Wait a minute, your take on family composition is way, way off: According to the US census and Bureau of Labor Statistics, 69% of children (<18) live in families with both parents present. — Bitter Crank

Millennials are less likely to form 'traditional' families — though that trend may be reversing
In 2009, the oldest millennials were in their 20s. And as The Wall Street Journal reports, of those older millennials who did have kids, most were unmarried. Meanwhile, a Pew report finds that just 46% of kids in 2016 were living in a household with two married parents in their first marriage, compared to 61% in 1980. — Millenials versus traditional families

So, yes, agreed. The terms "both parents present" and "two married parents" are not exactly the same. Furthermore, millenials may not yet be the largest group of families.

The current capitalist economic derangement is a critical part of the diseased social structure. — Bitter Crank

Yes, I have run into the remark more often that the corporations encourage the negative social trends, since they benefit from them.

On the long run, the economy matters way less than generally perceived. Social structure is much more predictive of societal outcomes than the economy. In fact, the population could even make do with less than half their current income, if the social structure wasn't so incredibly damaged and diseased. They used to have less money in the past and things were actually better. It's not that people fundamentally need more money. Even the problem of population aging would be much more manageable, if people lived in three-generation households. No need for elderly homes. Welfare does not need to be a government-run policy. It could also be handled by solidarity at the level of the extended family, along with charity at the level of the religious community.

so if you start with sets you don't need to "manually" include propositional logic, it's one of the things you can build along the way. — Pfhorrest

I have accidentally run into a comment on this issue:

Difference from set theory. There are many different set theories and many different systems of type theory, so what follows are generalizations. Set theory is built on top of logic. It requires a separate system like predicate logic underneath it. In type theory, concepts like "and" and "or" can be encoded as types in the type theory itself. — Wikipedia on type theory

It seems to suggest that your remark would be true for type theory but not for set theory.

I don't, and if I'm reading them correctly, they together contradict my understanding of predicate logic, wherein "for all x, F(x)" does not entail "there exists some x such that F(x)", but only "there does not exist any x such that not-F(x)". Which makes me think I'm not reading that passage correctly. — Pfhorrest

Well, I guess that we'll figure it out later. In the meanwhile, there's a bigger snag. The documentation (LEAN and Coq) suggests that we will regret using set theory as a foundation, because they went with type theory instead, even though all of type theory can be phrased as set-theoretical theorems. Any idea why? Is this just practical or so?

I think you may be confusing propositional logic with predicate logic. — Pfhorrest

Well, since first-order logic is a predicate logic (extended by quantifiers), I did not mention predicate logic separately. All the axioms of logic, however, are (supposedly) already included at the level of propositional logic.

Wolfram insists, however, that first-order logic adds two new axiom schemata.

The set of axiom schemata of first-order predicate calculus is comprised of the axiom schemata of propositional calculus together with the two following axiom schemata:

∀ x F(x) ⇒ F(r)
F(r) ⇒ ∃ x F(x)
— Wolfram on first-order logic

Do you know why this is needed? In my impression, these schemata are not mentioned in Wikipedia's page on first-order logic. I could not find other relevant documentation for this problem ...

By the way, Wolfram also describes first-order (predicate) logic as an extension to propositional logic. They do not see zeroth-order predicate logic as something that needs to be mentioned separately ...

It's kinda redundant to start from sets then derive quantifiers (like for some being arbitrary disjunction over set elements, or for all being infinite conjunction over set elements). — fdrake

The LEAN documentation (Microsoft Research) says that they fully support set theory but that their core axiomatization is actually dependent type theory:

The syntax of type theory is more complicated than that of set theory. In set theory, there is only one kind of object; officially, everything is a set. In contrast, in type theory, every well-formed expression in Lean has a type, and there is a rich vocabulary of defining types.

In fact, Lean is based on a version of an axiomatic framework known as the Calculus of Inductive Constructions, which provides all of the following ...

Given this last fact, why not just use set theory instead of type theory for interactive theorem proving? Some interactive theorem provers do just that. But type theory has some advantages ... — LEAN on Dependent Type Theory

It is certainly not the first time that I see them switching to type theory in the context of proof assistants and theorem provers (Coq does that too), even though type theory is so much less straightforward (at a basic level) than set theory ...

