It is not necessary to adopt platonism to accept that there are infinite sets. One may regard infinite sets as abstract mathematically objects, while one does not claim that abstract mathematical objects exist independently of consciousness of them. — GrandMinnow
Space and time are mathematically linked. — fishfry
Why does Trump flirt with Putin and Kim, but he harasses Iran? Real question. — frank
The concept “flow” is a condition of the concept “river”, but it is not a necessary condition, for a river that does not flow, i.e., tidal access rivers, is still a river. — Mww
The concept “free will” is a misnomer, because a free will that is not free in its volitional determinations cannot be a “free will”, but nonetheless a will. — Mww
Freedom is an indirect condition of the will, insofar as it is a necessary condition for autonomy, which in its turn is the necessary condition for the will to operate in conformity to its prerogatives. Forgive me; I took liberties with the theoretical philosophy of morals by not specifying the distinction between conditions and necessary conditions. — Mww
I gave no indication that free will is displaced; I specifically itemized free as being separated from will. — Mww
That being the case, it is more apt to say, “freedom is the condition the will takes place under”, which still isn’t quite right, but is close enough to work with, and incorporates the added bonus of showing how and why free and freedom both are necessarily separated/displaced from will. Logically separated because free will is always susceptible to self-contradiction, and temporally displaced because freedom is always antecedent to the will for which it is the condition. — Mww
The will existing as an autonomous casual means in no way requires it to be separate from time itself. It acts in time, is constrained by it, and to say it is temporally displaced is nonsensical. — Pathogen
4.) Non-deterministic factors do exist in the physical universe. — Pathogen
No it doesn't. It requires a definition of determinism that implies prediction-making. — Harry Hindu
Predictions can only be made if occurrences that we observe are consistently determined by prior causes. — Harry Hindu
Yes, agreed, the discovery of new knowledge is mostly carried out with other, non-knowledge, tools/mental faculties. — alcontali
Ha, but if we could "know" the nitty-gritty of these other, non-knowledge mental tools, then they are actually knowledge, and that would be contradictory. Therefore, I am opposed to any strategy that consists in trying to systematize these other mental tools, because in order to do that, we would need to thoroughly "know" them, which is is not possible, because they are not knowledge. — alcontali
am heavily "epistemized" and deeply invested in the idea of the existence of various knowledge-justification methods. — alcontali
Still, I completely acknowledge that non-knowledge mental faculties are key, not just for the discovery of new knowledge, but in general. But then again, systematization means converting things into knowledge. If it is not knowledge, but rather intuition, this is guaranteed to be a failing strategy. — alcontali
In the end, this kind of research rather amounts to playing with "cool toys". But then again, it is not possible to know what people will find unless they actually try. Furthermore, this type of research nicely emphasizes the true nature of axioms as fundamentally arbitrary starting points. — alcontali
If you predicted that it would break down, and it eventually does, then that is deterministic. — Harry Hindu
Deterministic means that the outcome of some system is capable of being predicted by some mind. It follows some logical pattern. It is logical. — Harry Hindu
Well, the link with classical, Euclidean geometry has long ago been abandoned in contemporary number theory. I suspect that it was completely gone by the end of the 19th century, at the same time as they dumped Euclid's Elements. I have never had to carry out arithmetic using a straightedge and compass, like the Greek in antiquity apparently did. — alcontali
I believe that there must be ingredients in the process of knowledge discovery that are fundamentally unknowable, because if we could know them, then we could even systematize the discovery of new knowledge, while this is fundamentally not possible. — alcontali
Yes, I did refer to non-knowledge mental faculties. Intuition is clearly one. — alcontali
For example, they did not start building the first computers because there were errors in the old mechanical calculators that preceded them. — alcontali
The universe would be the closed system. — Harry Hindu
The car is epistemically deterministic in the sense that the problem can be identified and the car repaired or an irreparable part replaced. On the other hand the human body is not like this; many things can go wrong that we do not fully understand and repair is often impossible. — Janus
Irrational just means that a number cannot be reached by merely applying the standard arithmetic operators (+ - x /) to integers. — alcontali
Still, the algebraics are not enough when you look, for example, at the roots of polynomials with rational coefficients. You will need to keep adjoining additional field extensions if you want to close the splitting field — alcontali
So, in this context, "irrational" just means that the problem cannot necessarily be solved by using basic arithmetic, but that it may requiring adjoining to the rationals Q, other numbers produced with more complicated operations. — alcontali
Existing knowledge cannot possibly be the main ingredient in the discovery of new knowledge, because in that case humanity would never have discovered any knowledge at all, or else, discovered all possible knowledge already. — alcontali
We simply do not know how to discover new knowledge, and we can certainly not justify how we managed to do it anyway. — alcontali
Gödel's first incompleteness theorem also provably dismisses the idea of running through all possible well-formed formulas as to question a knowledge machine whether the formula is provable or not. For example, in the language required to axiomatize the existence of numbers, it is possible to produce formulas that are logically true but impossibly provable by the knowledge machine. So, if you enumerate the well-formed formulas in that language (which happens to be first-order logic), from first to last, the knowledge machine will run into examples of formulas of which the provability is simply undecidable.
