I have come to the tentative realisation that I don't have any intuitive sense that a model of the world needs to be satisfy that criterion. Key contributors to this feeling are:Notice, though, that this proposed expansion only shaves off 'branching outs' from bifurcation point towards the future. Determinism is commonly defined as a property of a system whereby the state of this system at a time, in conjunction with the dynamical laws governing its evolution, uniquely determine its state at any other time (either past or future from this point in time). This is a time-symmetrical definition of determinism. Under that definition, if the laws are such that there remains bifurcation points in phase space that are branching out towards the past, then the system still is indeterministic. The system past or present states uniquely determine its future; but its future or present states don't always uniquely determine its past. — Pierre-Normand
This is not just an artificial construction. It is my best attempt at stating formally what I believe intuitively to be the case for a Newtonian model.Where there is more than one future movement pattern (locus) of an object that is compatible with the 2nd and 3rd laws and the conditions in place at time t, and one or more of those loci involves the object's velocity remaining constant for the period [t,t+h) for some h>0, the pattern that occurs will be one of those latter loci. — andrewk
In that case the path that involves the ball having always been at the top of the dome will not be consistent, under the 2nd law, with the current state of the cannon or the cue stick (eg heat, momentum) Also, the momentum of the dome will be different in both cases, as the ball transfers its horizontal momentum to the dome (3rd law) as it climbs to the top.Les us assume that the ball has been shot up with a canon, or hit with a cue stick, if you like. — Pierre-Normand
In that case it is impossible for the ball to have rolled up the dome, because there is nothing in the system that could have given it the necessary upward impulse. So if we observe it sitting at the top of the dome, the only possible history is that it has always been there. This can be derived from the 2nd law alone. The 1st law is not needed.I am assuming that the system consists in the dome, the ball bearing, the ambient gravitational field, and nothing else. — Pierre-Normand
Yes. Say it reaches the apex at time t2. Then there is a path compatible with the 2nd law in which it remains there for the period [t2,t2+h) for any h>0. So that path must be what happens rather than a path in which it continues down the other side.Is your law mandating that the ball will stand still indefinitely after it has reached the apex — Pierre-Normand
My expanded first law prohibits the ball rolling down (a solution not in U) because there exists a solution in U, ie in which it does not roll down, and the law requires that a solution in U be taken in preference to a solution outside it.both the second law, and your expanded law (if I understand it correctly) are silent regarding what happens next. — Pierre-Normand
I got a bit lost here. Newton's third law is that for every action there is an equal and opposite reaction. I can't see how that law is relevant to the questions being examined in this scenario. Can you outline what you had in mind here?this construal of Newton's first law would also have the very unfortunate consequence that it makes it inconsistent with the third law in other cases. — Pierre-Normand
True.The jounce wasn't zero on the way up. It was constant and equal to 1/6. — Pierre-Normand
The curve is constructed so that the displacement function is a constant multiple of (t-T)^4 for t>=T. The same would work for a displacement function proportional to (t-T)^n for any n>=4. In that case the non-differentiability won't appear until the (n-1)th derivative of the displacement function. So as long as n>=4 the nondifferentiability will be out of sight and out of mind.Any explanation for why this curve is somehow poised in a way that allows for the claimed indeterminism? — apokrisis
OK. I don't find assigning causality a productive exercise, so I'll leave the field to those that do.The point is about how we like to assign causality to particular triggering events, but if a triggering event is almost sure to happen, then the particular loses its hallowed explanatory status. — apokrisis
That is my view. The ball fell because when it was released by whatever was holding it on the apex, its centre of mass was not exactly above the point of contact with the dome, so it started falling.the answer becomes we couldn't prevent that because any placement on the apex had to involve infinitesimal error. — apokrisis
You're right. I thought exactly that as I wrote it and then - arrogantly - thought 'nah, this is a philosophy forum, not a finance one - nobody will pick me up on it'. I was wrong!I don't agree with the discounted cash flow not having any reference to buyers and sellers. The discount curve you're going to use is an interest benchmark in most cases, which in turn is based on actual transaction/quote data (spot and forward). — Benkei
This is another case of me being lazy. I didn't mean APT (Arbitrage Pricing Theory) but arbitrage-free pricing of derivatives (Black-Scholes and the like), but I forgot the 'free' bit and found it easier to just write 'arbitrage pricing'. Arbitrage-free pricing of course still depends on market prices because it relates the value of a derivative to the value of the underlying asset, but what I had in mind was that the relationship between the prices of derivative and underlying asset doesn't depend on market sentiment. Of course it does, at least at second order, because interest rates and implied volatilities come into it, at which point your first objection comes into operation.I'm on the fence about APT. — Benkei
Hell Does Not Actually Exist
A recent response I made in this forum has caused me to think a lot about the existence of hell. The response I made against the fact that God created hell resulted in me coming to the conclusion that hell does not actually exist. My response can be found here: https://thephilosophyforum.com/profile/comments/2793/francesco-di-piertro
I wanted to hopefully generate some more discussion on this topic and consider objections to this view. So, I decided to synthesize and lay out my argument in an outline form to make it a bit clearer. It is worth noting that my objection is targeted at the popular, modern Christian conception of hell, with hell being a satanic realm that serves as the eternal home of the unrighteous as opposed to an eternity in heaven with God.
