The thing about notions like ‘inborn’ and ‘instinctual’ is that they don’t differentiate between whole hog pre-formed contents and a capacity to learn to construct in stages a complex activity. Language and number I think are good examples of phenomena that can be understood in either way. Chomsky and Fodor belong to the ‘whole hog innate content’ group, believing inborn semantic as well as syntactic contents. — Joshs

My level of understanding comes from reading summaries of a few scientific papers and then "The Language Instinct." My intent was not to make a strong case for any differing views, but just to point it out as an interesting sidelight.

If number arises from counting, and if counting is something done by humans, then indeed maths is invented not discovered and it must be understood accordingly - which in practice means understanding how such an ability might have evolved. — Wayfarer

As an aside, I've read of some scientific papers recently that indicate that children have at least a preliminary understanding of number from a very young age. This leads to the hypothesis that a sense of number is inborn, instinctual, just as our ability to learn and use language is.

I know a person who suffers from anxiety and a few who suffer from depression. I got to thinking about how, if you are going to gaze at your own navel, you ought to at least have the intellectual curiosity to wonder what smarter people have thought who have likewise gazed at their own navels. — James Riley

I am a skeptic when it comes to western philosophy. I keep asking myself "What the fuck are these people talking about?" Much of it just seems like, as you noted, gazing at belly-buttons and getting in profound arguments about the different kinds of lint. But... here on the forum I have met people who were saved by philosophy. It gave them a place to stand. Then they used it to climb up out of the hole they'd dug for themselves or into which they'd been thrown. It is inspiring and moving. I still don't get it, but I get that there is something to be got.

For the record, fucked up people can be very good therapists.

Because if number is real but not material, then you have something real but not material, meaning materialism is false. And that is a no-go in secular scientific culture. Ought not to over-complicate it. — Wayfarer

Of course, it doesn't matter because both materialism and idealism are metaphysical positions and, therefore, are neither true nor false, but, rather, useful or not. I read that mathematicians tend to be idealists and scientists tend to be materialists, which, given that, makes sense.

Is proactive political action compatible with the principle of wuwei? It seems to me that getting out and doing something is very non-Daoist, in my conception of it. — Satyesu

Wu wei, no action or action without action, doesn't mean doing nothing. It means acting spontaneously from your true nature, your heart. One of the primary audiences for the Tao Te Ching was leaders, princes, generals; so clearly political action is consistent with it's principles.

Ideally, I want to try to describe emotion as mode of cognitive operation which could possibly make sense of the world in a similar way to how our rationality does. This type of processing would be pre-linguistic in nature (as reason is) and it would also be pre-conceptual (in a similar way to how logic is). — intrapersona

What subject does your thesis cover; philosophy, cognitive science, psychology, neurology? Whatever the subject, you should make sure you get the science right. I suggest "How Emotions are Made" by Lisa Barrett, suggested to me by @Possibility. I'm sure there are others. Philosophers like to gaze at their stomachs and burp out the answers. That won't work with this.

As already explained, this is not really the question at hand, rather it is a bit of a caricature of the more general question at hand, which was: How should we treat logical contradictions in mathematics? Should we reject or minimize them, as if they were a problem, or should we rather welcome them and treat them as a source of creativity? — Olivier5

Yes, the liar's paradox statement is shorthand for the overall argument.

This question was aimed at @TonesInDeepFreeze, who seems to understand this better than the rest of us.

Is the liar statement (this sentence is false) more about language than about logic? — TheMadFool

The Russell paradox is basically the same thing using sets instead of sentences.

There was an “efilist” on here a couple weeks back, seems like they bit the bullet on premise 3 :rofl: I’ve only met one other person who was a negative utilitarian, and even they thought killing everything WASN’T morally repugnant because the goods in life weren’t instrumentally valuable. Kind of bizarre if you ask me — Albero

As you probably know, there is a relatively small group of people who consider themselves anti-natalists. They propose achieving the goal of negative utilitarianism not by killing everyone, but by stopping reproduction.

I'm certain that a mathematical inconsistency could cause more than just bridges to collapse. — TheMadFool

As far as I have seen, which, admittedly isn't far, the inconsistencies in math are analogous to "This sentence is not true." The proof of Godel's first incompleteness theorem uses similar slight of hand to show that, as Wikipedia says:

...no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers.

From what I've read, the foofaraw about these ideas comes from the fact that they crush logician's and mathematician's dreams of a perfect formal logical system, not from any impact to any mathematical system that could have an impact on the real world.

Am I sure about this? No way, but it seems like that's what Wittgenstein was saying in the linked article that @Banno provided. Is it possible I have misunderstood? You betcha.

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.