It isn't that millions of Americans are starving, but many millions are living paycheck to paycheck, not because they are spendthrifts, but because their income simply doesn't cover the necessities of a family (adults and children). — Bitter Crank

There are two types of families now: single men versus single mothers (with children). Traditional families have become the exception.

Concerning single men, unless they are bogged down with alimony and/or child support, they are doing financially fine (but not socially fine). Single mothers (with children) tend to outspend their government subsidies and food stamps, and are more often in financial dire straits. Both types of families spend a lot more on rent (or mortgages) because of the housing shortage, because two times as many homes are needed, especially in the metropolitan areas where the jobs are.

The system (=society) simply wasn't set up to cater to single men and/or to single mothers (with children). All other problems get amplified and become worse because of this problem. It also causes the demographic time bomb: smaller number of active workers versus large number of retirees.

On the long run, it is the diseased social structure that will sink the economy and the living standards. I would not even worry about any other problem.

anything you can say in propositional logic you can say in predicate logic — Pfhorrest

Yes, predicate logic gets loaded automatically by first-order logic. I don't think it comes with a separate axiom pack. It is just additional language grammar. In my impression, the entire axiom pack of logic is already attached to propositional logic.

anything you can say in propositional logic you can say in predicate logic — Pfhorrest

Yes, and anything you can say in predicate logic you can say in first-order logic, which is what you need for PA or ZFC. Predicate logic is not sufficient. You need the universal quantifiers too (again, supposedly language-only).

so if you start with sets you don't need to "manually" include propositional logic, it's one of the things you can build along the way. — Pfhorrest

It would be fantastic if it were possible to derive the 14 axioms of propositional logic as theorems in ZFC, but I have not run into any documentation that confirms this or clarifies how to do that. I am absolutely not sure that it can be built along the way on top of ZFC. All documentation that I have seen up till now suggests that it is simply another, additional axiom pack.

Trump is the only person in Washington trying to not have a war. — fishfry

They knew that Suleimani was going to be in Baghdad yesterday. They wouldn't have struck him while he was on Iranian territory. That would have been a little too much of a provocation.

How did they know that Suleimani was going to be there? What is the most likely reason that they even knew in what car he would arrive and leave?

Suleimani must undoubtedly have been there because he was invited to negotiate with US officials, who must have promised him a fantastic diplomatic breakthrough or so, if only he showed up ... It must have been an ambush. They must have conned him.

Furthermore, I seriously suspect that Trump was informed about the operation only after the facts. This is quite a victory for "incorruptible" Benjamin, of course. He must have had a big late-night party with his friends in Tel Aviv after this.

I think US killed him for weakening the final threat to Israel and Saudi Arabia. — Wittgenstein

In fact, the timing was actually quite bad, given the ongoing impeachment-zilla, I cannot imagine that Trump really signed off on it. Of course, he does not want to look like he is not in charge. So, he has now resolutely taken ownership!

What surprises me, is that Trump even doubled down in his speech in West Palm Beach. His speech is insanely insulting to Iran. It is even more insulting than the extrajudicial killing itself of Suleimani:

"We caught him in the act and terminated him."
"We will find you. We will eliminate you."
"Suleimani made the death of innocent people his sick passion."
"Contributing to terrorist plots as far away as Delhi and London."
"We take comfort in knowing that his reign of terror is over."
"What the United States did yesterday should have been done long ago." --> subtly critical of Obama, of course. — Donald Trump on 'terminating' Suleimani

We took action last night to stop a war. We did not take action to start a war. — Donald Trump not not not going to war. Not at all.

After his barrage of insults at the dead Iranian state official, whom he "terminated" for good purpose, he still "don't want war". We'll spit in your face, pee on your mother's grave, fart in your general direction, and defecate in your living room, but hey, we are not interested in conflict! ;-)

Thanks to inflation, yes. But inflation erodes purchasing power, and inflation, stagnant wages, a rising cost of living, and new products becoming "essentials" has left most of the working class significantly worse off now than their working class parents were in 1955 or 1960. — Bitter Crank

Economic growth has not just been inflationary.

The working class really does have materially more purchasing power, but at the same time, the rising cost of living has been orchestrated through government policy, now indeed nullifying all economic progress. There is an ever growing need to funnel more money to the financial sector. Not negotiable. A financial system that requires "eternal growth or else" indeed exacerbates the problem even further. The worst problem, however, is caused by the implosion in the social structure, again, because of government policies. If everybody divorces, as subsidized by the government, then it is not just the housing stock that needs to become double in size. Lots of expenses start multiplying in that case. In my opinion, it is especially the corruption in social structure that cannot be rolled back.

