So computer programming have more in common with house construction work or something like that than with maths. — Ansiktsburk

House construction work is relatively well manageable as projects. You start, you build, and you finish within a particular time frame and budget. Corporations have attempted to to manage software development in the same way, and have failed for decades now to do exactly that. That does not mean that it is necessarily more related to doing original math work either. Still, viewing software as projects, is a failing proposition.

One problem here is that I dont really know much about the philosophy of maths. What is that all about? — Ansiktsburk

Philosophy of mathematics

The Platonic, formalist, and structuralist views certainly ring a bell with me. In fact, even the fictionalist take on mathematics makes sense to me. In my opinion, the different schools of thought do not necessarily exclude each other, even though my own opinion is certainly incompatible with the constructivist view. I cannot reconcile myself with people like Brouwer.

But whatever you call it, software engineering needs to take into account changing requirements when you can't nail them down before starting the project. — Marchesk

Well, the very concept of "project" is a problem. In a successful "project", 80+% of the cost will be incurred during later maintenance. Of course, most "projects" will never reach that stage.

In other words, setting a project goal to be achieved, and associating a budget for it, tends to fail. Successful software rarely emerges out of that kind of context. I am surprised that even civil service bureaucracies begin to understand the fundamental problem:


www.csc.gov.sg The Civil Service College (CSC) was established as a statutory board under the Public Service Division in 2001. As the heart of learning for the Singapore Public Service, we deliver an innovative, inspiring and impactful learning experience for public officers.

How to Build Good Software
Software has characteristics that make it hard to build with traditional management techniques; effective development requires a different, more exploratory and iterative approach.

It is the very notion of "project" with "start" date, "delivery" date, and definitive "budget" that is the problem. The larger the distance between what you want to achieve versus what you can download verbatim from github, the more costly the failure will be.

Agile is one of the recent fads, and it has been changed from its original (worthwhile) intent to something that can be taught in a classroom, and produce Agile Managers. — Pattern-chaser

In my opinion, "agile" is epistemically worthless. If knowledge is a justified belief, then the very last industry that feels the need to come up with reasonable justification, are the consultancy snake-oil factories. It is incredible how intellectually poor their conjectures are. The more money floats around in flogging the nonsense, the more nonsensical it tends to be.

For example, if someone says they love you or that they find a movie really good, how can you ever know they're not lying, since you don't have direct access to their minds? — AnonThinker25

You can't. You can try to make sure, however, that it does not matter either. As long as what you really try to get out of the situation, are verifiable results, then why would it even matter?

Seriously, can we have a stab here at defining and describing metaphysics? — Pattern-chaser

Metaphysics are presuppositionist views about the real, physical world. I agree with the logical positivists that a priori knowledge about the real, physical world cannot be justified; unlike a priori knowledge about abstract, platonic worlds, as in mathematics. We can believe particular things about the construction logic of the real, physical world, but we cannot justify these beliefs.

The choice is theirs to a point, but beyond a point the choice is no longer theirs. — god must be atheist

The most intolerant wins.

For a plethora of reasons, the side which wants to use coercion in order to limit population growth is in a strategically bad position. Not only is the other side known to be much more intolerant, but it can also more easily replenish any losses to its head count.

If it is obvious that you will always win by arbitrarily decimating the other side, then why not do it? This outcome is also logical. It is the ones who say that there are too many people, who are the ones who will have to vacate the premises first.

If you still insist on morality being ONLY what one feels one should be doing, and without outside influences or coercion or reasoning, then what one feels should be doing could potentially include murder, rape, theft, ... — god must be atheist

Morality does indeed also deal with conflict resolution. Making victims while breaking moral rules creates the issue of victim compensation. I don't see how a third party could claim to be a victim when someone else makes more children than he believes is suitable.

I would urge you to please consider that the entire history of morality in society has been based on instruction, and telling people what they must, ought, should, do, by moral consideration. — god must be atheist

People subscribe to these teachings or they don't. The choice is theirs.

We all will have to cut our growth rates. — Bitter Crank

Morality is about self-discipline, i.e. about what you feel that you should be doing. It is never about what other people should be doing. That is not morality. On the contrary, that is a mere delusion.

Maybe therein a set of clues that a philosophy-of might organize somehow. — tim wood

Concerning "Software development philosophies", they tend to be epistemic considerations, but not very rigorous at that. Furthermore, their applicability is rather debatable. The "Rules of thumb" section actually looks like a better starting point.

By the way, I accidentally ended up drilling down into expensive consultancy practices: Rational Unified Process (RUP). Like all snake-oil style consulting, IBM's RUP has a rather poor reputation.

There is a nascent meta-level to these things, but it is rather poor. Epistemology would be a good starting point, and seems to have the largest number of contributions; but philosophy is more than only epistemology.

it's philosophy in the sense of perspective rather than the topic of this site. You're looking for this kind of thing. — fdrake

Yes, that is a better page. Unfortunately, all it really says, is:

There is still no common understanding of the content, aim, focus, or topic of the philosophy of computer science, despite some attempts to develop a philosophy of computer science like the philosophy of physics or the philosophy of mathematics.

