Fishfry and, I expect most of the others that have responded to your thread, is/are perfectly familiar with Hilbert's Hotel, and why it is not an argument for any statement other than 'aren't infinities interesting?' Ditto for Aristotle's notions of potential and actual infinities.To understand why this is you should google up and read the mathematician David Hibert's famous thought experiment , "Hibert's Hotel". — John Gould
What do you have in mind with the term 'genuine normativity'? Is it the phenomenon of somebody making normative claims - that X is true, or that people should do Y - and believes those claims to be true in some absolute, objective, mind-independent sense?I don't think it's explaining genuine normativity — Mongrel
It seems to me that convention-following does explain normativity, but that nevertheless we cannot escape it, because language can only be understood if conventions are followed.The idea (as I understand it) is that if convention-following explained normativity, then we should be able to escape normative language......
Do you agree with that? — Mongrel
No, I was musing about why most other people are interested in those subjects. My primary reason for loving those topics is neither instrumental nor about truth, but aesthetic. I love the beautiful patterns they make. I feel like a child lying on the grass looking at the clouds, saying 'Oooh, look at that one!'.Are you really interested in QM, GR and thermodynamics because of their instrumental value? — Marchesk
Where is Landru? I fervently agree with half he says and fervently disagree with the other half. I haven't heard from him in ages. I miss him.So you've adopted Landru's beliefs about science. *sigh* — Marchesk
You don't mind if they harm you unintentionally? You would be happy to have as a friend a knife-wielding psychotic that believes he's surrounded by orcs?Any fool is a good friend because a fool will not harm you intentionally — TheMadFool
Really? In the trenches in the Great war, Helmut was Fritz's friend on the German side and Bill was Bob's friend on the British side. Yet Helmut and Fritz were Bill and Bob's foes and vice versa.Friends and foes are exclusive classes: No friends are foes — TheMadFool
I don't know why you have suddenly come to believe this. But it's not correct, as Michael points out.Both 1 and 2 contradict the truths of
All fools are friends
All fools are foes — TheMadFool
No, it's not. It's a Venn diagram, which is what you asked for.Note, it's not drawn in standard form re categorical logic. — TheMadFool
I can't see any paradox in that, nor even anything surprising.This is paradoxical. A fool suits both as a friend and as an enemy. — TheMadFool
I think it depends on what, if any, continuity, one wishes to attach to one's idea of reincarnation. If there is no practical continuity attached, in the form of memories or tangible characteristics, I think one can only make sense of the idea if one believes in Aristotelian essences. Then one can say that one's essence is the same as that of Napoleon, even though there is nothing else of note that is shared. This hypothesis is, of course, unfalsifiable.But is there a way around such objections? — Banno
(findprime<-function(x,n) if (sum(x %% 1:x == 0)<3) if (n>1) findprime(x+1,n-1) else x else findprime(x+1,n) )(2,10001)
The array processing paradigm of R (and other, older languages like APL) allows for compact coding of such problems. Here's an R coding that spits out the answer:If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.