So, it is just not possible to run new candidate knowledge claims through a knowledge machine filled with existing knowledge to check if these new claims happen to be justifiable. Gödel proved that this is not a legitimate knowledge discovery procedure. We will undoubtedly have to keep doing it with leaps and bounds, through serendipity, trial and error, and what have you, to slowly, gradually, and painstakingly, but surely, acquire new justifiable knowledge claims. — alcontali
I agree, but from what you've said, I think you and I have different reasons for thinking so. — T Clark
For example, the internal combustion engine is epistemically deterministic. That just means it is a simple system whose function is reliably predictable. — Janus
That is only the nature of falsificationist knowledge. That is absolutely not the nature of axiomatic knowledge. The Pythagorean theorem was provable 2500 years ago. It still is provable today. The same holds true for Thales' theorem. It is as provable today as 2500 years ago. Once provable, always provable. Hence, that particular view on the nature of knowledge is epistemically completely incorrect for axiomatic knowledge. — alcontali
For mathematics, these rules are arbitrarily chosen. — alcontali
So, then where is that elusive progress visible? Any link? — alcontali
The initially hypothetical knowledge was very often stumbled upon, through serendipity, trial and error, and sheer luck. — alcontali
So, yes, a better understanding of the solar system and other parts of the visible universe took a lot of observation. In fact, it first took quite a bit of haphazard progress in optics and construction of telescopes just to be able to observe these things in sufficient detail. So, yes, if they had had proper telescopes 2500 years ago, they would obviously have seen it too. It wasn't a problem of following the wrong principles at all. — alcontali
Sure, I can see that the equations may be strictly deterministic. but that doesn't mean the system in the real world is. — T Clark
(1) No ontological uncertainty in deterministic systems because... — fdrake
Oh that's right this is why I don't respond to you, ever. My mistake. — StreetlightX
Possible answers:
1. Jesus is a human being
2. A human being is Jesus — TheMadFool
But how do you know it is truly "first"? You do not. So, you will keep trying to find the really "true" first that comes before the current first. It just keeps going on. Ad nauseam. That is why it does not work. — alcontali
The most widespread and successful approach to morality is what the three offshoots of second-temple judaism propose, i.e. religious law. — alcontali
Read up on it, and then you will understand that what you are doing in the realm of morality, i.e. "metaphysics", is just un-methodical bullshit. Seriously, that is why there has been no progress whatsoever in metaphysics for over 2500 years. That was to be expected, because there is simply no logic in that madness. — alcontali
A fixed system can and does capture real phenomena. — StreetlightX
A great deal - if not all - of experiments in science involve fixing possible variables in order to isolate some dynamics of some system or another. That does not make scientific results artificial. — StreetlightX
He didn’t state it publicly. Like many of these stories some “official” told the press, they sensationalized it, the Danish prime minister criticized it. More misinformation. — NOS4A2
If you reason toward first principles, you will look for the principles underlying these first principles, and again, ad nauseam. It obviously leads to infinite regress. — alcontali
That is why this particular direction is forbidden in axiomatic systems. — alcontali
The metaphysicist is wasting his time, simply because the direction of reasoning is necessarily incorrect. — alcontali
Justifying the starting-point rules is an exercise in infinite regress and futility. Can you give even one example of where an approach like that has worked? — alcontali
Epistemology really works, while metaphysics is nonsense. We know that for a fact, because after 2500 years of metaphysics, it has never produced anything else but nonsense. — alcontali
That a coin toss is random is entirely a real, and not artificial property of a series of coin tosses. — StreetlightX
One thing that follows from this understanding is that randomness can only be spoken of in relation to a fixed system. — StreetlightX
People thought the purchase of Alaska was stupid. The Danes sold the Virgin Islands to the US for $25 million. These aren’t stupid ideas and the outrage about it was misinformed. — NOS4A2
Reasoning from first principles in the context of the real, physical world looks like a serious epistemic mismatch to me. That is why I reject the practice of metaphysics. — alcontali
For example, the axiomatic method certainly does an excellent job in mathematics; but it also does an excellent job in morality, where axiomatic derivation from basic rules is also the method of choice. — alcontali
Why then the emphasis on stillness? — TheMadFool
I think the ‘misunderstanding’ is due to equating ‘leisure’ with ‘freedom’ — I like sushi
Sensations, incongruous feelings, memory, anticipation, planning, the observed passage of cause and effect... These are all what past and future 'really' are because they are all what we use the terms 'past' and 'future' to describe. — Isaac
Past and future are just words. We can use them to describe whatever phenomenon we like, so long as we're understood. — Isaac
How are you going to demonstrate that anyone has the answer right? — Isaac
The point of it is that we have to give up individual freedoms in order to live together in harmony. — I like sushi
Very recently I saw a tiny praying mantis and as I approached it it sensed my presence and immediately froze. It stopped moving completely. This is, if I'm correct, death mimicry. Dead or lifeless things don't move. — TheMadFool
Suzuki-roshi, in his well-known book Zen Mind Beginners' Mind, indeed says that the practice of zazen is to sit perfectly still, but completely alert, like a frog waiting for a fly to appear. — Wayfarer
Is it possible to describe the origin of the material world in materialistic terms only? — Gregory
Well, there you go. Your intuition tells you they are different. The fact that we can't measure that difference is unproblematic for you because you already believe that not all knowledge is measurable. I'm not seeing the problem you're trying to resolve. — Isaac
Supposing that each of us always carried a mobile phone and that we agreed to eliminate "the present", "now", " currently" etc. from public discourse by replacing each of their uses with the exact current reading of the International Atomic Time supplemented with the Gregorian calendar. Likewise, we respectively do the same for "the past" and "the future" by replacing their use with time-intervals that are before or after the exact current TAI time.
Doesn't this elimination of temporal indexicals also eliminate all talk of change, and therefore reduce MacTaggart's A series to his B series? — sime
The only possible method by which to study temporality is to approach it as a totality, as an original synthesis, which dominates its secondary structures and which confers on them their meaning. — Number2018