That is exactly what I thought ...

How about having a matrice A.X=Y where A,X and Y have infinite number of rows and columns,X is the solution set which contains the secret, a row or a column in the matrix can specify the operations to perform on A to obtain A inverse. — Wittgenstein

If X is the secret and Y is the public key, then A would be some kind of generator of sorts. That would require that each non-zero element of the domain of Y can be written as A*K for some value of K.

In ECC, the variable A (aptly named G) is a/the generator of the Galois field. Its multiples can produce every element in it.

If that would not be the case, then it makes particular values of Y impossible. If it makes enough values of Y impossible, then it makes it easier to work your way back from Y to X, and solve the elliptic curve discrete logarithm problem. It would certainly damage the intractability of the elliptic curve discrete logarithm problem and hence reduce the strength of the encryption algorithm.

Adding along a Weierstrasz elliptic curve thoroughly distorts the addition operation in arithmetic. That is the first source of encryption/distortion strength in ECC. A second source of strength/distortion, is that it also operates in a finite field that automatically wraps around the result of arithmetic calculations. For example, in a mod 7 Galois field, 2+4=>6 (smaller numbers) while 3+5=>1 (larger numbers), you get the strange result that adding smaller numbers gives a larger result. As such, it destroys any expectation of monotonicity in calculations.

You would need matrix A to unleash a strong source of distortion. Also elliptic?

This sounds really naive and stupid but l hope you can suggest improvements to using matrices in cryptography. — Wittgenstein

Daniel Bernstein is arguably the top guru in the field of practical design of algorithms. This is his home page. His most famous implementation is undoubtedly nacl.

The theoretical top number one is Adi Shamir. He came up with many of the theorems. He is also the "S" in the famous (but now probably outdated) RSA cryptosystem.

You are asking me to weigh in on stuff that is rather at their level. I am just a user of their stuff, really. I don't come up with the theorems by myself, and actually, not even the core implementations. I just build in the stuff into other things, hopefully, without creating too many additional issues ... ;-)

I think it is possible to use an infinite field but more difficult than a finite field. — Wittgenstein

There's a stack exchange discussion on this question, "In cryptography, why do we reduce elliptic curves over finite fields?".

ECC over infinite fields are certainly not in use.

Imagine that P = s * G is the public key computed by multiplying a secret s of arbitrary size. A first step in the protocol will be to transmit P to the recipient while keeping s secret. If P can be arbitrary size, then you would need to transmit to the recipient a message of arbitrarily long size. I think that this problem alone is already a show stopper.

If you solve the problem by computing P = s * G mod 2^m, then you can guarantee that P will never be larger than m bits. That would already be one reason -- there could certainly be more -- to restrict calculations to finite fields.

I've been thinking about what would happen if everyone were to care for others more than they cared for themselves. If everyone was the opposite of narcissistic and took care of others instead of caring about themselves. Would the world be a perfect place to live on then? Would one care as much for everyone or would one care more for some compared to others? And what sort of problems would arrise under these circumstanses? — Ines

That could amount to giving unilateral hamlet-style sharing rights to everybody else on your income and/or assets.

It certainly works in relatively small communities, but it does not scale. No matter how large your income/assets, you will always end up in Gambler's Ruin.

If you live in a metropolitan area with 10 million people, you cannot recognize 10 million unilateral sharing rights on your income/assets.

There is that persistent myth that people became gradually more selfish.

Well no, that is not what happened. Over the centuries, the population grew dramatically, even exponentially, making any system of unilateral sharing rights simply unsustainable. The problem can be alleviated through charity, though.

But for most I've met, although they may still go to Temple, many marry outside their religion; live, work, go to school, and have close friends among non-Jews; and consider themselves Americans and local community members. — T Clark

Yes, they certainly exist. That is the kind that will assimilate, i.e. disappear in the night of history. They will not be around as a separate identity in 2000 years from now. Probably not even in 100 years from now.

African-Americans and other racial minorities were artificially kept separate through laws that forbade interracial marriage which were abrogated only in 1967. Distinct racial groups nowadays barely exist in countries like Brazil or Mexico. It got all mixed up over probably less than 200 years.

Jews also participate in interracial marriage, but they still manage to keep their separate identity afloat, even for 2000 years, because race is rather irrelevant in it. There is always a proportion of the Jewish community that assimilates and drops their separate identity, but the remainder carries on. African-Americans won't do that, because the only distinguishing feature in their community is some flimsy notion of race, which is no longer legally enforced either.

In my limited experience, although Italians, Irish, and Jews maintain a sense of national identify, it is just one among others. — T Clark

Italians and Irish may want to preserve their attachment to Catholic religion, but marrying any Catholic spouse would do, who would not even need to be Italian or Irish. Furthermore, attachment to Catholic religion is generally not even that strong any more nowadays. So, they will trivially consider any Christian, non-Catholic spouse for that matter, if they even bother with that, because I can see them picking a spouse amongst other religions and even amongst atheists. So, I can see them assimilating and their unique differences disappearing altogether. That won't be the case for the Jews, which is actually not a national identity, but a tribal+religious one. Otherwise, it would already have happened, and it clearly didn't. Nationalities are flimsy. They don't last, and therefore, they do not mean much. On the long run, it is a waste of time to identify with that.

