I just proved the number of unique things that can or will ever exist, both physical and imaginary, is finite. What part of the proof can you possibly doubt? — Zelebg

Consider any non-standard model of PA. How can we capture this non-standard model in a set of sentences? — Nagase

It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism. — Wikipedia on Löwenheim–Skolem theorem

Even the title of the thread you posted is wildly, clearly and egregiously incorrect:

"You can do with numbers everything that you can do with sets, and the other way around" — GrandMinnow

When you write "set theory" but mean "the theory of herditarily finite sets" then you need to write "the theory of hereditaraily finite sets" and not "set theory". — GrandMinnow

There might be such a notion in a branch of study, but not in ordinary mathematical discussion. — GrandMinnow

Whatever you read on a forum, it's not ZF minus infinity that is, in a certain sense (a qualification I'll leave tacit henceforth), equivalent with first order (a qualification I'll leave tacit henceforth) PA. Rather it is ZF minus infinity plus the negation of infinity that is equivalent with PA. — GrandMinnow

Folklore Result.The first-order theories Peano arithmetic and ZF set theory with the axiom of infinity negated are equivalent, in the sense that each is interpretable in the other and the interpretations are inverse to each other.
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the notion of ‘ZF set theory with the axiom of infinity negated’ turns out to be ...
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For example, Chang and Keisler [5,§A.31] specify one particular choice of axiomatisation of ZF; for this axiomatisation a weak form of interpretation-equivalence of ‘ZF with infinity negated’ and PA can be proved, but for stronger notions of interpretation-equivalence a different axiomatisation of ZF seems to be required.
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By ZF−inf we mean the theory in the first-order language L∈o f set theory with all the usual axioms of ZF except infinity, which is negated.
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It was observed in 1937 by Wilhelm Ackermann [1] that N with the membership relation defined by n ∈ m iff the nth digit in the binary representation of m is 1 satisfies ZF−inf. — On interpretations of arithmetic and set theory

No, PA has successor (adding one), addition, and multiplication as primitive. — GrandMinnow

The Peano axioms can be augmented with the operations of addition and multiplication and the usual total (linear) ordering on N. The respective functions and relations are constructed in set theory or second-order logic, and can be shown to be unique using the Peano axioms. — Wikipedia on Peano's axioms

That seems to be your main point. And it is wildly and clearly incorrect. PA cannot prove the existence of an infinite set — GrandMinnow

No, the equivalence of PA and FINITE set theory, aka known as the theory of hereditarily finite sets. — GrandMinnow

Not if you're talking about basic mathematical logic. A language is not a set of sentences. A language is a set of symbols with arity functions. — GrandMinnow

model is not a set of sentences. A model is a certain kind function from the symbols of a language. — GrandMinnow

I'm not sure how you are using the term axiomatize. However, I will say that life does not have ideas, only people do. People choose to have offspring. — schopenhauer1

They are following the ideology that ways of life of a society are good. — schopenhauer1

Yeah, you can give me some fringe exceptions, but besides that this isn't sustainable as a widespread thing, these fringes are only in relation to the non-fringes, so you need both. — schopenhauer1

You're also shitting on Turkey's national political hero, Atatürk, the reformer, who apparently is not a Muslim by your standards. — fdrake

They are against Kemalism and the aggressive secularism which attacked Islam and banished it from public life, not Ataturk per se. — Yasar Yakis on Ataturk

But the debate isn't about which society is best — schopenhauer1

whether it is good to bring someone into any society — schopenhauer1

I guess I'm curious if anyone has heard of something like this, or has any ideas about what it is, or how to deal with it. I ingenously tried the psychiatric establishment, but it didn't work (even if that's my fault), and I'm not sure what else to do. — csalisbury

Would you agree that generally, a society has a "way of life", general patterns that people follow that are more-or-less the same? We generally have things like work, money, exchange, consumption, etc., right? — schopenhauer1

First, it's not clear what is for languages to be isomorphic. A model M is isomorphic to a model N iff there is a bijection between their respective domains that respects the interpretation of the non-logical symbols. What does it mean for languages to be isomorphic? — Nagase

More importantly, you claimed in your first post that your procedure was meant to express the bi-interpretability of PA and ZF-Inf. What I'm saying is that this is very far from the truth. You have not shown how to define the relevant notions in PA (i.e. you have not shown that PA proves that your definitions are well-defined). You have not shown that, using your definitions, we can prove the axioms of ZF-Inf. And finally, you have also not shown that your "interpretations" are inverses, which is crucial for bi-interpretability. — Nagase