They were angry working class people fed up with a decline in their living standards, and they weren't out to crush the state. — Bitter Crank

Well, at the same time, you cannot make an omelette without breaking eggs. They won't get anywhere by merely beating around the bush.

The French state is simply no longer viable. You see, if the French state does not manage to increase its revenue because of yellow-vest style tax revolts, it will still and automatically keep spending, simply by printing money. Because of demographic reasons, expenses are scheduled to keep snowballing long into the future. What's more, French social policy is incredibly expensive and the expense grows rapidly year after year. Furthermore, a multi-country currency such as the Euro -- too many cooks spoil the broth -- cannot weather endless money printing.

In my impression, the decline in living standards has only started. We have arrived in the long term of lots of past, misguided, short-term decisions. It is time to pay the bill now.

What form does the thought, All bachelors are unmarried, take in your mind? How do you know when you are thinking it and when you aren't? — Harry Hindu

It wasn't my example by the way. I was just quoting from a canonical text. You are questioning and rejecting very basic principles in epistemology. That is ok, but I am not the right person to make useful comments in that regard. For once, I am actually happy with the mainstream beliefs in this matter.

Well, Ernie, the economy is already in very bad shape for a good share of the population. — Bitter Crank

Income per capita is today a multiple of what it was in the golden era of the 1950ies but expectations are much higher than back then. So, everybody naturally believes that things are worse now. Well, they are, but not necessarily economically. The real difference is that the social structure is now falling apart.

They will march on the headquarters of the institutions that sold them the Big Lie, and CEOs, Senators, Governors, Bishops, Deans, Publishers, Presidents, Priests, Police, et al will be swept away. — Bitter Crank

Well, not sure either. I thought that the yellow-vest guys would already have done that in France by now. They haven't. These people are clearly not made of the same cloth as Alexander the Great's Macedonian infantery. It must be Scipio Cunctator at work again! ;-)

how could you possibly simulate qualia in it — Zelebg

In philosophy and certain models of psychology, qualia (/ˈkwɑːliə/ or /ˈkweɪliə/; singular form: quale) are defined as individual instances of subjective, conscious experience. The term qualia derives from the Latin neuter plural form (qualia) of the Latin adjective quālis (Latin pronunciation: [ˈkʷaːlɪs]) meaning "of what sort" or "of what kind" in a specific instance, such as "what it is like to taste a specific apple, this particular apple now". — Wikipedia on qualia

No, I don't think qualia can be supported, since we can't simulate the stuff even without doing qualia.

So, no, flag the feature request as either WONTFIX or more elusively as NEXTVERSION.

(There will be no next version! Just like Windows 10 this version will be the "last version"! haha ah ;-)!)

The game is to start with the most elementary of mathematical structures, and build from there up to the structure that is (on our best current understanding of physics) identical to (or if you really prefer, the perfect model of) our physical universe — Pfhorrest

So, we are going to build the Theory of Everything from scratch, starting from an empty virtual inference machine (VM).

Of course, we'd better load the propositional-logic language-extension pack, along with first-order extensions (universal quantifiers). Language must of course be "pluggable". Still, if we load the propositional-logic language extension pack, we must also load its axiom pack with the 14 basic rules of propositional logic. Language packs and axiomatic packs are not entirely independent.

(According to Wolfram, we also need to load a few first-order logic axioms too. Not sure, though.)

So, our two extension types are: language packs and axiom packs, i.e first-principle packs.

Not sure, though, that the elusive ToE is a first-order logic theory. We assume already quite a bit by saying a thing like that!

Ok. Now our VM can reason in first-order logic.

To begin with, there is the empty set, and the empty set is without contents and void. — Pfhorrest

So, you have already decided that we are supposed to load something like the ZFC axiomatic extension pack?

In my intuition, I would rather load the PA number theory pack. It can certainly "see" everything that ZFC considers to be provable, but it does not trust quite a bit of it. I do not consider ZFC to be necessarily more powerful than PA. ZFC could just be more gullible!

as I understand it the logical operations are all equivalent to set operations — Pfhorrest

Operator symbols must be mentioned in the language pack, but some of their invariants will have to be mentioned in the axiomatic pack. The other invariants can be derived. So, yes, do we load the logic operator rules from the logic pack or do we use a translation layer running on top of the ZFC pack?

