I was merely pointing out that your approach to linking violations of other rights such as right to life to hate speech by insisting on statistics or data is wrong and as a matter of fact, they are logically interlinked. As a result , we have the paradox of tolerance or paradox of freedom, however you phrase it.

There is a paradox of freedom. Basically, freedom in it's absolute sense may create environment or a society which restricts other freedoms. So to advocate for freedom of speech on all matters solely on the supremacy of the value of freedom seems contradictory.

The set of natural numbers does not have an upper bound, so it will always have a number that is smaller than another number. In other words, there is no largest number. If you disagree with the axiom that a set can have infinite elements, then it is possible to say that there is a certain largest number in a set but otherwise no.
The problem with axiom of infinity is that it fails to fall in one of the two categories. Intension and extension.

intensional definition gives the meaning of a term by specifying necessary and sufficient conditions for when the term should be used.

This is the opposite approach to the extensional definition, which defines by listing everything that falls under that definition

Some logician view that infinite extensions are meaningless as extensions must be complete in order to be well defined, so infinity cannot be defined by extensions. ( They reject Cantors proof too )
The problem with definition using intention is that they are circular.

The situation is bad.

.

Infinity doesn't exist as a number but a concept and l think even the concept has faults.

In maths, how would you interpret limits that do not exist to those that exist. For example, lim x-->o ( 1/x )does not exist but lim x--> 1 ( x-1/x^2-1) . The second one has removable singularity. Somehow we can assign useful value when using infinity but not always,so there are problems sometimes

to take an infinite number of steps

If l say, l have taken 100 steps, l am using the word "steps" in a different sense, to mean a numerical quantity.
When l say infinite number of steps, the word "steps" specifies the nature of steps ( they do not end) in such a system, it does not refer to a numerical quantity.
Therefore we cannot such a definition for infinity.
It is very difficult to define infinity using any concept other than infinity itself. Hence it is often circular, self referential.

The movement now is directionless and it is more about causing riots, l don't see how any western country would defend public vandalism and use of arson

I won't talk about possibility as that is clearly beyond our scope here. We are nor physicists. Time being a circular path is possible

Entropy increases with time but if time is a circular path, does that cause entropy to decrease at the starting point.

If time is a closed circle, then we can get to a stage where the entropy reaches the maximum value possible and suddenly it becomes ordered. The question deals with the arrow of time. Is time a linear line or a circular path

If someone yelled

fire fire !!

in a crowded closed place with bottleneck type entrance and they cause death, it will have consequences in the court when the case is considered. It also falls under free speech.

Hey, I'm back. I have to admire your consistency but l think you have used a disanalogy here,

if you think that hate speech is sometimes a causal factor for violence, and it should be regulated because of that, why don't you think that video games, movies, etc. are sometimes are causal factor for violence that should be regulated because of that?

Video games, movies which include violence generally without an underlying racial theme or fascist political agendas do not provoke violence. On the other hand, you have movies that are banned in various countries, like nazi era movies are banned in Germany. Games are even less likely to provoke violence and the main purpose of movies and games is entertainment while hate speech has the primary motive being to cause violence or harm.

I don't know what OP is talking about, couldn't get my head around it . I thought it was related to logical paradoxes since those were the exact statements of OP.

The following statement is false
The previous statement is true

Is that logically possible ? :meh:
It can be possible if we drop law of the excluded middle.

Oh for fucks sake!

Haha, lmao. :lol:
But credit goes to you for capturing the spirit of every philosophical debate. :rofl:

Philosophy falls under liberal arts and all liberal arts tend to express the obvious in new ways or perspective. Science on the other hand tries to explore new stuff.The greatest benefit of philosophy is it allows you to see the weaker side of almost everyone's viewpoint.Which will cause people to tolerate each other and explore new ideas with an open mind.But academic philosophy can get boring and pretentious pretty quickly.

Before getting to the density of the infinite sets, l would like to comment on the following remark

sets (A) and (B) are both infinite and infinite countable sets are equal. The argument can't work if both sets are equal

Consider the people in simulation to be set of natural numbers and the stimulators to be set of even numbers, they will have the same cardinality but they won't be equal.

The most straightforward way of making this notion precise in an infinite universe is via the idea of limit density. Start by picking an arbitrary spacetime point. Then consider a hypersphere centered on that point with radius R. Let f(A) be the fraction of all observations that are of kind A that takes place within this hypersphere. Then expand the sphere. Let the typicality of type-A observations be the limit of f(A) as R--->infinity.

I believe the best way to compare two infinite sets of same cardinality is by density measure, and the density of natural numbers will will greater as R ---> 100 such that f(a)=100 and as R--->100, even sets will have f(a)=50.

