This whole discussion started from the question of whether the liars paradox has any implications for the design of bridges, i.e. if the paradox undermines the basic aspects of using math to solve problems. Thoughts?

Or the very example you used, you associated a sound with thunder. Only that it wasn't thunder, it was a truck. The sound appeared to you as belonging to thunder. Sounds appear or are represented (if you prefer this word) by us as belonging to certain objects automatically, but they need not produce these specific effects in us. — Manuel

So, since I have heard the sound of a horse pulling a wagon before, the sound of a horse pulling a wagon would resemble a horse pulling a wagon to me. If that's what you mean, I'm ok with it.

Wittgenstein is literally asking why should one be afraid of contradictions in mathematics. What you or the author are saying, I don't know. I would answer that mathematics as we know them are built on the LEM, so the reason why we should be afraid of contradictions in mathematics is to keep that body of work alive and well. — Olivier5

I'm ok with that. As I said before, this is not my area of expertise. It feels good that Wittgenstein agrees with me, even if Turing and you do not.

I am trying to point out sensations, the way ice feels to our fingers, the way thunder sound to our ears, etc. A horse pulling a carriage produces a sound which I would not initially associate with such objects, that these objects could sound this way. They could sound completely different from what they appear to me. — Manuel

You recognize the way ice feels on your fingers because you've felt ice with your fingers before. You recognize thunder because you've heard thunder before. I've mistaken thunder in the distance for a truck going over a bump. I live on a busy street. I've heard a horse pulling a wagon before, so I'd probably recognize the sound for what it was.

I still don't know what you mean when you say "sound completely different from what they appear." What does a sound appear like?

The issue is that of resemblances. Reid points out that if you are walking down a street and hear the sound of a horse pulling a wagon and then you turn around and look at it, the sound produced does not resemble the objects producing it. — Manuel

What would it mean for the sound of a horse pulling a wagon to resemble a horse pulling a wagon?

We can do this for almost all of our senses, with the apparent exception of sight. It makes no sense to say (for example) that the red sensation I get from this apple does not resemble red. And so on. — Manuel

You've run a bait and switch. It's not a question of the red sensation resembling red. It's a question of the sight of an apple resembling an apple. In what sense does the sight of an apple resemble an apple that is different from the sound of a horse pulling a wagon resembling a horse pulling a wagon.

Answer - none.

This is a really interesting discussion.

I don't read this in the only (?) direct quote provided in that article, which reads as follows:

“Why are people afraid of contradictions? It is easy to understand why they should be afraid of contradictions in orders, descriptions, etc. outside mathematics. The question is: Why should they be afraid of contradictions inside mathematics?”
(emphasis mine)

Also from the article (though not a direct quote):

In relevance to this essay, Alan Turing (1912–1954) strongly disagreed with Ludwig Wittgenstein’s argument that mathematicians and philosophers should happily allow contradictions to exist within mathematical systems. — Olivier5

This from the article's author:

All the above means that if mathematics is a human invention, then any contradictions and paradoxes there are (within mathematics) must be down to… us. And if they’re down to us, then they aren’t telling us anything about the physical world (which includes Turing’s bridge — see later) or even about a platonic world of numbers — because such as thing doesn’t even exist.

And this:

Wittgenstein’s argument (at least as it can be seen) was that the Liar paradox does indeed lead to this bizarre conclusion because — in a strong sense - it was designed to do so. That is, it is part of a language-game which was specifically created to bring about a paradox. And because it’s a self-enclosed and artificial language-game, then Wittgenstein also asked “where will the harm come” from allowing such a contradiction or paradox?

And this:

Indeed many (pure) mathematicians have often noted the complete irrelevance of much of this paradoxical and foundational stuff to what they do. Thus if it’s irrelevant to many mathematicians, then surely it would be even more irrelevant to the designers who use mathematics in the design of their bridges.

Whether or not Wittgenstein means what I said he means, I think this shows that the author of the article thinks Wittgenstein means what I said he means.