My argument against Christians who adopt this belief in the existence of hell hinges on the assumption that Christians believe the Bible to be true. By saying, “believe the Bible to be true”, I do not mean to imply that I think Christians have to believe every nuance and story in the Bible to be verbatim truths about reality. What I want to communicate is that I believe Christians have to commit themselves to the fact that what is contained in the Bible is true insofar as it is inspired by God, reveals truths about God’s character, and informs us of how He interacts with His creation. From this understanding, my argument against Christian belief in hell is as follows:
1. If hell exists, there would be Biblical evidence for its existence, or it exists only conceptually in the minds of human beings due to misinterpreting the Bible.
2. Things that only exist conceptually in the minds of human beings do not actually exist.
3. There is no Biblical evidence for the existence of hell.
4. Therefore, hell does not actually exist.
As previously mentioned, my rational for this argument can be found in another response I made recently on this forum that is linked above. Thanks for considering this argument and I look forward to reading objections. — Francesco di Piertro
Pragmatic Encroachment and Pascal’s Wager
If knowledge is circumstantial, it is seemingly impossible to make a knowledge claim about atheism. Under the view that knowledge is circumstantial and subject to the stakes of the circumstance, atheism faces several problems. According to Pascal’s Wager, the belief in God is a high stakes situation. If God is real, then belief in him is infinitely rewarding and non belief is infinitely punishing, if he is not real then belief in God is slightly punishing and non belief is not rewarding or punishing. So in any case, belief in God is a high stakes situation. Pragmatic encroachment affirms that if the stakes are higher in a given circumstance, then more evidence is required to obtain a justified belief. This presents some problems for atheism. Since the stakes for atheism are greater than theism, it requires more evidence to claim knowledge of atheism given equal evidence. Granted that the evidence is equal, it is near impossible to have a justified belief in atheism.
If pragmatic encroachment is true, atheism falls short in the burden of proof debate. Since the stakes are higher for atheism it requires more evidence to be proven true, and the evidence is equal, so the burden of proof must fall on atheism. While atheism can still be true, it is far from justified under pragmatic encroachment, therefore it fails to be knowledge. — Dgallen
Only if one is curious about that, which seems to bring things back to Mariner's point about curiosity.It would make sense to first examine why they believe what they do, wouldn't it? — S
I expect so, but do you expect it to ever convince anybody to change their view, other than the occasional rare exception?The debate itself will forever be on fire. — Modern Conviviality
For any opinion one holds, be it ever so little grounded in reflection, one can say the same about people who don't share it. So the statement doesn't seem to say anything at all.They might be mistaken and they might be unreasonable. Some almost certainly are.
I see no reason to criticise your position, because in the OP, you do not suggest that people are mistaken if they have a different position.So, there you have it. That's a summary of my position. Have at it. Any questions, ask away. — S
You have defined a new term in relation to sets - 'fully defined'. What then?Ok let’s use the language ‘fully defined’. A set is only fully defined once we have listed all its members. Clearly infinite sets are not fully defined yet maths tries to treat them in the same way as a finite set (which is fully defined). — Devans99
This works for a logical theory in which the only objects in the domain of discourse are natural numbers. In that case, we can just use the following axiom of induction:All that mathematical induction requires is that what is true of one number is true of the next, and therefore true of all the following numbers — MU