Finally, I'm confused by your use of the sign function. For any x, sgn(x) is either 1, 0, or -1, corresponding to the cases x>0, x=0, x<-1. So there are only three possible values for 1-sgn(x), namely 0, 1, 2. Hence this term can only code at best three possible objects. — Nagase

So every object in the universe is built out of the empty set in a structured way. So your set {2, 4}, for example, is actually the set { { {}, {{}} }, { { }, { { } }, { { }, { { } } }, { {}, {{}}, { {}, {{}} } } — Nagase

set = "{" "}" |
       "{" set "}" |
     "{" set "," tail_of_sets "}"
tail_of_sets = set |
                    set "," tail_of_sets

(2) The universes of ZF-Inf are all infinite. This is clear from the fact that ZF-Inf has the power set axiom, so that there's no bound for the size of its sets. — Nagase

With this in mind, note that, under Ackermann's interpretation, the empty set is coded by 0, the singleton of the empty set (i.e. {{}}) is coded by 1, the number two is coded by 11 (i.e. by 3), the number three, by 111 (i.e. by 7), and so on and so forth for every von Neumann ordinal (note that I'm considering the leftmost digit as the 0th digit, the second leftmost digit as the 1st digit, etc.). On the other hand, the set {{{}}} is coded by 10, since it does not contain the empty set, but it does contain the singleton of the empty set.

Note that simply having a coding scheme is not nearly enough for an interpretation (let alone bi-interpretation). You also need to show that (i) the elements in this coding scheme are all definable in the theory that is doing the interpretation and that (ii) all the axioms of the target theory are provable under this coding scheme. These are not trivial matters and some ingenuity is required to see that everything works smoothly (see the chapter by Hájek and Pudlák that I linked in the previous chapter to see how it is done). — Nagase

You're not a Muslim. — frank

Takfir or takfeer (Arabic: تكفير‎ takfīr) is a controversial concept in Islamist discourse,[1] denoting excommunication, as one Muslim declaring another Muslim, or any individual, as a non-believer (kafir). The act which precipitates takfir is termed mukaffir.

It has to be noted that Shiraz Maher do precise that the major Salafi jihadi theoreticians like Abu Hamza al-Masri, Abu Muhammad al-Maqdisi, Omar Abdel-Rahman and Abu Basir al-Tartusi ask to exercise caution while doing takfir, as declaring a Muslim unbeliever wrongly makes the one who accuse to himself get out of the religion.[3]

In general, the official clergy considers that Islam does not sanction excommunication of Muslims who profess their Islamic faith and perform the ritual pillars of Islam.[1] — Wikipedia on Takfir

You ever use Spring (a java technology)? — christian2017

How do you even come up with this stuff. — fdrake

In the Name of Allah, Most Gracious, Most Merciful.

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
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A Muslim is always asked to keep very remote from any thing that stimulates him or stirs his sexual urge. This includes looks, gestures, or free mixing.
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Undoubtedly, the free mixing of young boys and girls, close to the period of adolescence, in the relaxed environment of a school is very serious. It is a duty of Muslims to unite their efforts to eliminate this system in their countries and to set up schools, colleges and universities for both genders. Parents should search for separate schools to enroll their children. However, if a Muslim, male or female, is pressed to study at a mixed school, then he should exert his utmost to observe the Islamic standards of morality and keep away from all unlawful things.
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Therefore, we say that co-education is Islamically unacceptable, because of what it leads to, not because of the process of teaching or of the meeting of the two sexes in a classroom.”
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In fact, the tremendous loss caused by co-education is moral degeneration.
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This reality coupled with the fact that they are mostly devoid of the supervision of any true and sincere mentor at school in that their teachers themselves do not present their students with a role model of morality, cause the innocent students to fall prey to the deadly predator of sexual impurity. — Religious advisory on co-education

The science of physical infinities is much less developed than the science of mathematical infinities. The main reason is simply that the status of physical infinities is quite undecided.

Although some have speculated that three-dimensional space is infinite, cosmologists generally believe that the universe is curved in such a way as to make it finite but unbounded—akin to the surface of a sphere.

In the light of the big-bang model of the origin of the universe, cosmologists generally believe that the universe has a finitely long past; whether it might have an endless future is an open question.
— Encyclopedia Brittanica on physical infinities

Is anything infinite in the physical world? Although the concept of infinity has a mathematical basis, we have yet to perform an experiment that yields an infinite result.

