wayfarer

Yes, thought is being; I think therefore I am. When we think our minds move through eternity/God, as a fish moves through the sea. Intellectual philosophy is an activity of the intellect.

Trick question. As long as you are talking about tiny triangles the sides add up to more than the diagonal. No matter how small they get. So the only question is what do the sides add up to in one tiny triangle. Then multiply by the number of triangles to get 2. A triangle is not a diagonal!

Is violence ethical, and if so, when and where? — john27

Yes. The Battle of Britain.

I don't think science would collapse. It would be like the beginning of the last century when they thought the subject of science was this 4 dimensional universe of macroscopic objects. Then the quantum cowboys came along and discovered weird things and it turned out that the ordinary physical universe is only a simple thing compared to the weird thing.

Likewise with mind-brain. If they discover non physical mind, brain stuff will seem relatively simple.

If there is no free will accountability becomes a mere social convenience and not a moral issue.

The observation here is quite specific: hell is immoral. The simple answer is that assuming god is good, then there is no hell, and various popular forms of christianity and other religions are simply wrong. — Banno

What if good ultimately involves allowing creation to risk suffering by being free?

The essence of the doctrine of The Fall is disobedience. And disobedience is its own punishment.
— EnPassant

That's like saying that drugs are bad because one disobeyed the order not to take them.
And not perhaps because they are toxic substances that mess up one's body. — baker

What I mean is that it leads to its own punishment.

A rich and powerful person can kill, rape, and pillage, and it has no bad consequences for them

What happens to them in the next life?

Scientism is the view that science is the best or only objective means by which society should determine normative and epistemological values. — Raymond

I think in modern times the line between hypothesis and scientific knowledge is being blurred. The theory of evolution is often presented as done and dusted with only some loose ends to be tied up. The reality is, there are many gaping holes in it. (The theory is right in some aspects but it is far less complete than a lot of science writers pretend.) Another problem is the gene-of-the-gaps theory: all kinds of things are routinely explained away with vague references to genes. As a result people are wont to say things like "Cricket goes way back in our family, it is in our genes.". Likewise with the 'alcoholic gene'. That was very popular some years back but has gone out of fashion now. The line is being blurred between science and scientism and this is not a good development.

The problem is not science, it is the abuse of scientific knowledge, among other things. But scientism probably exacerbates anti science because it blurs the distinction between science and non science.

The question has to do with what the world is. Theists maintain there is a spiritual reality to the world. If the materialist denies the existence of that world it hardly exists for them in the same way as it does for the theist. So if you say theists and atheists live in the same world you deny the existence of the spiritual reality of the world.

It seems to me that 'equal rights' somehow got confused with 'equality'. People are not equal. Is an idiot equal to Einstein? No. A man equal to a woman? No, there are hormonal and emotional differences. Is a bird equal to a fish? Be careful how you answer or you might end up in jail...

Believers understand the world differently.
— EnPassant

So do bats, I'm told.

How can you tell? — Banno

That is my point. Do bats live in our world? The world of art, literature, commerce, finance, politics? If bats are not conscious of these worlds they can hardly live in them. And that's my point, it is a question of consciousness and whether theists are conscious in a different way.

Is faith exactly a matter of your opinions on certain questions (the reality of God, hell, and so on)? Is it just some propositions you assent to? — Srap Tasmaner

As said above, faith has more to do with consciousness than teachings or intellectual beliefs.

Believers do not experience a different world. — Banno

Believers understand the world differently. Even a mathematician or artist experiences the world differently. That is because they are conscious in a different way and is that not equivalent to experiencing a different world, if consciousness allows us to enter realms of reality that are beyond normal experience? But that would require levels of being beyond ordinary, everyday experience and this is exactly what theists would say exists.

What you are really saying is that a different world does not exist. More precisely, this physical world is all there is. But even some mathematicians believe mathematics is a 'Platonic' realm that is in some way real.

I am a theist, an artist and I study mathematics. These three aspects of consciousness do lead into levels of being that transcend the physical world.

As to Christianity, might we agree there was a time in the world when there was no such thing? And then, following on some events, there were such? And some of those meeting and considering the matter, established criteria for being Christian? And just these having an original claim as to what being a Christian is and isn't? — tim wood

I'm afraid the church is like a wagon that picks up a lot of sticky things on its wheels as it goes along. Christianity is full of pagan or useless ideas because some people like to decide what God wants before He even has a chance to tell them. One needs to be very discerning when it comes to what God wants of us.

As to Christianity, might we agree there was a time in the world when there was no such thing? — tim wood

The essence of Christianity is 'I am the Way.' The Tao is the way. So is Buddhism. Enoch, in genesis, 'walked with God'. There is a way of being and the way may have existed from the beginning.

:100:

And when you get to the pearly gates and Peter himself asks your warrant for presenting yourself, are you going to say that you're there because Joe the whackdoodle sent you? That is, claimed you were a Christian. — tim wood

That depends on what you mean by Christian. If by that you mean a person who lives according to God's Will - and indeed, if I live by God's Will - I guess I will have avoided many disasters and tears.