Aren't we trying to rebuild Isabelle or Coq from scratch now?
It increasingly starts looking like an exercise in reinventing the wheel ... ;-)

Microsoft Research recently did exactly that. Apparently dissatisfied with Coq and Isabelle, they ended up concocting their own lean theorem prover. They probably consider Coq and Isabelle to be "bloated".

Still, myself, I have unlearned to give in to the temptation to rewrite from scratch. It is always a lot of work while the final result will probably end up being as bloated as the thing it was going to replace, once you add all the intricate bug fixes that may at first glance appear to be superfluous. If you don't know why all that shit is there, then unceremoniously stripping it away, is rarely the solution ...

Why do you think the USA is going into war with Iran? — god must be atheist

One word: Israel.



Well, yeah.

Obama was apparently not too keen on it. So, Benjamin did not manage to get his way. This time, it may actually work, but again, not sure. It must have been hard to get CENTCOM to "accidentally" press that button.

I wonder how much you need to "infiltrate" for that?

ha ah aha ha! ;-)

P.S. This time, it's even better than the fake "Zimmerman telegram":

The Zimmermann Telegram (or Zimmermann Note or Zimmerman Cable) was a secret diplomatic communication issued from the German Foreign Office in January 1917 that proposed a military alliance between Germany and Mexico. If the United States entered World War I against Germany, Mexico would recover Texas, Arizona, and New Mexico. The telegram was intercepted and decoded by British intelligence. — On how to drag the unwilling Americans kicking and screaming into a new war.

And what will they want? — Brett

Not sure.

I suspect that there will be a bout of serious chaos for a long while, before the new system will finally materialize.

It is a bit like the situation in Libya. So, they got rid of arsehole Gadaffi. Fine. But what's next? That was 2011, by the way. We are now 2020 ...

The vast majority of men worldwide, or in your country, or in your town, or in your street, or in your front room, or in your bed? — Brett

The ones who understand the T&C do not accept them.

Since marriage arrangements are also mere biological behaviour, there are still quite a few men who are not aware of the T&C enforced by a (western) government. These men simply do not know what the T&C are, until they end up in family court.

But then again, that demographic of ignorant men is getting increasingly smaller.

In that respect, Islamic men were just the canary in the coal mine. They did not really know the implications and ramifications of these T&C but because these T&C are so incredibly contrary to Islamic law, they could not accept them solely on those grounds. That is what has caused the "endless wars" (Afghanistan, Iraq, Syria, ...)

What do you think the effect on women is of this social change? — ernestm

Look, when the shit hits the fan, and when things become seriously violent, people are not going to vote over the solution; which means that only combatant men will have a say.

Answer: It will not matter.

Can you explain that a bit more? — Brett

It is not just the marriage rate that is plummeting. Cohabitation is collapsing as well. That is a important factor in the latest drop in the fertility rate. As expected, the lowered fertility rate of the last few decades, which had already dived below replacement rate (=2.1 children per woman) was not stable.

You see, the vast majority of men do not accept the terms and conditions (T&C) of the contemporary marriage contract.

If men sign up to it anyway, it is because they are ignorant of the T&C -- after 50 years of no fault divorce this is less and less the case -- or because they are being irrational, given the fact that there are quite a few emotional and otherwise irrational elements at play in the context of a marriage contract.

The general consensus is : that contract is not good for you.

In terms of Islamic law, we can safely say: The T&C of that contract are haraam.

So, in that case, why not cohabitation? No, because of the ongoing land grab. Example, Australia:

A de facto relationship is defined in Section 4AA of the Family Law Act 1975. The law requires that you and your former partner, who may be of the same or opposite sex, had a relationship as a couple living together on a genuine domestic basis.

Can I apply to the Family Court or Federal Circuit Court to have my de facto financial dispute determined?

Yes. From 1 March 2009, parties to an eligible de facto relationship which has broken down can apply to the Family Court or the Federal Circuit Court to have financial matters determined in the same way as married couples. — Cohabitation in Australia

In many western countries, cohabitation is, in one way or another, treated in the same way as marriage, with the same T&C being applied, that are generally unacceptable to men.