I have no problem with that, but if it became widespread, there would probably be negative consequences. — T Clark

Well, according to the article, it was supposed to be widespread in the first place ...

I think the same is true for other minorities in America - Irish, Hispanic, Italian, Jewish. It seems to me the difference is that those other minorities will fairly quickly join the mainstream. Maybe that will happen eventually for black people, but it hasn't happened in 400 years and there is still a long way to go. — T Clark

I doubt that African-Americans want "assimilation". Well, not sure. Maybe they do. Maybe they don't.

The Jews certainly don't want it. They must like their own clan and their own Rabbinical take on Second-Temple Judaism, because otherwise they would have dropped these things a long time ago already. The fact that they are still around after almost 2000 years, points to the idea that they probably do not even want to assimilate, even when offered the opportunity, which wasn't always the case either.

Concerning African-Americans, they would only be preserving a skin colour, which is a flimsy concept anyway. So, that would be a long-term losing proposition anyway. If you want to preserve your difference to the mainstream, you will need something more "conceptual" too. They don't have their own religion. So, I don't believe that they can do it.

Maybe, but I don't think that applies to black people, Hispanics, and other unpopular minorities. White American society defined black people as black starting 400 years ago. — T Clark

African-Americans were not in the driver's seat in that respect. They did not choose to identify according to race. That decision was clearly made for them.

Concerning other minorities, it really depends whom we are talking about.

For example, Jews may have other things to identify to than race. The very term "Jew" does not denote any particular race. In fact, you probably have Jews in every race on the planet. To what extent, race is a defining characteristic for them, is not clear. If your mother is Jewish, then you are too; especially, if you also subscribe to Judaism. Race does not seem to be the major factor there.

Africans are also different from African-Americans in that respect.

For example, someone will be considered a member of a Somali clan, regardless of his race, simply, because his father is part of that clan. Someone could have a very different skin colour from the typical Somali, because of his mother, but I somehow suspect that it doesn't matter much to the clan, or to the person himself. I am sure that you have relatively light-skin Somalis who still totally identify with the same clan, just as their parents do.

Whether you want to replace --> with =, they are relations and quantification over infinite terms does not makes sense. That's my point. — Wittgenstein

I certainly agree with that. In my impression, it is indeed not possible to use infinity in every slot where you can fit finite numbers.

Concerning "-->", yes, every arrow is fundamentally bidirectional, but when you rewrite expressions, you will generally only use one direction. So, a+b --> c obviously implies that c --> a+b. Still, only one of both will be useful in your rewrite strategy, in order to obtain a closed-form expression, or when trying to prove a theorem.

Finitist mathematics is not meant to discount the standard mathematics, we are just exploring a new world which is limited. — Wittgenstein

Galois fields? Pick a prime power p^n and carry out all arithmetic modulo p^n. Approximately all algebraic structure that exists over infinite/countable will turn out undamaged! ;-)

Irrespective of Augustines 'mental prowess' or otherwise, you don't seem to have considered that 'the church' benefitted materially by acquiring estates of unmarried cousins which would have hitherto remained in the family. This fact raises issue with the meaning of the word 'virtuosity'. — fresco

Yep, agreed. It is all about the Church "overcropping" their flock until ... they really turn into sheep.

Mathematics and logic is one thing ... but reality is temporal and spacial. — luckswallowsall

Only one part of the domain of knowledge, i.e. in Kantian lingo, "synthetic a posteriori", deals with the real, physical world. The other part, "synthetic a priori", only deals with abstract, Platonic worlds.

In my opinion, there may be too much emphasis on "reality".

In my professional activities, I have never dealt with "reality". I have only ever dealt with Platonic abstractions and their implementation in software. That is why I cannot comprehend why anybody would be so obsessed with the real, physical world to the exclusion of everything else.

Infinity is clearly a Platonic abstraction. Why would anybody try to shoehorn it into the real, physical world? For what purpose?

"White Privilege" is a recently coined and is an empty concept if applied to ordinary -- most -- white people. Wealth Privilege strikes me as much more convincing. Money talks. "White trash" are trash because they are poor, and have been poor for a few generations, and have had as few opportunities as poor blacks. Whiteness doesn't help them at all. — Bitter Crank

Well, the fact "Whiteness doesn't help them at all" is probably what they experience as being "unfair". I guess that we already know what they really want:

The National Party's election platform stressed that apartheid would preserve a market for white employment in which nonwhites could not compete.

As soon as people identify strongly with race, then race politics can never be far away. Still, the concept of "race" has always been nebulous, because it is not just about skin colour.

The European Jews were also white, but that did not make a difference in the 40ies, in German race politics. Polish and Russians are technically also white, but somehow still deserved the label of "Untermensch", i.e. subhumans, while the Japanese didn't. They were considered honorary white.

So, there clearly were nonwhite whites and white nonwhites. Of course, all of that did not make racial politics any more rational ...