But yes, if we extend R to infinity, how will that work to compare densities. How would you define density, is density equal to rate of growth or observation ?
Really interesting but confusing too.
:smile:

I hope that you won't mind my questions as l am confused by your term, " consequential truth ".
.

In other words S is provable in T+Con(N), that's why its said to be a logical truth, in reality it means that it is a consequential truth from the rule following game T+Con(N), notice that it is not a consequential truth of T itself. "Logical truth" is provability in some system

T+con(N) would rule out any statements like " this is not provable " and so on. Other than that, what will be a consequential truth of T itself and how does it differ from consequential truth of T+con(N) as a S that is a logical truth in T should also be a logical truth in T+con(N) .

I will address your other points to but l need to get my head clear on these terms

So mathematics is about studying rule following games. I call them games because the choice of the primary rules is IMMATERIAL, we can even call them ARBITRARY, the most important is to harvest consequential truths in those games. The reality of the games, i.e. the stance of its primary rules and consequential outcomes from reality, is not relevant to mathematics itself, it is however relevant to its application, but not to mathematics per se.

If rules are arbitrary, would you allow contradictions in it.
Will a system have logically interlinked rules such that they have to be consistent and if so, they won't be arbitrary strictly speaking. Will a different system be created by only removing certain rules or creating new ones. How would you create new rules ?

Can you list your complete set of axioms for arithmetic in a system where godels theorem doesn't apply. ( it cannot be recursively innumerable )

CT truth and logical truth (LT) have also nothing to do with each other. For example, in "var b = true" the variable b does not correspond to anything in the real, physical world, but we cannot deny that it is logically true, if only, because we defined it to be.

Provability (PR) and logical truth (LT) have also nothing to do with each other. For example, in first his incompleteness theorem, Gödel encodes a statement that is logically true but not provable

I would say that tautology and contradiction have nothing to do with CT truth but the truth value of the rest of propositions are linked with CT truth. Second of all, we can define probability of a proposition to mean assigning truth value ( T or F) . In that case, l dont think godels theorem would work. It will be great if we can create a discussion to understand the incompleteness theorem.

Is this explanation valid or have l got it wrong. It can be hard to interpret wittgenstein sometimes

....Yes, it is quite often used in mathematics and computer science, like the iterative function f(x)=x , hence f(f(x))=x and so on. I don't think wittgenstein defined function in set theoretic terms and a function was more or less considered to be a transformation , so f(x) was a propositional function of the following statement
f(x) = x belongs to a set A, let x be any natural number.
f(f(x))= f(x) belongs to set A, but f(x) isn't a natural number. He was trying to show that it was a problem of semantics and I think this was a little of what wittgenstein was getting at

I just don't see how it makes any sense to say something is deterministic if it can't be used to determine, i.e. predict,

I have two questions for you regarding this statement.
Choatic system are deterministic but does it say in theory ( not practise ) that it is impossible to predict the future states, as you have mentioned in a discrete manner ?

Let's suppose it does, but why is predictability a neccessary condition for a deterministic system ?

You should try to refute AUP, even though it seems wrong intuitively. Maybe it is talking about lack of information causing the unpredictability and we can perhaps predict chaotic system if the initial values are accurately known or maybe it is inherent in the system

Are you familiar with this guy?
To a certain extent. Actually, his name comes up a lot when you type "determinism vs. predictability" on the web. How is he specifically relevant?

That guy is in mentioned in the article you posted, l think he hasn't checked it out yet. :smile: I will try break down the article in some basic points so we can remove the scholarly jargon and discuss the real matter at hand and l will fail possibly but let's give it a try.

1. asymptotic unpredictability. (AUP)
This unpredictability is due to how little changes or inaccuracy in initial measurement of system will drastically undermine the accuracy of our predictions in a deterministic system. The reason is that such small or little conditions or values of the system spread over all the predictable range in a short time.
However asymptotic unpredictability is not unique to chaotic systems as some systems can be simple and not complicated and still have asymptotic unpredictability.

... has argued that approximate probabilistic irrelevance is the kind of unpredictability that is unique to chaos. Unlike asymptotic unpredictability, approximate probabilistic irrelevance is a probabilistic concept of unpredictability. According to this concept, any measurement (i.e. knowledge of the initial states that the system may currently be in) is irrelevant for practical purposes for predicting outcomes sufficiently far in the future

Here we can see that the author (Werndl) is placing probability as a kind of predictability. Hence instead of saying all choatic system are associated with AUP, he states that are probability of future states cannot be obtained from initial values of the system.

2.The link between determinism and stochastic systems

Hence what is meant by the phrase that the deterministic model and the stochastic model give the same predictions is that the possible observed values of the stochastic system and deterministic system are the same, and that the probability distributions over the
sequences of observations of the deterministic model and the sequences of outcomes of the stochastic model are the same.