So, the tactical response to the problem is to stay away from both, or to offshore your private life outside such western jurisdiction. Still, the tension is clearly mounting, because it is obvious what the only "real solution" is.

The 5% extremist fringe, who were only pushing for killing in self defense and open carry in 2015, are now pushing for civil war. When the economy flips, how big will the blood bath be? — ernestm

There are a lot of people disgruntled and waiting for the earliest opportunity to "get even".

In fact, the list of grievances seems to be endless.

A really interesting evolution is the red-pill philosophy, which has a growing number of followers.

The laws enforced by western governments in the realm of marriage and divorce make generational reproduction impossible. So, men are being advised to stay clear of marriage and having children.

The elephant in the closet is that there is one dangerous, logical, unspoken conclusion. Either the government (the entire regime, actually) has to go, or else society will come to an end.

Furthermore, it paints the conflict between the West and Islam in a completely different light.

A really popular meme in the red-pill philosophy is: "Islam is right about women". As you can see, after decades of fruitless, endless wars, quite a few men now seem to be changing sides. The enemy is not Islam. No, the enemy is the government.

So, the concept of cheese is not itself cheese. It is idea - it is just the idea 'of' cheese. — Bartricks

The map is not the territory. — December 28, 1931, American Association for the Advancement of Science, Alfred Korzybski, New Orleans

There is no justification for why they discovered it. — alcontali

Hence, the knowledge-discovery process is not rational. The output product, knowledge, clearly is, but the process clearly is not.

Both were the products of pure reason — Mww

They are not the output product of pure reason. Creativity is not reasonable.

The justification for the why of the proof was nothing more than the mere existence of the theorem — Mww

It took 350 years to produce the proof, the discovery process of which was not reasonable. There is no way anybody could find the proof merely by "reasoning". Thousands of people tried and failed. Once the proof had been discovered, it was indeed possible to verify that it really was the proof by mere reasoning.

The fact that we haven’t, and the fact that we understand knowledge is always tentative, makes explicit either knowledge isn’t that which is discovered, or reasoning isn’t the means for it. — Mww

Agreed. Knowledge discovery is not guided by reason at all. The third millenium prize goes to the core the problem. They offer $1 million if you can clarify the following:

P vs NP Problem

If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. — Third millenium prize

In the case of Fermat's Last Theorem, it is obvious that it does not take 350 years to verify that Andrew Wiles' proof is correct, even though it took 350 years to discover it. The discovery process is not rational while the verification process definitely is.

Pure reason does not explain why knowledge gets discovered. It is only able to verify the justification for knowledge. Hence, reason cannot possibly be the most important ingredient in the progress of human knowledge.

So you’re saying Fermat didn’t reason to his theorem and Wiles didn’t reason to his proof? How would you account for either the theorem or the proof, if the cognitive faculties of each of their respective originators were not in play? — Mww

There is no justification for why they discovered it.

That is in fact the case for any discovery. If it were possible to discover new knowledge by reasoning, i.e. by using a documented procedure, we would have discovered all knowledge already. Such procedure cannot possibly exist. If such procedure existed, we could use it to solve, for example, Turing's halting problem, while it is provably unsolvable.

There is no procedure for knowledge discovery.

By the way, reasoning, i.e. verifying justification, is a mechanical faculty. Computers can do it too.

Why would you confuse "an argument" with "knowledge statements"? — Galuchat

Well, neither the knowledge statement (Fermat's last theorem) nor its justification (Wiles' proof) can be discovered through reason.

Why Pierre de Fermat discovered his last theorem cannot be documented. Why Andrew Wiles finally discovered its proof 350 years later, is also a mystery. The only thing that is reasonable are the verification steps that confirm that Wiles' argument proves Fermat's theorem.

Reason(n): human faculty which creates and/or develops an argument. — Galuchat

Reason cannot create or develop knowledge statements nor their justification. Reason can only verify them.

For example, it took 350 years to discover the proof for Fermat's Last Theorem, while the process was clearly not reasonable. On the contrary, the process cannot even be documented.