I don't know what to make of this other than fucking your cousins helps Black Lives Matter. — fdrake

Well, I think we all understand that it is a bit late in the game to start bug fixing. The multitude of layers of family ties that would need to be restored in order to rein in excess racism and nationalism is ... daunting.

But then again, without that multitude of layers of family ties, even the nuclear family seems to fall apart. The following article clearly identifies a link there too:

Marriages of first cousins, first cousin once removed and second cousins compared to unrelated marriages, decreased the risk of divorce. Therefore it might be concluded that consanguineous marriages are a way which chosen by these populations in order to maintain their own social stability. Taken together it might be concluded that consanguinity has social advantages.

I have no clue how families can be reintroduced in a society that is so incredibly individualized and atomized. Still, in my impression, it is the only way out of the conundrum. It is probably a question of doing it, before it is too late.

Concerning "black lives matter", the African-American population also has a serious problem with individualization and complete atomization of their demographic. The question of how to reintroduce at least some form of nuclear family is not simple to answer, let alone the additional extended-family layers required to keep the nuclear family together.

Identifying with race and/or nationality are feeble substitutes for identifying with extended family and religion. Of course, for people who do not have an extended family nor a religion, it is understandable that they acquire that kind of mental deficiency. I often do not agree with the Papacy, but I can only endorse his 1937 "With burning concern" admonition to the Germans:

8. Whoever exalts race, or the people, or the State, or a particular form of State, or the depositories of power, or any other fundamental value of the human community - however necessary and honorable be their function in worldly things - whoever raises these notions above their standard value and divinizes them to an idolatrous level, distorts and perverts an order of the world planned and created by God; he is far from the true faith in God and from the concept of life which that faith upholds.

But then again, the Papacy conveniently fails to mention how it is the Church itself that had been instrumental in dismantling the extended families in Europe:

Cousin marriage was once the norm throughout the world, but it became taboo in Europe after a long campaign by the Roman Catholic Church. Theologians like St. Augustine and St. Thomas argued that the practice promoted family loyalties at the expense of universal love and social harmony. Eliminating it was seen as a way to reduce clan warfare and promote loyalty to larger social institutions -- like the church.

It is not the Church that ultimately turned out to be the big winner in the millennium-long policy of dismantling the clans and the tribes in Europe. It is the State, along with an irrational and unsustainable notion of race, that became the winners.

Therefore, the year 1937 was a bit late in the game for the Church to decry the consequences of their "own goal", i.e. the inevitable mental illness that the Papacy so aptly describes as: "Whoever exalts race, or the people, or the State".

It is possible to discover the meaning of life in the ancient scriptures. But then again, it will only work for those who believe that it is possible.

It is obvious that unbelievers cannot find meaning or purpose in that what they do not believe. According to the scriptures, that is the reason why the unbelievers will fail to find meaning and be unable to fulfil their destiny.

Second-temple Judaism successfully evolved out of Moses' congregation. It judiciously faced off the Hellenic-Seleucid threat. It turned out later on, however, unable to handle the looming threat posed by the Roman empire and its imperial cult.

Even before the inevitable calamity struck, and even before second-temple Judaism imploded completely during the destruction of the temple in 70 AD, several of its offshoots frantically sought to survive.

The following three offshoots managed to overcome the challenge and survive. In chronological order: the Ebionite (=Islam), Pauline (=Christianity), and Rabbinic (=modern Judaism) offshoots. This chronological order is indeed a paradox:

Hans Joachim Schoeps observes: "Thus we have a paradox of world-historical proportions, viz., the fact that Jewish Christianity indeed disappeared within the Christian church, but was preserved in Islam and thereby extended some of its basic ideas even to our own day. According to Islamic doctrine, the Ebionite combination of Moses and Jesus found its fulfillment in Muhammad."

In the scriptures you will find the most straightforward answer as to the meaning of life:

Quran 51:56: We have created jinn and human beings only that they might worship Me.

Hence at the highest level of meaning, one can fulfil his destiny by praying to God, and keeping his law. Still, we have also been tasked to sexually reproduce:

Genesis 1:28: Then God blessed them and said, “Be fruitful and multiply. Fill the earth and govern it. Reign over the fish in the sea, the birds in the sky, and all the animals that scurry along the ground.”

We will do that, because we are predisposed to do so:

Fitrah. According to Islamic theology, human beings are born with an innate inclination of tawhid (Oneness), which is encapsulated in the fitra along with compassion, intelligence, ihsan and all other attributes that embody the concept of humanity.

Hence, the reason why we axiomatize these beliefs, is because they are part of our blueprint:

Quran 30:30: Set thy Face to religion as a Hanif in the primordial nature from God upon which originated mankind. There is no altering the creation of God. That is upright but most mankind know not.

Therefore, the job you do, such as bookkeeper, manager, social worker, or psychiatrist, and the tasks you carry out in secular, worldly affairs are insufficient to give meaning to your life. Even helping other people, is insufficient to fulfil your destiny. You will still need to pray, keep God's law, and sexually reproduce to find fulfilment.