How does having the same prediction indicate a similar system ? There is also a problem with predicting stochastic systems behavior but simple deterministic system can be easily predicted. I hope l am not missing something here. The author doesn't seem to connect the 1st topic with the second one.After that, they discuss underdeterminism, which is refuted by stating that evidence supports deterministic systems over stochastic systems, hence they are favourable. Personally, l dont think this is related to our topic.

The real problem is the eternally faulty epistemic stance of the populace of retarded imbeciles in the West. They do not believe something because of its justification -- they are way too stupid to verify the justification anyway -- but because of whom says it, e.g. the blue-pilled narrative of the manipulative mainstream media and official, state-controlled education/indoctrination system.

I would agree with you if you could replace retarded imbecciles with right wing islamophobes who watch fox news 24/7 .

Both of you are right according to your viewpoint and l don't think you guys will solve it here . Lets call it a day.

I take back my argument if it undermined your stance but l do see a problem with your idea that the sole deciding power of morality lies in the general consensus of society. If you disagree with germans beliefs and morals in nazi Germany, you will have to judge him by our present standards, not their standards but l think it is an unfair move on our part. We cannot judge a standard of morals by itself and to me it appears that we don't have tools to decide which system is better, other than feelings and common culture which are not in any sense reliable.

The truth is that we get things wrong, we have always got things wrong, and we will continue to get things wrong, as far as we can see. Well probably also get some things right.... :chin:

But how can we get something wrong in a system if it is act according to it and there is no objective criterion for deciding which system is better ? :smile:

Why is free speech an important human right, and above the right to life ? In my opinion, both views are okay as long as the society works well and if the society tends towards anarchy and disorder, we will have to change certain laws or perish.

have trouble coming up with a rule or set of rules. I am probing Terrapin because fortunately, I think, for this discussion, he is an absolutist (at least so far) so that helps us understand what this entails. But honestly I don't have any easy answer here. I'd go into gun control but it would be a tangent. I hate gun culture. On the other hand with the militarization of law enforcement, the increasing centralization of power in the US and also centralization of media, the changes via executive order in the ways martial law and use of troops on american soil and a bunch of other trends I find menacing, I am also glad that there are a lot of armed citizens. It would make a direct shift over the full on open fascism - as opposed to the oligarchy that pretends to be a democracy - much easier if we took away those guns.

Let's take this thought experiment for clearing the problem on gun control. If the USA government suddenly turns into a fascist regime or a dictatorship, the people won't win the battle against an armed force, this isn't the old civil war. The technology that is in dispose of army is vastly superior to what the common public has and l doubt that anyone country in the world would try to liberate America if such events happen to take place.
Gun control is a positive move, military type rifles that are only required in warfare shouldn't be legal. There should be a greater restriction on what types of arms people can have to defend themselves and feel secure.

So nazi Germany beliefs and ideas were okay because all of them thought so. People in the past, agreed on a global level that slavery was okay. We don't always progress towards improving our morality, but we can try to correlate better morals with better living conditions in a society.
:wink:

Good questions. Here is one thought-train, offered as another example: unconstrained freedom of speech gives us the freedom to insult and provoke. The freedom to own guns allows this to progress easily to violence and murder. Empirical observation confirms that this is a path humans are likely to follow, unless they are discouraged or prevented. Yes? Too many unconstrained freedoms lead to unacceptable results (unjustified violence) in some cases; far too may cases to ignore, I think

What is wrong with violence and murder, despite the fact that we don't like to be involved in it. We have created such social constructs to be safe but does that make if right or wrong ? :naughty: :naughty:

Would you allow a speech act which states
" Let's ban free speech " and if it gets implemented, you won't have free speech anymore.

If we claim that words don't influence action, we can allow a teacher to have indecent conversation with underage students and if they end up having sex, we shouldn't blame the teacher right ? Consent is recognized as a speech act so it also falls under free speech.

A classic slippery slope argument.

I have been screaming this along the whole thread. People are really paranoid on losing their free speech by banning hate speech.

Ideals and ideas are a fine thing, but The Philosophy Forum, Wikipedia, your favorite publishing house and preferred media outlet, and so on wouldn't exist if it weren't for all that plethora of industrial units (computers, cables, routers, server farms, high speed printing presses, broadcast equipment, electricity, telephones, and so on.