sum((x<-1:1000)[x %% 3 ==0 | x %% 5 == 0)
For those of us who are not scholars of the Enlightenment, but just celebrate it and enjoy reading Hume, Paine and Voltaire, where is this 'Doctrine of Progress' specified, in order that we may read it and decide whether to assent to it or not. I cannot recall encountering it in Candide.Every scholar I have encountered who is looking at the Enlightenment and modernity says that a central feature of theirs is belief in science, reason, free markets, democracy, etc. yielding ever-increasing freedom, material well-being, etc. It is better known as progress, the Idea of Progress, the doctrine of progress, etc. — WISDOMfromPO-MO
I am a big fan of many enlightenment thinkers, and am tremendously glad that the Enlightenment happened.the Enlightenment progress narrative is false, delusional, dangerous — WISDOMfromPO-MO
What makes you you think that?The issue of the infinitely long decimal line is actually finite. — WillowOfDarkness
That isn't my reason. My reason, which I did give, is that my observation is that most people use the phrase 'a truth' in that way and, in order to facilitate communication with others, I adopted what I judged to be their practice.I was wondering whether your reason for counting truths as a subset of propositions is that there are both true and false propositions — John
I expect there are truths that no human could ever know, because even the statement of the truth is too long to be held in a human brain. Further, for any organism of limited size, be it ever so much brainier than humans, there will be truths long and complex enough that the same restriction applies to them, just farther down the road.To extend it then, are there truths which can never be known? — John
That is simply my understanding of how the word is used. If there is a significant group of people that use it in some other way, I have yet to encounter them.Also, would you be able to explain why you think that truths are a subset of propositions? — John
Yes. I could too, but I don't see that that amounts to a mound of beans.I am not armed with evidence right now, but I bet if I had the time and other resources I could find a lot of evidence of horrible things done in the name of "progress — WISDOMfromPO-MO
My understanding and, I would venture to guess, the understanding of the person in the street, is that the set of all truths is a subset of the set of all propositions.The KP principle can be formulated as a claim about all truths (as it appears in the Stanford article) rather then all propositions — Fafner
Progress is relative. We aim to make things better in the foreseeable future than they are now, and to maintain the improvements we have over the past.Would your worldview, philosophy, etc. implode if progress is an erroneous idea? — WISDOMfromPO-MO
Sure. That's why I'm pointing out that the problem doesn't exist in natural language, because the proof is written in formal language. This isn't a case of a natural language statement that we all believe being unfairly torn down by formalism. It's a case of an attempt by Fitch to formally prove a natural language statement that nobody believes. So it is entirely pertinent to point out that the purported formal proof is syntactically invalid.My point is simply that if you solve a certain problem in a constructed formal language, it doesn't by itself prove that you've solved the problem as it exists in natural language. — Fafner
It's a variable, because it's written Kp, preceded by a universal quantifier over p.And how do you think 'P' is treated in the formulation of the paradox (say in the Stanford article) as a constant or a variable? — Fafner
KP seems like a perfectly consistent thing to say — Fafner
Sure, we can interpret a sentence to mean whatever we want it to mean. Thus, we can make sense of the famously uninterpretable sentence 'This sentence is false' by just interpreting it to mean 'Blue is a colour'. But I don't see how that is any way a useful thing to do.But there's no such thing as a theory of types, and there could be no "syntax errors" in a language (because every sentence in language can be potentially made sense of with the right interpretation). — Fafner
That's not the way syntax rules work. Most syntax rules operate on a 'rule in' basis, not a 'rule out' basis. A positive justification is needed for a sequence of words being valid syntax - not just an absence of breaching any 'thou shalt not' laws.If you cannot put 'know' in front of every sentence then there should be a principled explanation why — Fafner
There's no problem with that statement, provided P is a constant, not a variable.KP seems like a perfectly consistent thing to say — Fafner
KP. For every proposition P, it is possible to know P. — Fafner
I don't think many people these days would bother to contest the Son of God claim, since that claim needn't be blasphemous or controversial. When I was a young RC, we used to sing a modern hymn called 'Sons of God', about how we are just that.Jesus DID claim to not only be the Son of God, but to be one with the Father. — Agustino
Really?Don't act like you don't know what I'm talking about here and haven't ever done this sort of thing or thought in that sort of way about these sorts of people, because I don't buy that for a second. — Sapientia
What does that mean?Crazy is crazy, now matter how you dress it up, how widespread it is, how prominent it is, and so on and so forth — Sapientia
not very well at all.And how does that compare if you swap "God" with "extraterrestrials" — Sapientia
What is it you want to say about evidence? We have this:The context makes it highly appropriate to talk about evidence. — Sapientia
to which the obvious answer is 'to somebody else - probably none, and so what?'What evidence is there that someone has experienced the presence of God, as opposed to having had an experience and concluded that they experienced the presence of God?