Yes, metaphysics is difficult. If we look at wikipedia, and the Stanford dictionary of Philosophy, and so forth, we find many different descriptions of what metaphysics is, most of them unclear (IMO). About the only thing I am sure about is that metaphysics has nothing to do with physics. — Pattern-chaser

Metaphysics is presuppositionism about the real, physical world. In Immanuel Kant's lingo, it would be "analytic a posteriori", which he resolutely rules out as being possible. To the extent that metaphysics investigates the real, physical world, it can safely be considered to be a failed discipline. Presuppositionism itself, however, lives on in, for example, mathematics, where presuppostions, i.e. axioms, are the building bricks of abstract, Platonic worlds.

That’s over and above ‘falsification’ into the general aspects of scientific method. — Wayfarer

Yes, falsificationism is just the core of the method. Pavlov's dog was also falsificationist. It is obvious that it was not enough for the dog to understand what was really going on. So, scientific control is what is needed to avoid behaving like Pavlov's dog in an otherwise legitimate falsificationist situation.

There are a lot of scientific publications in otherwise prestigious journals of which the merely basic falsificationism does not exceed the level of intelligence of Pavlov's dog.

It's simply that if you can't falsify it by an objective observation, then it's not an empirical hypothesis. — Wayfarer

Agreed, that is obviously the core of it. Still, that is not enough:

A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable. This increases the reliability of the results, often through a comparison between control measurements and the other measurements. Scientific controls are a part of the scientific method.

As you can see, there is the need for an additional battery of anti-spam measures.

Statistics is a very tricky and philosophically fraught subject. Nevertheless, statistics is where the rubber meets the road, as far as philosophy of science is concerned. If your philosophy has no implications for statistical methodology, then it has little relevance to science. — SophistiCat

I like Nassim Taleb's rants on how statistics is being abused nowadays. They are a cautionary tale against brainless number crunching and phishing for correlations.

Beyond that, the question in science is rather: How did you test that? How did you take care of scientific controls? Has anybody else tested it again? These anti-spam measures neatly hark back to Popperian falsificationism, which in my impression, still rules as king over the epistemic domain of science.

Bernard D'Espagnat is an interesting philosopher of physics ( obit: https://www.nytimes.com/2015/08/16/science/bernard-despagnat-french-physicist-dies-at-93.html) — Wayfarer

Unfortunately, NY Times has a policy of endlessly nagging for readers to create a "free" account and give up lots of personally-identifying data, in order to access the information linked to. I have a personal policy that says, if the only source is NY Times, then it has no source, and then the information simply does not exist. My policy works absolutely fine. We do not "need" NY Times. How could we "need" them, if they are not even convenient to use?

So, I ended up checking Bernard D'Espagnat's wikipedia page, but it is scant on useful details:

D'Espagnat remained troubled by the scant attention most physicists paid to the interpretational questions raised by quantum mechanics.

From his wiki page, it is not clear how much further D'Espagnat gets than discussing Schrödinger's cat and the paradoxical nature of entanglement.

Even though it is certainly interesting and even intriguing, I personally do not have access to multibillion supercollider installations, such as CERN's Large Hadron Collider. So, as an outsider, I look at these things from quite a distance. So, my perennial remark is always: "Yes, but what do you need me for in all of this? I can't see anything, really ..."

George Ellis and Joe Silk are two current physicists who have launched a movement to debate whether string theory really is a scientific theory or not. That has given rise to much interesting debate also. (See here.) — Wayfarer

Interesting link:

But, as many in Munich were surprised to learn, falsificationism is no longer the reigning philosophy of science. Nowadays, as several philosophers at the workshop said, Popperian falsificationism has been supplanted by Bayesian confirmation theory, or Bayesianism, a modern framework based on the 18th-century probability theory of the English statistician and minister Thomas Bayes. One concern with including non-empirical arguments in Bayesian confirmation theory, Dawid acknowledged in his talk, is “that it opens the floodgates to abandoning all scientific principles.”

Concerning "Bayesian confirmation theory, or Bayesianism, a modern framework based on the 18th-century probability theory", we will probably need to unleash the king of the epistemology of probability onto these guys, Nassim Nicolas Taleb (NNT), the master at slagging off exactly this kind of stuff:

Taleb contends that statisticians can be pseudoscientists when it comes to risks of rare events and risks of blowups, and mask their incompetence with complicated equations ... Nonetheless, [a critic] calls the book "essential reading" and urges statisticians to overlook the insults to get the "important philosophic and mathematical truths ... Yet beneath his rage and mockery are serious issues ... Taleb and Nobel laureate Myron Scholes have traded personal attacks."

In my opinion, anything based on probability theory and statistics must be treated with utmost scrutiny, because these things are core ingredients in the snake-oil industry. Not only NNT complains about that.

If Dawid wants to replace falsificationism by Bayesianism -- people would think that he is not serious, but ok he probably is -- he will have to fight a lengthy and acrimonious uphill battle. He will not manage to reach the other side of the hill in my life time. Seriously, I can't imagine. So, my own take is that headquarters need to throw in some extra regiments from the standing reserves into the fray after duly carpet bombing the enemy's position, called "Bayesianism", prior to authorizing a general advance.