Except that Wittgenstein rejected the idea that words represent reality and maps represent territories. — Joshs

Yes. Wittgenstein and I agree. Wittgenstein and I both think that mathematical inconsistencies are meaningless. I think. Maybe. I think that's what the article said.

That's because you take the whole question of 'can the liar's paradox break bridges' a bit too literally. The real question hidden behind this tag line is: should math allow contradictions? I.e. should we get rid of the law of excluded middle in math, or would that lead to poorly designed bridges? — Olivier5

I think what Wittgenstein was saying is that the trivial inconsistencies associated with the paradoxes don't matter. Are meaningless. There's a good chance I'm wrong about that, but that's how I read the article @Banno linked to.

I don't see what this has to do with the law of the excluded middle.

As you note, this is not exactly an argument for natalism or against anti-natalism. Our anti-natalist friends will not be convinced in the slightest. I'm sure you know that.

I see that you have become a moderator. Thank you. I'll try to be nice.

Why yes. What's in our mind at some point translates into real material structures like bridges, that are designed by someone using mathematics. If you allow contradictions to spread uncheck in engineers' minds and in their math, you may well end up with poorly conceived bridges. — Olivier5

To me, that's like saying the sentence "This sentence is not true" may slip it's leash, escape, and undermine the usefulness of the English language.

Wittgenstein made the point in Philosophical Remarks (IIRC), that whilst such inconsistencies would lead to physically untrue predictions if applied blindly, there is no reason why the occurrence of such events would discredit uses of the system for which inconsistency plays no role. And since it is impossible to predict the existence of mathematical inconsistency before it arises (due to the the second incompleteness theorem), there is no reason to fret about the possibility a priori. We only need to patch our systems as we go. — sime

From my limited perspective, it seems like the kinds of inconsistencies we are talking about are trivial and, really, meaningless. As I noted previously, when I read the proof of Godel's theorem, I couldn't understand why mathematicians and logicians thought it was important. As far as I can tell, it may tell us something about the foundation of mathematics defined in a very rigid way, but it says nothing about anything that might apply in the world.

Please, convince me I'm wrong. I find it hard to believe that my thoughts would overturn the concerns of the greatest philosophers and mathematicians.

Mathematics are in our mind, and science and technology too. — Olivier5

I'm not sure what you're saying in relation to my post. Are you disagreeing?

Please, explain what you think I said, and how you think your idea of good child-rearing is different from mine. — Athena

Yes, I think I misunderstood you. I thought you were putting Sparta's way forward as an example of loyalty to traditional ways of life and duty to country.

So, could the liar paradox cause a bridge to collapse?
— Banno

On balance, I think the answer might be yes.

The real harm will not come in unless there is an application, in which a bridge may fall down or something of that sort [] You cannot be confident about applying your calculus until you know that there are no hidden contradictions in it.
— Turing

And it's yes in part because of Turing. Nowadays engineers will to some degree rely on software to design bridges. It is fact that software complexity has created enormous challenges, and that it is not nearly so simple to verify correctness as one might wish. (In some fields like aircraft design there are strict, explicit standards for the provable correctness of programs, and still ... 737.) — Srap Tasmaner

I read your post yesterday and have been thinking about it since then. I am far from an expert on computer programming or mathematics, but it seems to me the kinds of contradictions described by Russel, Godel, and Turing don't have anything to do with the real world, computer generated or not. I guess that's what Wittgenstein was saying.

In my school days, I took a couple of courses in computer programming and did a little programming for an engineering project. That was in Fortran, which I guess tells you how long ago it was. Even with the simple programs I worked on, it was difficult keeping track of references and connections within and between algorithms. I find it hard to imagine how they do it with the incredibly complex programs that run the world now. There is so much complexity I find it hard to believe that a little meaningless self-reference of the kinds we are talking about will gum up the cogs in the machinery.

The more I think about it, the more I believe that the kinds of paradoxes we're talking about have no connection to anything outside our minds. It's another example of people mistaking words for reality, the map for the territory.