The universe could be infinite, both in terms of space and time, but there is currently no way to test whether it goes on forever or is just very big. — NewScientist on physical infinity

None of this has to do with the simple observation that a surplus of young, testosterone-filled males is not good for a stable society. — Nobeernolife

Are you an engineer or a math major? — christian2017

You can actually discover alot of stuff about mathematical principles by studying how 3d engines are made such as Blender. — christian2017

This is the exact process I am describing, you are simply using "ideology" as short hand for "my ideology is right". — boethius

It’s because our culture continues to celebrate and encourage the ignorance, posturing and false bravado of boys and men that the education of our boys is failing them. — Possibility

this is usually done by way of the Ackermann interpretation, namely "x belongs to y" is defined as "the xth digit of the binary expansion of y is 1". — Nagase

Unfortunately, the disciplines of psychology and economics and large parts of medicine are simply made up for profit; this behaviour can be investigated, and trust diminished where trust is not earned, but it is a complex task. Is it all false? no, but the best propaganda is mostly true and yet yields a radically different conclusion compared to removing the small amount of lies. — boethius

Nassim Taleb uses medicine as one of his primary examples, arguing that physical stress is good for you, and medicine is, with very few exceptions, bad.

Because antifragile entities benefit from a little stress, he spends a great deal of time belaboring his wariness of “iatrogenic” effects (in which the treatment is worse than the original illness). To a point, most of us would agree. For example, if your blood pressure is only slightly outside of the range of normal, you might be wise not to choose medication as your solution. Slight stresses on the body are indeed natural. I’m not sure I’d agree that your higher reading will make you stronger, but certainly in this case the downsides of the medication may be considerable higher than the benefits it might provide.

Taleb argues that the side effects of medication are unpredictable. We simply don’t have enough history to truly predict outcomes. Medicine is like tobacco, which when it first was introduced was purportedly good for you. There was no “proof ” to the contrary as it took decades for the evidence to accumulate. Thalidomide was prescribed as an antinausea medicine but its side effects on the unborn fetus weren’t clear for a few years. — Derek G. Hennecke on Nassim Taleb's take on medicine

Iatrogenics is when a treatment causes more harm than benefit. As iatros means healer in Greek, the word means “caused by the healer” or “brought by the healer.” Healer, in this sense, need not mean doctor, but anyone intervening to solve a problem. For example, it could be a thought leader, a CEO, a government, or a coalition of the willing. Nassim Taleb calls these people interventionistas. Often these people come armed with solutions to solve the first-order consequences of a decision but create worse second and subsequent order consequences. Luckily, for them at least, they’re never around to see the train wreck they created. — Iatrogenics: Why Intervention Often Leads to Worse Outcomes

For instance, calling out the pharmaceutical industry's manipulation of the medical scientific community seems to invite casting doubt on man-made climate change and the urgency to act with respect to it. — boethius

For, if the opium crisis resulted from a corrupt manipulation of the scientific medical community, why can't we assume the climate science community is likewise manipulated? — boethius

People who were told "opiods, totally safe, science says so" by "scientific medical authorities" and live the terrible consequences are entirely valid in doubting the next important thing scientific institutions tell them to believe. — boethius

In otherwords, dismissing alternatives as ideological whereas one's own position is just "clear epistemic givens" is simply to assume one's ideology is correct and the other's are incorrect without any proper examination. — boethius

ou may recognize I'm no idle flatterer, but you have presented this in a masterful way that is a delight to read (even if I don't completely get it). Very nice! — tim wood

Some people really believe it's possible to subsist without eating and that various gurus have accomplished it. "Eating to live" is very much an ideology; it's more accurate to say we just happen to think it's actually true and dismiss the alternatives. If "living off sunlight" is an ideology, then so too is the alternative of "living off material food". — boethius

survival-through-economic-means for example — schopenhauer1

There is no way out of this ideology (of living generally to survive in some sort of economic system), once born, not even suicide. — schopenhauer1

An ideology is a set of beliefs and values attributed to a person or group of persons, especially as held for reasons which are not purely epistemic.[1][2] Formerly applied primarily to economic or political theories and policies, in a tradition going back to Karl Marx and Friederich Engels, more recent use treats the term as mainly condemnatory. — Wikipedia on the term ideology

It’s important to note that that the intention in education has not been to ‘feminise’ boys, but to address the imbalance that has been disadvantaging girls in education for centuries. — Possibility

it’s also true that while single gender education can assist academic progress, it can be harmful to a boy’s (and a girl’s) capacity to interact effectively in the real world. — Possibility

This is particularly relevant to sexual ethics, because much of it has to do with how we conceptualise ‘biology’ and ‘acceptable’ behaviour, both in gender-specific and ‘mixed’ company. — Possibility

We cannot solve our problems with the same thinking we used when we created them. — Albert Einstein

On a daily basis this usually equates to a set work week, probably a weekend and non-work hours, maybe retirement on the horizon, educational institutions while growing up, with overlap. There's literally millions of other things to add here but I don't need to list them all. — schopenhauer1