“The Bayesian framework is much more flexible” than Popper’s theory, said Stephan Hartmann, a Bayesian philosopher at LMU.

Ha ha ah! Stephan Hartmann clearly does not get it. Something that is "much more flexible", is exactly what we do not want. We want much, much more shit testing of novel ideas, and not less.

“The imprimatur of science should be awarded only to a theory that is testable,”Ellis and Silk wrote, thereby disqualifying most of the leading theories of the past 40 years. “Only then can we defend science from attack.”

I completely agree with Ellis and Silk. In my opinion, we certainly need an entire battery of extra anti-spam measures against the snake-oil industry. We need to build a huge wall against non-testable theories, and it is Mexico who will pay for it! ;-)

You necessarily have to presuppose some information, but ideally it seems like you shouldn't presuppose anything at all. — thewonder

Idealized worlds necessarily have an abstract, Platonic nature, which are built from presuppositions only. You cannot investigate an idealized world without building it first. So, no, the idea that ideally "you shouldn't presuppose anything at all" cannot possibly work for idealized worlds.

I will avoid further derailing this thread as none of this has all that much to do with bias against Philosophy in scientific circles — thewonder

Indirectly, or even directly, it does.

It is incredibly easy to say something like "you shouldn't presuppose anything at all", and still somehow sound reasonable, while it simply isn't. That is the core problem with philosophy. Nothing to painstakingly test. Nothing to painstakingly prove. So, where is the barrier to mere bullshit? Where are the anti-spam measures?

As Linus Torvalds so beautifully said, "Talk is cheap. Show me the code."

Hence, it is trivially obvious why scientists do not want to discuss with people who want to talk about the philosophy of science but who seem to be incapable of doing anything worth mentioning, in science. It is just too easy, peasy to do that, and that is why they should not take anybody seriously, who does exactly that.

You will first need to show skills and experience in a field that is substantially less forgiving than philosophy. So, if you want to talk philosophy of science with scientists, scientists will demand that you first show that you can operate successfully at a very high level in science proper.

A critique of a Rationalist epistemology could be that a priori truths are presupposed. We presuppose things all of the time, but that one should do so in Philosophy, I think, would indicate that they haven't thought critically enough about their subject matter. — thewonder

Well, as Aristotle wrote, if nothing is assumed then nothing can be concluded. Being critical about axioms almost always leads to infinite regress. That is why we do not much think critically about axioms. We simply presuppose them.

The better opinion about axioms is to consider them to be arbitrary inputs, i.e. arbitrary construction bricks. That is why you can axiomatize whatever you like. What matters, is that particular conclusions are unavoidable outputs from a given set of such presuppositional inputs. From there on, some kind of structure will emerge that will make an entire world of conclusions either unavoidable or impossible.

So, presuppositionalism is meant to be evaluated at the level of an entire system of rules, not at the level of one individual rule. Therefore, if you do not like a particular system or its building bricks, you can always propose an alternative one. People do that all the time.

I think that I understand what you are saying, but I don't think that I would define Metaphysics as being "presuppositional". Metaphysics assumes that there are things that are "out there" that are "true". — thewonder

Metaphysics study is conducted using deduction from that which is known a priori. Like foundational mathematics (which is sometimes considered a special case of metaphysics applied to the existence of number), it tries to give a coherent account of the structure of the world, capable of explaining our everyday and scientific perception of the world, and being free from contradictions.

"To know a priori" is a synonym for "to presuppose".

A "presuppositional" approach to the world is viable when it concerns issues where we have enough degrees of freedom. Morality is like that, but technology is, to an important extent, also like that. We do not merely accept the world as it is. On the contrary, we actively shape it, not because the things we want, are true and out there, but because we want them to become true and out there.

Is that Metaphysics, though? — thewonder

If we define metaphysics as "presuppositionalism", then automata theory, being clearly axiomatic, is in a sense, indeed, "presuppositionalist".

By presupposing what we want the world to be, we occasionally manage to change it to match our presuppositions.

I feel like "Science" is better suited to discover what actually exists. — thewonder

Concerning "discovering what actually exists", that is only a small part of the story. A good part of the world we live in, was purposely built like that. We do not live in pristine nature. In fact, we would probably not be able to survive in pristine nature. We probably never even did. We have always shaped nature around us, to suit us.

For example, by merely studying nature, and looking for patterns in it, you cannot uncover the world of automata, because they simply do not exist in nature. Automata theory was painstakingly designed and developed long before Jon Von Neumann proposed his now ubiquitous computer architecture (1945).

Automata theory and abstract machines are epistemically out of reach for science. In a world where all knowledge must be acquired through experimental testing, i.e. in a world of scientism, we would still be living in caves.

Can you generate infinity from that function ? I dont think so, unless you think we can construct an infinite number of characters in a string. — Wittgenstein

Not sure. For example, if there is a rewrite rule "x/0 = ∞" for x not zero, the symbol could start popping up in output expressions. If you feed that output expression into your function F(x), it depends on whether F will accept it as an argument, and if so, if can successfully associate an output to it. Not sure at all.