What form does "All bachelors are unmarried" take in your mind? How do you know that you're thinking it? Is it just hearing the words in your mind, seeing the words in your mind, or seeing images of bachelor's and married men? You seem to be saying that you were born knowing "All bachelors are unmarried". — Harry Hindu

The common understanding is as following:

Empirical evidence may be synonymous with the outcome of an experiment. In this regard, an empirical result is a unified confirmation. In this context, the term semi-empirical is used for qualifying theoretical methods that use, in part, basic axioms or postulated scientific laws and experimental results. Such methods are opposed to theoretical ab initio methods, which are purely deductive and based on first principles. — Wikipedia on the distinction between empirical and ab initio

You are questioning the validity of very, very basic epistemic principles. I really do not see what you want to achieve by doing that. Frankly, I do not think that it will lead anywhere.

The tactile sensations are empirical and are the input. — Harry Hindu

A priori knowledge or justification is independent of experience (for example "All bachelors are unmarried"), whereas a posteriori knowledge or justification is dependent on experience or empirical evidence (for example "Some bachelors are very happy"). The notion that the distinction between a posteriori and a priori is tantamount to the distinction between empirical and non-empirical knowledge comes from Kant's Critique of Pure Reason.[3] — Wikipedia on empirical evidence

If the fact that knowledge is transmitted through sound, vision, or tactile sensations makes it empirical, then non-empirical knowledge cannot exist. I do not subscribe to that kind of view. I prefer to use Kant's characterization of knowledge.

What is the origin of the concept "reason", how did its applications develop, and what does the term mean in relationship to current knowledge? — Enrique

Reasoning is the procedural act of verifying the justification for a knowledge claim. It is an entirely mechanical activity, in the sense that a machine can do it too.

On the other hand, discovering the justification for a knowledge claim -- as opposed to merely verifying it -- is not reasonable. There cannot exist a mechanical procedure that is capable of discovering new knowledge. That is probably the most far-reaching conclusion of Gödel's first incompleteness theorem.

Creativity is not mechanical, but it is also not rational.

Given the strong and growing competition from computers, you will no longer get particularly far if you all you can do, is to reason. The ability is not entirely worthless, but it also no longer that valuable.

Why set theory? Set theory is pretty uninteresting really, apart from Venn diagrams which are fun and useful. — A Seagull

In my opinion, the most successful offshoot of set theory is relational algebra, for which the canonical language is SQL:

The main application of relational algebra is providing a theoretical foundation for relational databases, particularly query languages for such databases, chief among which is SQL. The relational algebra uses set union, set difference, and Cartesian product from set theory, but adds additional constraints to these operators. — Wikipedia on relational algebra

Relational algebra is massively big. Very little modern software can do without.

Furthermore, separate from relational algebra (which is a niche application), there is a strong trend to moving to executable (general) set-theoretical expressions in modern programming. The flagship library in this regard is certainly underscore.js.

Set theory is an incredibly invasive species which, over the last two decades, has increasingly invaded the practices of contemporary software engineering. Set theory is slowly but surely turning into the primary foundations in programming. In fact, it is so intuitive that few people actually realize that all of that is almost pure ZFC set theory.

Then for the application to the 'real world' (applied maths) one takes a particular part of mathematics and applies a mapping between the abstract symbols and concepts that apply to the 'real world'. — A Seagull

Yes, I think so too.

Furthermore, the mapping back to the real world must go through the regulatory framework of an empirical knowledge discipline, such as science. Direct application of mathematics to the real world should be discouraged, because mathematics does not seek to create such regulatory framework for empiricism, while such framework is clearly needed.

Therefore, real-world considerations are the domain of downstream users of mathematics, such as science, engineering, and so on. Mathematics itself should stay clear of those, in order to preserve its purity.

Then what form do their, and your, thoughts take? How do you know you're thinking? — Harry Hindu

Computers do not require empirical input either.

You could learn how to accept a text stream, character by character, through a device that makes a short stroke on your palm to represent a zero, and a long stroke for a one. Every collection of six strokes represent one 6-bit character in base64. That would be your input. Next, you can output what you thought about the input by moving your index finger on a touchpad to produce short and long strokes. The process would be slow, but it would work absolutely fine. No vision nor sound needed.

I'm not talking about what the words are about. I'm talking about the words themselves. You would never know about those imaginary universes if you didn't have eyes to see the scribbles in the paperback sci-fi novel, or ears to hear a reader read the scribbles. — Harry Hindu

That is not sure at all. People who are blind and/or deaf, still think. Sensory input is not a requirement for thought.

I asked how you learned and use language without using your eyes and ears. — Harry Hindu

So? That does not mean that language can only be used to describe the physical universe. It can also be used to describe imaginary universes. You can use language to write science fiction. You can use language to describe an idea for something that does not exist yet. Your eyes never saw it. Your ears never heard it.