If you don't want this, you have becoming destitute and homeless — schopenhauer1

So is society itself a sort of ideology, a sort of "brand" that we as individuals perpetuate through the gateway of birth? It has a way-of-life. — schopenhauer1

I think it is an ideology, forced in perpetuity on others. — schopenhauer1

A shaitan is assigned to every human (with Jesus as exception), and shayatin are said to move through the blood of human. Sahih Muslim mentiones among the shayatin five sons of Iblis, who bring everyday calamities: Tir, “who brings about calamities, loses, and injuries; Al-A’war, who encourages debauchery; Sut, who suggests lies; Dasim, who causes hatred between man and wife; Zalambur, who presides over places of traffic." — Wikipedia on Shaitan

Oh, please do clarify ‘feminise’ for me - I’m curious what it is exactly that you think we’ve been doing to these boys that is such a travesty. — Possibility

• How the Schools Shortchange Boys. In the newly feminized classroom, boys tune out.
• Boys are lagging in schools: has feminization gone too far?
• Feminization of Schools. If young boys are being left behind, what targeted teaching strategies can lead them to reach their potential?
• Has Feminized Schooling Contributed To The West’s Male Crisis?

• The Feminization of Everything Fails Our Boys
• Black boys are too feminised
• Boys Without Fathers: 3 Myths, 3 Miracles

Do a quick search of “boys raised without fathers” and you’ll quickly find yourself buried under an avalanche of horrifying statistics. More likely to drop out of school, more likely to develop drug or alcohol problems, more likely to be incarcerated; the bad news goes on and on. — Boys Without Fathers: 3 Myths, 3 Miracles

PA and HF can be interpreted in each other. — GrandMinnow

People become aggressive usually as a response to social conditions. — Bitter Crank

Am I supposed to be afraid of these guys? To run for cover? Don’t worry about me - I may be ‘feminine’, but I’m no ‘pushover’. We have our means. — Possibility

I don’t doubt that your ignorant and primitive concept of ‘male biology’ seems to be working for you personally in your isolated little corner of the world. — Possibility

The Puerto Rican Mob/The Puerto Rican mafia, consists of 6 crime families, in the northeastern coast of Puerto Rico around the cities of San Juan, Puerto Rico, Carolina, Puerto Rico, Canóvanas and Loiza Pueblo. The family was founded by Quitoni Martinez, José "Coquito" López Rosario whom later split from the Family to form his own which became a family within the Puerto Rican mafia, Henry Vega, Iván Vega, and Luis Albertos Rodríguez. They had strong connections with The Cali Cartel and small connections with Los Pepes, Paulino Organization, Gulf Cartel and the Puerto Rican street gang Ñetas.[1] — The Puerto Rican Mob/The Puerto Rican mafia

The way we conceptualise ‘male biology’ in the first place might be a good place to start... — Possibility

But surely you’re more than just a bunch of animals ‘forced’ to comply with the socio-political framework of the day? — Possibility

You won't realise how your beliefs are shifting until you're a dogmatic Muslim living somewhere off grid subsisting solely off of Bitcoin — fdrake

you are unworthy of sexual intimacy because of the shape of your skull — fdrake

I think the only effective means of combatting this crap from influencing you (as much as possible anyway) is doing what you can to curate your exposure to it. — fdrake

The Coven-Meyerowitz Conjecture states that being a tile is equivalent to a purely arithmetic condition on the set. — Arithmetic Sets in Groups by AZER AKHMEDOV and DAMIANO FULGHESU

Finnish efforts to educate their public about fake news — frank

Procreation is a responsibility, but it is NOT a right. — Possibility

a sexual relationship negotiated on the freely agreed terms of all participating parties is always preferable to legality, however temporary. — Possibility

Therefore, how can we distinguish "a priori" knowledge from innate ideas/knowledge? — Meichen Fan

If the mind with "a priori" knowledge is not born with ideas/knowledge, what is the trigger here to adopt the "a priori" knowledge? — Meichen Fan

Pairing up early in one's life, not having the experience of sharing in a variety of sexual styles, preferences, wishes, wants, etc., seems like an impoverished life. — Bitter Crank

Isn't licensing an overreach of government authority in your view? — Pfhorrest

The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too. — Preamble of the GPL

The fact that the Defendant acted pursuant to order of his Government or of a superior shall not free him from responsibility, but may be considered in mitigation of punishment if the Tribunal determines that justice so requires. — Charter of the International Military Tribunal - Annex to the Agreement for the prosecution and punishment of the major war criminals of the European Axis