This is an interesting article. I also followed some of the links. To be honest, it starts about level with the bottom of my nose and quickly goes over my head. It has always confused me when people talk about paradoxes as if they undermine the validity of mathematics. In particular, I've always found the reactions to Russell's paradox and Godel's theorem hard to understand. Godel's proof of his theorem has always seemed goofy to me. I don't understand how the claim that one odd, trivial contradiction proves that math is incoherent in any meaningful way makes sense.

I've been meaning to bring this up as a subject, but I'm not a good enough logician to even figure out a way to formulate the question. This article has been helpful, even only by showing me that I'm not alone in my skepticism.

Thanks for the link.

I found myself, as an anarchist...uh...Libertarian, dismayed by the force of Fukuyama's reasoning, wondering if any serious challenge could ever be made to the democratic nation-state, or if any eventuality might break what I view as the soul-crushing monotonous security provided thereby. — Michael Zwingli

I think the end of history claim is likely to go the way of the belief in the end of physics at the end of the 19th century. People are not very good making these kinds of judgements. They generally represent a lack of perspective and an inability to see beyond prejudices. We'll see. Probably not me, I'm 69, but maybe you.

I reduced the quote to memory many decades ago. — James Riley

Thanks.

I would argue that while fears about the end of history have often arisen, especially in connection with religious beliefs, the threat is different at this stage in history because there is a major threat of mass destruction through nuclear warfare. Also, with climate change there is so much concern about the way humans have destroyed the planet and the view that the planet may be uninhabitable for future generations. — Jack Cummins

You seem to be equating the end of history and the end of the world. I thought they were different. To me the end of history has meant the end of the linear nature of life, i.e. progress. It makes me think of physicists in 1900 who thought that all the important questions had been answered and that all that remained to do was clean up the loose ends. Then came 1905, and physics started over.

Politically and socially, I thought it meant there wouldn't be many more milestones. All the major countries have finished their consolidation and are relatively stable. Smaller countries have mostly been released from colonial control. There won't be any more major wars. The world will become more homogenized.

Was I wrong in my understanding?

A weed patch in front of the house, on the other hand, is proof of one's failure in society. Success = nice grass; failure = weeds. I have weeds in my lawn. I agree with Veblen: large chemically dosed lawns are bullshit and ought to be stamped out. Screw the middle class lawn mower. — Bitter Crank

Ahh.. Philosophy for lazy people. My favorite kind.

Forgot - welcome to the forum. I hope you'll hang around when your class is over.

We're learning about T/Daoism in my Eastern Philosophy class, and I'm a little disturbed by its prescription of acting "with nature," i.e."going with the flow," "letting what will be, be," etc. I think this can bring contentment with existence, but the individualist in me says I don't want to settle for "chopping wood and carrying water" - leading a simple, unremarkable life. — Satyesu

I assume you've read The Tao Te Ching. It's the best of all the religious/philosophical foundation documents. Why you ask? Because it's short. You can read it in an hour. If you have read it, you've noted that many of the verses are aimed at leaders - princes, generals. It's not primarily aimed at people who "want to settle for chopping wood and carrying water."

Eastern philosophies have often gotten a bad rap from western philosophers. They say that states of heightened awareness are a way of muffling our intellect, living in a hazy state of bliss with no content. That's a complete misunderstanding that highlights the difference between eastern and western approaches. Western philosophy is, generally, about intellect and reason. Eastern philosophy is about awareness. Awareness of the world and awareness of ourselves. Westerners say "think about this rationally." Easterners say "pay attention." The power of paying attention can be hard for westerners to grasp. It seems lazy, sleepy.

Here is my favorite summary of how I understand the eastern approach. It's written by a western writer, Franz Kafka. Not a happy-go-lucky hedonist. I don't know if he was influenced by eastern thought.

It is not necessary that you leave the house. Remain at your table and listen. Do not even listen, only wait. Do not even wait, be wholly still and alone. The world will present itself to you for its unmasking, it can do no other, in ecstasy it will writhe at your feet.

The part of this that always hits me is "Do not even wait."

The concepts of non-action and action-without-action, wu wei, are central to Taoism. They don't mean "go with the flow." They mean to wait until right action arises from within you spontaneously. Don't act from nature, act from your nature. It is possible to act without intention, from the heart if you will. You need to be patient, aware. Pay attention. Then action will arise. I can do this.... sometimes. I'm sure you do too. Very few of our actions come out of rational thought. That's one of the things you need to be aware of.