You're not reading my entire post. — Harry Hindu

I don't see how it demonstrates that language would be an empirical input. I reject that point of view.

And algebraic symbols have curves and circles and lines. — Harry Hindu

Language-only communication also uses visual representations but of text and symbols only. It is not considered empirical input.

f the procedures you follow aren't visual, then how do you know you're following a procedure? What form does your mathematical procedure take? How would you describe the experience of performing a mathematical procedure? — Harry Hindu

By visual procedures, I mean a procedure in which the use of circles, lines, triangles, polygons, graphs, and similar visual representations are essential. Nowadays, only the algebraic symbol manipulations are essential. Mathematics is now essentially language only. For example, you do not need to create any drawing to solve the roots of a quadratic equation. In fact, that was the first non-visual, language-only procedure that appeared in the Middle Ages, in the Liber Algebrae by Algorithmi. Nowadays, mathematics has completely algebraized, including geometry.

In describing it you will be using visual scribbles on a screen to reference the visuals in your head. — Harry Hindu

You can represent language visually with written letters but you can also represent it verbally with sounds. You cannot do that with a line, triangle, circle, or polygon. In algebra, the visual aspect is not essential.

What form do these underlying structures, patterns, properties, phenomena take? Structure, pattern, phenomena and properties are all visual terms. — Harry Hindu

Their canonical description is in language only; while language is not necessarily visual. Language also has an isomorphic auditory representation. Language is not considered an empirical input.

Yet 'provability' is a philosophical criterion, or principle, and not a mathematical concept. — 180 Proof

Likewise, 'falsifiability' is a philosophical criterion, or principle, and not a scientific concept. — 180 Proof

Provability and falsifiability are epistemic criteria. So, there is a way to back the proposition with objectively verifiable paperwork of a particular type.

If paperwork of a particular type exists to justify a proposition, in terms of epistemology, then there exists a particular procedure to fill out that kind paperwork, i.e. according to computability.

Therefore, in another thread, we have been discussing and investigating whether epistemology and computability are essentially not one and the same thing?

Hence, it is a question mark if epistemology will not some day be migrated to (meta)mathematics, just like logic has been already.

That they "will be accepted" or "nobody will contest" them are mere dogmatic, or anti-philosophical, shibboleths (e.g. scholasticism, physics/math-envy, etc); instead, convergence without terminating consensus (Peirce, Popper, Feyerabend, Haack). — 180 Proof

If the justification cannot be verified objectively/mechanically, then the epistemic status of the claim being justified is not knowledge. Therefore, seeking objective justification is a legitimate goal, simply, because it turns what would otherwise be mere conjectures into sound knowledge.

If it is not possible to turn particular conjectures into knowledge, then let them remain mere conjectures. I have absolutely no problem with that. Furthermore, I do not seek to convince anybody of the conjectures that I may personally believe in. In the end, we all use them, and people are free to believe what they want.

Ay-vey, Immanuel. Just because you can see it, it does not mean it can't be a priori existant. What a narrow-minded little block-head that Immanuel was. Or square head. Or take your choice of synthetic a priori geometrical shape, and apply it to Immanuel Kant's head shape. You can't lose. — god must be atheist

Even though I very much appreciate Immanuel Kant's Critique of Pure Reason, I am still not one of his cheerleaders. On the one side, Kant says that pure mathematics has the potential for being pure reason:

Mathematics gives us a shining example of how far, independently of experience, we can
progress in a priori knowledge.

If this be demurred to, I am willing to limit my statement to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure a priori knowledge.

Mathematics presents the most splendid example of the successful extension of pure reason, without the help of experience. — Kant in Critique of Pure Reason on mathematics

But Kant denies that the visual puzzles in classical Greek geometry are pure reason:

The mathematician meets this demand by the construction of a figure, which, although produced a priori, is an appearance present to the senses ... but their employment and their relation to their professed objects can in the end be sought nowhere but in experience, of whose possibility they contain the formal conditions. — Kant on geometry and its visual puzzles

At some point, Kant engages in infinite regress by demanding a justification for the axioms in mathematics from "transcendental philosophy". Of course, that will never work:

In the Analytic I have indeed introduced some axioms of intuition into the table of the principles of pure understanding ... For the possibility of mathematics must itself be demonstrated in transcendental philosophy. Philosophy has therefore no axioms, and may never prescribe its a priori. — Kant demanding a justification for axioms

Kant believes in metaphysics, i.e. in infinite regress, while I absolutely don't:

Now if in the speculative employment of pure reason there are no dogmas, to serve as its special subject-matter, 1 all dogmatic methods, whether borrowed from the mathematician or specially invented, are as such inappropriate. All knowledge arising out of reason is derived either from concepts or from the construction of concepts. The former is called philosophical, the latter mathematical. — Kant insisting on dogma-less views, i.e. insisting on infinite regress

Since its very beginning, 2500 years ago, metaphysics has never produced anything of value or anything actually worth knowing. The reason for that, is, that the method of infinite regress is faulty. It literally leads to nowhere.

My primary interest was whether your choice of philosopher and philosophies is hardwired. — Brett

No, not possible. For example, I came to realize that conclusions about ethics outside the regulatory framework and system of religious law can only be spurious. That makes me reject all forms of system-less ethics.

This has wide-ranging ramifications on my political opinions. I reject every possible political claim about morality or even legitimacy. This means that I never allow politicians to lecture me on ethics or to invent new obligations or laws. I do not owe them anything. Islam is the ruthless solution to that problem. And no, I wasn't born into the religion.

Can we really throw something aside and change horses, or be persuaded to change our perspective on those big questions by the arguments of others? Have you ever convinced someone to change their mind? — Brett

In mathematics it is trivially easy. If the claim is provable, then nobody will contest it. In science it is also relatively easy. If the claim is falsifiable but nobody manages to falsify it, then it will also be accepted. There is, however, no such benchmark as provability or falsifiability in philosophy. There is no paperwork procedure of which one can verify the output documents in order to accept or reject a claim. Therefore, I do not even try to persuade anybody of philosophical viewpoints. As far as I am concerned, everybody believes what they want. Some people will believe what I say but others won't, and, as far as I am concerned, that is entirely expected.

It is illogical to severe empiricism from rationalism, or to think of them as opposing views. Making an observation entails using your eyes and brain - making sense of what it is that you are looking at. It is one process, not two separate ones that can be done without the other. — Harry Hindu

Well, in Critique of Pure Reason, Immanuel Kant pointed out the existence of a type of knowledge that is not empirical. It is synthetic a priori. At the same time, he rejected classical Greek geometry as NOT being synthetic a priori, because it is highly visual, as it is an exercise in fiddling with visual puzzles.

In the meanwhile, mathematics has changed. It has migrated from visual fiddling to pure symbol manipulation. Nowadays, its essence is language only. We no longer follow visual procedures in mathematics.

Therefore, I disagree with relying on empiricism in mathematics. The progress in mathematics in the last few centuries has only been possible by removing its dependence on visual input. Mathematics has now finally become pure reason only.

Like I said, you weren't born knowing 3+0=3 because you needed to observe this rule in order to know there is a rule and then observe how such a rule is useful in the world. The rule itself stems from our own observations of individual things and the need to quantify those individual things that share similarities. So these "axiomatic" domains themselves require at least two observations - one to learn the rule and the other to learn what the rule is for. — Harry Hindu

For a starters, we simply end up cutting off the real-world origins of mathematical theories, if there were any to begin with:

Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.[1][2][3][4] — Wikipedia on abstraction in mathematics

Secondly, quite a bit of mathematics does not have a real-world origin. For example, where in nature can you find something like look-ahead left-right parsers? Where in nature can you find Turing machines? Von Neumann machines?

These things are abstraction only. They started studying them in mathematics because these at first imaginary devices were potentially useful for computing. If they had limited themselves to what is readily visible in the surrounding universe, we would simply never have had computers. Nature does not have them to begin with.

I other words, it doesn't qualify as software. If it doesn't execute, or do anything, then the programmer didn't follow the rules for writing a program in that particular language. It's merely observable scribbles on a screen. — Harry Hindu

Well, for example, even C/C++ header files contain mostly definitions that are not even meant to ever execute. For example, what is chromium/base/barrier_closure.h supposed to do? Even the source code of something like a web browser such as Google Chrome contains seemingly absurd abstractions that are concept heavy while being low on actual code to execute. In other words, it is not even meant to do anything. It just structures things in one way or another ...