Let's consider your example KK*-->K+, how about this case ab(ab)*-->cd+ . Would that be rule if and only if ab=cd — Wittgenstein

You will need to apply two successive rewrites:

ab(ab)* -(1)-> ab+ -(2)-> cd+

(1) rewrite rule: KK*-->K+
(2) rewrite rule: ab-->cd

An absolute formal view will lead to many problems and there is also another problem with this language as it allows a function to take itself as an argument, that may lead to paradoxical self referential statements. Like a set of all sets for example. — Wittgenstein

Yes, Russell's paradox and Gödel's Incompleteness obviously apply. Axiomatic systems are quite powerful, but they also tend to be incomplete.

By alleging infinity to be a platonic abstraction doesn't help us understand its nature at all. — Wittgenstein

The nature of infinity is what you can do with it in your system. It will participate in rewrite rules. From there on, its nature emerges out of the rewrite rules in which it participates. If:

x & %SYMBOL = %SYMBOL

then %SYMBOL could have the role of the identity element, if domain D with operator "&" is meant to be a group. It could be part of the kernel of a homomorphism of sorts. The nature of %SYMBOL will become increasingly clear by considering the other rewrite rules.

When the need arises they let p+0=0 so l dont see how the point at infinity is related to infinity that we are discussing here. — Wittgenstein

It is just an example of an algebraic structure in which adding a concept of infinity keeps the entire system consistent. Otherwise, the domain has no identity element, and then is no longer a group. That is not allowed, because the system effectively makes use of the systemic property that the domain is an abelian group under addition. You can clearly see that in the definition of the encryption/decryption functions and of the sign/verify signature functions. When you prove that decryption is the inverse of encryption, you make use of the fact that it concerns an abelian group under addition.

This has nothing to do with the real, physical world. In this case, a point at infinity is just a tool to keep that cryptographical system consistent. This principle can be generalized. Adding infinity to a domain is just an instrument that can be used to achieve a particular purpose.

What is the constructivist alternative to doing that?

This approach is deeply embedded in existing technology nowadays:

The U.S. National Institute of Standards and Technology (NIST) has endorsed elliptic curve cryptography in its Suite B set of recommended algorithms, specifically elliptic curve Diffie–Hellman (ECDH) for key exchange and Elliptic Curve Digital Signature Algorithm (ECDSA) for digital signature. The U.S. National Security Agency (NSA) allows their use for protecting information classified up to top secret with 384-bit keys.

Therefore, it is a bit late in the game to argue whether extending a domain with the infinity symbol makes sense.

I think that mathematics is primarily based on substitution where we replace a set of symbols with another set of symbols which are equal or equivalent in some cases. How do we decide that ? By "meaning" l meant the criterion for substituting one expression to another. — Wittgenstein

If there is a match between a rewrite rule and an expression, you can rewrite the expression. So, it all depends on the rewrite rules of the system. These rewrite rules have no particular "meaning".

Say that there exists the following rewrite rule in the system: kk* --> k+, with k any arbitrary subexpression, then we can rewite the expression xyabc(abc)*rs --> xy(abc)+rs. This has no "meaning". The resulting expression is just the result of the mechanical application of the rewrite rule on the original expression.

Formalism has axioms and there are rules of inference etc. It cannot work without them. — Wittgenstein

Both axioms and rewrite rules are arbitrary. For example, the SKI combinator calculus uses the following rewrite rules:

Ix --> x. Kxy --> x. Sxyz --> xz(yz).

We can use this rewrite system to rewrite input expressions to output expressions, and derive new theorems from the system. For example, since SKxy -> y, we can see that SKx = I for any arbitrary choice of x. This theorem is meaningless, because the statement, which is provable from the construction logic of the SKI system, that "∀x in D: SKx = I" does not correspond to anything in the real, physical world.

It is a single character but can we substitute it with numbers ? — Wittgenstein

Infinity itself is a Platonic abstraction that is compatible with numbers, which are themselves also Platonic abstractions. Numbers are themselves no real-world objects either. Infinity is compatible when you can extend the rules for arithmetic to support the inclusion of infinity. while not damaging the algebraic structure.

Consider the real line, all the real number lie on it but infinity doesn't. — Wittgenstein

We don't care about lines in this context.

Therefore by allowing infinity, we sort of compromise the formal system. This is the basic idea behind the constructivist approach, if l am wrong, you are more than welcome to correct me. — Wittgenstein

I think that you correctly depict the constructivist view on infinity. But then again, I don't read much constructivist literature, because in my opinion, they are missing the point anyway. Cantor's elaboration of the concept of infinity is nicely consistent. I have no problem with it. I really do not see what the fuss is all about.