Welcome to the forum.

You write well and your ideas are interesting and well presented. I hope you'll hang around for a while. As I noted, I won't be much help with any Hindu philosophy/religion questions, but it will make @Wayfarer happy.

Does Western philosophy comment on Advaita specifically? If so, what is the general consensus on Advaita in Western philosophy? — Paul Michael

My knowledge about Hindu religion is minimal, but it is my understanding that when eastern philosophies became known in the west, they were considered by western philosophers. In particular, Schopenhauer and Nietzsche expressed interest in Buddhism. Although I don't think there is any evidence that he had come in contact with eastern thought, it has always seemed to me that Kant's concept of noumena has similarities with the Tao.

You know, like Athens and Sparta. When Persia began invading and Athens imitated Sparta to some degree. Athens expecting all men to defend the country and in return giving them a say in government, but it did not start taking care of everyone's needs as Sparta did. — Athena

Apparently it was a difficult life for children in Sparta. Among other harsh child care practices, it is reported that "unfit" children were killed soon after birth. I think your idea of good child raising is different from mine.

I have some really crazy ideas — Athena

Yes.

Eighty percent of non-religious individuals of Western-European culture you would ask about this - in my urban living area at least - would decry the Judeo-Christian moral set and fully maintain the order of the other at the same time. Surely there must be some type of explanation for this change, which I'm not fully gasping. — kudos

Two thoughts. First, if you ask a non-religious person about religious principles it's no surprise if you find negative attitudes. Second, just because people are not aware of the connection between religion and personal liberty doesn't mean it isn't important. Religion has been politicized to the point that it is hard to get perspective. It hasn't been long since the two were inextricably entwined, the civil rights movement being one example.

Is it expressly social, political, technological, anthropological, etc.? — kudos

As I said, I think it's primarily political.

From my own observation the West seems to be in this sort of transition process moving from cultural institutions and structures of individual life derived from these 'unclean' histories to a sort of ideologically automated version. Another way of putting it would be tying up the histories into a type of self-sustaining loop that negates the full extent of their intended meaning but still allows them to survive in a symbolic form through practice. This is done in such a way that over time they would almost certainly become deteriorated and lost or at least alienated from their original meaning. — kudos

I don't understand.

But maybe there is a greater theory of everything: one that explains not only physics but any question proposed to it, something that could explain consciousness, possible diseases, the types of technology we could produce and everything the universe is capable of manifesting - a “singularity” that would revolutionise our understanding of all things. — Benj96

This is a bit too cute, but that doesn't mean it isn't true - The Tao that can be spoken is not the eternal Tao.

In a universe where everything is ineffectual does this make moments precious and worthy of reverence or do we require a more apathetic approach? — Benj96

The purpose of each human's life, to the extent there is one, is the experience of that life. The inability to face that is what religion and philosophy are all about.

I don't think so. Space expands (inflates like a balloon, or warps) and is not "created". — 180 Proof

But I think the zero-point energy density of space is always a constant and greater than 0. I don't see that as necessarily contradicting what you have written.

I see it as irrelevant if Jefferson himself believed personally and individually in a G-d. The basis of the matter is there is nothing evidently binding the liberal idea to religion, but we can then not easily conclude that these two are fully separate and distinct.

You seem to consider it an accident that there are themes and references in the writing that refer explicitly to a Creator. There is still undeniably something implicit in the writing that implies religious ideas and contingencies. For instance, the concept of liberty itself. Why should we have had this idea without carrying along with it a notion that we were each a valued individual with a personal internal relationship with G-d, each deserving as such a right to our own freedom of will? Before this notion much of the West lived in a state that was a great deal less centred around freedom of private individual desires and choice and a little more deterministic, wouldn’t you agree? I think if you didn’t you’d be a little out of step with the commonly held vision of what the lifestyles of antiquity were like. — kudos

I don't think you can separate religion and human and civil rights. Did Christianity cause the drive for rights to liberty and self-government? Probably to a certain extent. They certainly are intertwined in the political evolution of the west. I don't think this contradicts anything you have written.