This seems to be the related paper: Divine Evil — Banno

I read the first few pages. The writer judges God by human lights and that is suspect from the beginning. The problem of evil is concerned with free will and while free will exists it is possible for people to misuse it. It is not that God punishes anyone - 'punishment', in scripture, seems more like a rhetorical admonishment, or warning, from God. But reality must be more complex than simple scripture can tell us. (the writer seems too literal about scripture)

The essence of the doctrine of The Fall is disobedience. And disobedience is its own punishment. You can see this any day of the week: the teenager is told, repeatedly, of the dangers of drug abuse. Does that deter him? Very often no. He will rebel and he will create his own hell on earth, because that is what hell is, our own creation. People create their own hell every day of the week.

But can't God show us how to live wisely so we won't turn our lives into hell? This is what religion is meant to do.

But people don't always listen. They want to live by their own lights even if that leads to hell. They will drink even if they risk ending up in the gutter. They will commit crimes even if that risks ending up in jail. God is the light by which we should live and if we turn away from it there is only darkness. Some are determined to go their own way. "My way or no way" - self will. No matter what the danger and no matter how many warnings "I will not serve". So be it.

- There are very few (or no) syntactic mistakes.
- The ideas are clear and well-written.
- It says something philosophically interesting.
- There are no logical fallacies.
- There is no plagiarism.
- The paper is on-topic.
- Forget about word counts, fonts, APA format, and all other 'peripheral' issues.

Does the paper get an "A?" Why or why not? — jasonm

Not necessarily. Logic and truth are not the same thing. A statement can be - or seem - logical but it may not be true.

Premise: Elephants fly.
Logic: Elephant poo falls from the sky.

Logical but not true. And that's one of the most difficult things about philosophy; the logic can be correct but a premise can have almost undetectable flaws.

What I am saying is that all opinion is subjective (of the subject). Agreement produces a sort of "intersubjectivity", whereby we say one's opinion is the same as another's. But intersubjectivity is still dependent on subjects, so it cannot support a definition of "objective" (of the object) which extends beyond the existence of subjects. — Metaphysician Undercover

What then about proofs that are independent of the subject? Proofs in Number Theory that are demonstrably true? For example $\phi(n), \tau(n), d(n) etc$ are indisputable values. They are what they are beyond any subject's opinion of them.

That something is "undecidable" is an opinion.

Godel's theorem demonstrates the reality of undecidables.

if a mental event M supervenes on a physical event P, and P causes a further physical event P* on which a further mental event M* supervenes, serious doubt can be cast on the claim that M causes M*. The account at the physical level of how P causes P*, together with the supervenient relations, is sufficient to account for the occurrence of M*. The M-to-M* doesn’t seem to be a genuine causal relation. — Ignoredreddituser

It depends on whether M causes P. If M does not happen and as a result P does not happen then P* does not happen and M* does not happen. This means that M* does not happen unless M happens, which sounds suspiciously like M indirectly causing M*

I think a non physical event can supervene/intervene in a physical chain of events-
https://thephilosophyforum.com/discussion/4458/determinism-and-mathematical-truth/p1

Here is the main argument-

Extreme determinsts maintain that the physical universe is just an outworking of the laws of nature and everything is predetermined by these laws. It is even argued that our brains are determined by neurological processes etc that are physically deterministic.

There seems to be a way around this determinism. It involves making a list of possible actions and making a choice from that list in such a way that the choice is not determined by either neurological states or any physical state in the world.

Here is how it works. Make a list of ordinary events and label them 0 to 9.

0. Read a book
1. Go to the library
2. Play tennis
3. Drive your car
4. Go to the cinema
5. Go to the supermarket
6. Listen to the radio
7. ...
8. ...
9. ...

Next get the decimal expansion of an irrational number such as the square root of 11
or 1/23.

Let us take the square root of 11

The square root of 11 is 3.3166247903554

Now take the first digit in the decimal expansion, 3
and go to your list;

3 = Drive your car

the next is 1

1 = Go to the library

6 = Listen to the radio

etc.

Now our choice is not determined by any physical or neurological state. It is determined by purely non physical mathematical entities. So we seem to have broken with any previously determinism by letting digits make our choice for us. If we are in the library, for example, we are engaged with a series of physical activities that, as a set, cannot be traced back to any previous physical state because the digit intervened and determined what set of physical events we would enter into.

Is there a mathematical and or logical expression for comparing the properties and lack of properties of Objects? — Josh Alfred

You seem to be talking about Boolean algebra.

What you are demonstrating is that the set {///} has the value signified by 3. Do you not accept the fact that mathematics works with values? If "{///}" means the same as "3", and "3" means the same as "{///}" then you have a vicious circle of definition. But clearly this is not the case in set theory. Sets have all sorts of different values like cardinality, extensionality, etc.. To say "there are no values ascribed here" is rather ridiculous. — Metaphysician Undercover

But you are talking about subjective value: something that can be open to disagreement. How can there be disagreement about the cardinality of a finite set? And if there was disagreement about the cardinality of infinite sets it would not be because of subjective opinion it would be highly technical and concerned with Godel's undecidable issues - such as the cardinal in the continuum hypothesis which was shown, by Cohen, to be undecidable.