I think that when we introduce the infinity symbol, we will have to drop associative law and commutative law too. — Wittgenstein

Concerning commutativity, the problem does not seem to occur in x + ∞ versus ∞ + x, as both expressions get rewritten to ∞. In my impression, the arithmetic rewrite rules handle the symbol perfectly well. Adding ∞ should not modify the algebraic structure. Otherwise, you should not add it to the domain that you are dealing with. So, for example, if D' extends D with ∞, and <D,+> is a group, then <D',+> should also be a group. Otherwise, don't bother adding it.

By introducing the symbol into the rules and not being able to generate it from the real numbers is cheating. Is this extension valid ? — Wittgenstein

If adding it, can be done while preserving algebraic structure and therefore consistency, you can go ahead and add it. It does not even need to be about numbers.

In fact, there are situations where you must add ∞ in order to guarantee the consistency of field operations. For example:

For current cryptographic purposes, an elliptic curve is a plane curve over a finite field (rather than the real numbers) which consists of the points satisfying the equation y² = x³ + ax + b along with a distinguished point at infinity, denoted ∞. This set together with the group operation of elliptic curves is an abelian group, with the point at infinity as an identity element.

Without identity element, point addition would not be a group operation. The domain here does not consist of numbers but of two-tuples (x,y):

The equations (for point addition) are correct when neither point is the point at infinity, (0,0). When adding the point at infinity to another point, the result is simply the other point.

Elliptic curve arithmetic has obviously nothing to do with the real, physical world. It was not abstracted away from the real, physical world. Elliptic curve arithmetic is a Platonic abstraction that has characteristics and properties that turn out to be interesting, while adding a point at infinity is not only a requirement for consistency, but it also happens to work absolutely fine.

Are you making the case that a more rational approach to morality is less corruptible? — T Clark

From the altercation between the Church and Martin Luther, the impression emerges that the Church is fundamentally an occult society that occasionally uses a book, i.e. the Bible. However, from its deepest secrets the Church very well knows that its book is an arsenal replete of deceptive arguments.

So, we may probably somehow conclude that the Vatican Secret Archives contain these secrets, and that they utterly discredit and disparage the Bible.

So, yes, we had better use an approach to morality that is more rational than that. Again, there are good reasons to believe that Rabbinical-orthodox Judaism and Islam offer exactly such alternatives.

Without unique readability we wouldn't even have true in one reading and not in another. Without unique readability we wouldn't even have the recursive definition of 'true in the model'. — GrandMinnow

Yes, and mentioning the issue "unique readability" forcibly drags the entire, seemingly endless field of formal language and therefore related automata theory into the fray.

That means that the "language game" now pushes you right into the middle of the mathematics that govern computer science and in front of the issues that arise in programming languages.

Automata theory is not something that was abstracted away from reality. There are no automata in nature. You have to painstakingly build them, and you have to know how they work, and why they work, before you can even build them. Furthermore, through the problem of unique readability, they strike at the core of mathematics.

If you cross over from the realm of computability into pure mathematics, the term "language game" does not sound controversial at all. Brouwer's accusation that Hilbert was merely "playing language games", gives the impression that Brouwer was seriously missing the point. Hilbert, on the other hand, was asking all the right questions, during the end of the 19th century and the first half of the 20th century, long before the first computer was even built.

Are you making the case that a more rational approach to morality is less corruptible? I don't necessarily disagree with that, although I don't think it changes the basic nature of morality. — T Clark

Well, it's not that axiomatic theology cannot be done, or even that it would not work:

Principles of Islamic jurisprudence, also known as Uṣūl al-fiqh (Arabic: أصول الفقه‎, lit. roots of fiqh), are traditional methodological principles used in Islamic jurisprudence (fiqh) for deriving the rulings of Islamic law (sharia). This interpretive apparatus is brought together under the rubric of ijtihad, which refers to a jurist's exertion in an attempt to arrive at a ruling on a particular question.

According to the majority Usuli view, it is legitimate to seek general principles by induction, in order to provide for cases not expressly provided for. This process is known as ijtihad, and the intellect is recognised as a source of law. It differs from the Sunni qiyas in that it does not simply extend existing laws on a test of factual resemblance: it is necessary to formulate a general principle that can be rationally supported.

In both Rabbinical Judaism and in Islam, axiomatic theology, "through scripture and reason", is perfectly accepted. Therefore, Martin Luther was only advocating what is actually self-evident. It is the proposition of an infallible and "indefectible" Papacy that has turned out to be unsustainable.

Furthermore, concerning the oral secrets that the Church would have received and which would be the source of its legitimacy and origin of its power. For the sake of the argument, I am even willing to accept that these secrets could possibly exist. In early Christianity, under the persecutions of the Roman empire, the Church actually was a secret society. Therefore, the idea of orally transmitted secrets is not that far-fetched. However, I also believe that society-wide morality is not well served when keeping essential rules a secret. Furthermore, as far as I am concerned, justifying from these hidden secret teachings, the sale of indulgencies, was clearly one bridge too far.

On the whole, I side with Martin Luther's argument in favour of axiomatic morality, which is a principle that has clearly been elaborated successfully in Rabbinical-orthodox Judaism and Islam, and of which the very nature has substantially better guarantees against corruption and depravity. In that sense, axiomatic theology effectively preserves the basic nature of sound morality.