You seem to consider it an accident that there are themes and references in the writing that refer explicitly to a Creator. — kudos

I don't agree that there is any accident or that I suggested there was one.

Judeo-Christian ideological baggage — kudos

The Declaration of Independence was written almost 250 years ago by people steeped in the western traditions of culture, including Christianity. What language do you expect them to use. Thomas Jefferson may not have been a theist, but he knew the correct way to say what he wanted to say in the language of those who would read what was written. And it wasn't just him. The Declaration was signed by more than 50 delegates. Most of them probably were theists.

I guess Jefferson was not a theist. I'm not either, but I can't think of any better way to say what needed to be said. There are unalienable rights that are built into the structure of the universe. Say that how you want. "Endowed by their Creator," works fine for me. That's a lofty statement of principle, but that's not how it really works. What works is people making a commitment to making sure those rights are manifested. That's what the Declaration is - a declaration of commitment to principles.

My issue with this is that people with religious morality often seek to change laws and behaviour of others - presumably to please God. We don't just have to consider the Taliban or the Wahhabi Saudis in this enterprise, there are Western Christians working to turn the clock back on science education, gay rights, women's rights, capital punishment, euthanasia - what have you. — Tom Storm

I think you and I are talking about different things. I'm talking about what moral agency means to me. It has to do with my obligation to behave in moral way. By "moral" I mean consistent with my values. There is no room for moral judgement of others in this.

You're talking how some people judge and try to control other's behavior based on their moral understanding, either religious or not.

In my daily experience there are common references to the familiar adage of 'all men and women are created equal.' — kudos

Here's a more complete quote from the Declaration of Independence:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, -

This language is clear - All people are created equal. All people are endowed by their Creator with certain unalienable Rights. We're not equal in height, wealth, strength, or any other physical or social measure. We are all equal in moral value. That leaves open the question of how differences in social standing, race, genetics, physical ability, birth and other such factors will be addressed. What is fair? Does society need to be fair?

It's an old story that one of the biggest obstacles to space travel is our primitive technology. — TheMadFool

I think the biggest obstacle is the speed of light.

I can have macaroni cheese as often as I like! — unenlightened

Made with Velveeta!!!

if someone were to say
"you must severely spank your kids every day, or they'll turn into immoral losers, and, besides, they probably did something wrong anyway"
then I'm thinking most would say that's not the right thing to do, i.e. passing judgment, a bad starting point. — jorndoe

I believe we should protect vulnerable people. Child abuse hurts children. I have a moral obligation to try to stop child abuse if I can. If I gather together with like-minded people, we can pass laws that protect children. That is not a negative judgement on immoral behavior, it is positive acceptance of a moral obligation.

We might say that, in principle, autonomous moral agency is a prerequisite for (would-be) autonomous actors. — jorndoe

It comes down to this - Judging the morality of other people or beliefs is not an autonomous moral action. Morals have to do with how you live your life, not how other people live theirs.

.

I'm totally envious of your non-judgmental prowess. — unenlightened

Yes. It's pretty impressive. I think he thinks he's all rational and stuff.

Man, I think you're just envious of Bezos.
After I started doing WHM breath work and reading Yogic books, I feel happy and totally non-judgemental. :) You should try that, too. Also add some Sowell / Friedman, as you don't seem to understand that people like Bezos, Gates, Zuckerberg ( while I'm totally not a fan of those guys ) did a huge and valuable organizing work for which they are rewarded. — stoicHoneyBadger

I'd say you are trying to make the facts fit your theory when they clearly contradict it. Once the self is expanded to include others, you really have stretched the concept of self-interest way past its breaking point. The only question of interest, is the psychological one, why many people like to cling to the bankrupt notion of the inevitability of self-interested behaviour. — unenlightened

I'm with @Unenlightened on this. You're afraid to engage with people who disagree with you, so you refuse to address directly those who have a less mean-spirited understanding of people than you do. Saying things over and over again doesn't make them true.