As long as industrial units support and allow cultivation of ideas and our general well being, they can be an indicator of development but on their own, l wouldn't agree that they indicate development as such structures will tend to collapse on themselves when difficult times come. If North Korea succeeds in becoming self sufficient and turns its economy around like China, we won't seriously regard their industrial development as step towards betterment because they have neglected fundamental human rights and destroyed their culture.
On another point, we can manage to live without the printing press, internet and other facilities. It won't be convenient but people were used to studying philosophy in ancient Greece with very little resources

One of the reasons it won't stop people from running the rat race is that the "universal wage" is, in one version, intended to provide a survival income base for people whose jobs have been eliminated by computers or automation. It's nothing like a 'living wage'. Another version of the universal wage is that it would be available to everybody -- universal. It would allow more self-development (education) and allow for more risk-taking. It is pitched as a good sized supplement. The universal wage isn't intended to finance a nation of philosophers and artists.

When robots are developed to the extend that they can
perform common labour and have set of skills that can replace low skill labourers, that will not be enough to rule labourers out. The cost and the efficiency of robots at a large scale is still a big question and l don't think we will ever find ourselves in such a situation. Let alone turing computer as consiousnnes is not even understood in human beings and it is impossible to vision a computer executing it. Professional philosophers and artists are not a special breed of people but they won't be affected if full automation becomes the rule of the day. Their fields are secure and a universal income will supplement them. The idea of a survival income isn't accurate. In a lot of capitalist societies, consumerism has driven up what a survival income means and we can surprisingly survive on very little income if the economy helps us to, so universal income in a capitalist society will fail easily. There has to be a transformation at an economic level too.

Such a goal is not only naive, it's absurd. Most people don't want to spend their days studying philosophy or very much else. It isn't that most people are stupid, or troglodytes, or beer-swilling slobs (even if some are). A lot of people are not adept at productively filling vast stretches of time. They like structure; they live and work well with in a structured environment. Or, they might spend their days listening to National Public Radio, or laying on the couch, smoking, and watching TV. And so on.

I would agree on this statement but it maybe due to the anti-intellectualism present in present age. It is easy to understand why as people can seek entertainment in activities that require less physical or mental labour, hence they will rather watch a movie than read a novel. Watch a documentary over reading some philosophical article and so on. Certain activities can reduce the attention span of a person and the brain functions like a muscle. I don't think doing maths or studying philosophy ,enjoying art is superior to average day activities and what matters is that people should have a freedom to be idle and the glorification of work has been over the edge due industrial revolution. Being on time is another moronic concept which l despise so much, it reminds me of a line from some unknown poet, as he writes and ridicules the society

you have watches and clocks and we have time

The rat race yields rewards--like money, social contact, a sense of belonging, having a role.

There is false human connection in corporate environment as they thrive on jealousy and competition.
It has led people to being depressed and feeling lost even after acquiring all the money, a status in the community because in the end of the day, it is a fake show. There is no genuineness in it. We need to overcome our desire to gain power, fame and wealth because if we set to acquire it, there is no end to it and we will be disappointed.

There is a very real question of whether "Society" which enables individuals to be artists, philosophers, thinkers, creators, ingenuous inventors, and so forth can exist without a lot of excess labor. Again, I don't know.

In the present day and age, artists can struggle to make a decent living. In the past, the emperors and the elites in the society gave patronage to them. Labour is not bad in of itself as long as we work for ourselves, otherwise it is a form of chattel slavery. The term artists has been restricted to music,art and acting for some reason but it is supposed to be a broad term. There was a famous mathematician by the name of Erdos, who travelled around the world and was as close as we can get to an ascetic mathematician. I would consider him to be an artist of first order but it hurts my mind whenever people ask this question ; what's the use of this " insert mathematical terms " when l leave school ?
The society does not like those who learn for sake of learning. It has to be applied somewhere. The idea of a universal salary is naive and l doubt if it will stop people from participating in a rat race. Materialism is a spiritual sickness and progress always happens in ideals and ideas not in building skyscrapers and countless industrial units.

There is a very real question of whether "Society" which enables individuals to be artists, philosophers, thinkers, creators, ingenuous inventors, and so forth can exist without a lot of excess labor. Again, I don't know.

In the present day and age, artists can struggle to make a decent living. In the past, the emperors and the elites in the society gave patronage to them. Labour is not bad in of itself as long as we work for ourselves, otherwise it is a form of chattel slavery. The term artists has been restricted to music,art and acting for some reason but it is supposed to be a broad term. There was a famous mathematician by the name of Erdos, who travelled around the world and was as close as we can get to an ascetic mathematician. I would consider him to be an artist of first order but it hurts my mind whenever people ask this question ; what's the use of this " insert mathematical terms " when l leave school ?
The society does not like those who learn for sake of learning. It has to be applied somewhere. The idea of a universal salary is naive and l doubt if it will stop people from participating in a rat race. Materialism is a spiritual sickness and progress always happens in ideals and ideas not in building skyscrapers and countless industrial units.