If (a), the generation of this initial given (call it X) was then necessarily to some extent limited or bounded (hence, determined) by an end – for the sake of which it was generated – which, as end aspired toward, could not have been generated by God prior to God’s very first, intentional generation (i.e., his generation of X). Here, then, God was himself to some degree limited or bounded (determined) by his actively held intent (telos or goal or aim), an intent held by him which he did not create and which he did not instantaneously realize. Therefore, God was not - and thereby is not - omnipotent.
Exactly. Frequentism is what underlies actualism, a form of determinism.
Imagine that you're rolling a die at a craps table. You'll say that the 5 has a 1/6 chance of appearing face up. This is an assessment of logical possibility. We have to be careful about what we say after the die has landed. If it was a 5, we know it's possible that the 5 could appear face-up because it did! But could the 2 also appear face up? Logically, you can't have more than one side of the die face up. If the 5 appeared, it isn't possible for any other number to be face-up. So what happened to the other possibilities? Where did they go? What exactly are those other possibilities?
One way to look at it is to say those other possibilities are information we possess about how the universe works. We use that information to make predictions. But we can back off of imagining that those other possibilities have some ontological implications. They don't. They're just the result of our analysis.
When we say that bullet to the head has the potential to cause brain damage, this reflects experience with brains and gun shot wounds. It's fully possible for a person to receive a GSW to the head and suffer no brain damage. It happens all the time, especially in suicide attempts where they just end up blowing their faces off. Again, you have to take it case by case.
I think probability can be taken one of two ways: it's either an assessment of some number of iterations (so we toss the coin 100 times, it comes up heads once, so we say it has a 1% chance of coming up. This assessment has to be considered in the light of the data from which it came.
The other way to assess probability is to examine the logical possibilities. Look at the coin and determine how it's weighted. If it's evenly weighted, there's logically a 50% chance it will come up heads.
We can't use the iterative form of probability either, because by definition, the universe is a one-off. However it is, it had a 100% chance of happening that way because the assessement is 1/1.
There is a echo here of other threads - you seem to presuppose time. If the next moment everything is different, there is nothing to say that it is 'next', rather than any other configuration where everything is different. Time has no meaning unless there is continuity and change, that produces 'succession'.
You seem to be drawing probability (with the word 'unlikely") and possibility ("necessary") into it.
Incompatibility makes it impossible to have immutable axioms which would be applicable to all systems.
That's what makes it reductionist. You can set aside the first person perspective, and with it, the reality of existence, by treating it as a model, or a board game, as if you were surveying the whole panorama from outside it - when you're actually not.
Have you ever encountered Bertrand Russell's A Free Man's Worship?
To go back to Bateson's initial quote, what would a numberless measurement of length, for example, be?
how can one have numbers in the complete absence of discrete amounts of givens - i.e., of quantities?
We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.
Mathematical entities are indispensable to our best scientific theories.
Therefore, we ought to have ontological commitment to mathematical entities.
Today has shown that in one thing Putin was more successful than he probably expected - he wanted to have a politically apathetic population and that is exactly what he got... He could be deposed and nobody would bat an eye, no jumping on the tanks for him.
Also, Putin has historically been able to shore up his power by military ventures. He benefits from a quagmire as much as he would a victory, just in terms of eliminating any hint of democracy in Russia.
We have seen that SR rules out the idea of a unique, absolute present: if the set of events that is simultaneous with a given event O depends upon the inertial reference frame chosen, and in fact is a completely different set of events (save for the given event O) for each choice of reference frame in inertial motion relative to the original, then there clearly is no such thing as the set of events happening at the same time as O. As Paul Davies writes (in a variant of the example given by Penrose above), if I stand up and walk across my room, the events happening “now” on some planet in the Andromeda Galaxy would differ by a whole day from those that would be happening “now” if I had stayed seated (Davies 1995, 70).
From these considerations Gödel concludes that time lapse loses all objective meaning.But from the same considerations Davies concludes, along with other modern philosophers of science, that it is not time lapse that should be abandoned, but the idea that events have to “become” in order to be real. "Unless you are a solipsist."
As I argued in Chap. 3 above, events “exist all at once” in a spacetime manifold only in the sense that we represent them all at once as belonging to the same manifold.But we represent them precisely as occurring at different times, or different spacetime locations, and if we did not, we would have denied temporal succession...
...in each case we are presented with an argument that begins with a premise that all events existing simultaneously with a given event exist (are real or are deter- mined), and concludes that consequently all events in the manifold exist (are real or determined). But the conclusion only has the appearance of sustainability because of the equivocation analysed above in Chap. 3.If a point-event exists in the sense of occurring at the spacetime location at which it occurs, it cannot also have occurred earlier. But if the event only exists in the sense of existing in the manifold, then the conclusion that it already exists earlier—that such a future event is “every bit as real as events in the present” (Davies), or “already real” (Putnam)—cannot be sustained.Thus, far from undermining the notion of becoming, their argument should be taken rather to undermine their starting premise, that events simultaneous with another event are already real or already exist for it in a temporal sense. For to suppose that this is so, on the above analysis of their argument, inexorably leads to a conclusion that denies temporal succession.
This, in fact, was Gödel’s point.As mentioned in the introduction to this chapter, he had already anticipated the objection that the relativity of time lapse “does not exclude that it is something objective”. To this he countered that the lapse of time connotes “a change in the existing”, and “the concept of existence cannot be relativized without destroying its meaning completely” (Gödel 1949, 558, n. 5).To this he countered that the lapse of time connotes “a change in the existing”, and “the concept of existence cannot be relativized without destroying its meaning completely” (Gödel 1949, 558, n. 5).As we saw in Chap. 3, however, the sense in which events and temporal relations “exist” in spacetime is not a temporal sense.This would amount to a denial of the reality of temporal succession.20
So the root of the trouble with the “layer of now’” conception of time lapse is a failure to take into account the bifurcation of the classical time concept into two distinct time concepts in relativity theory. The time elapsed for each twin—the time during which they will have aged differently—is measured by the proper time along each path. The difference in the proper times for their journeys is not the same as the difference in the time co-ordinates of the two points in some inertial reference frame, since they each set off at some time t1 and meet up at a time t2 in any one ...
We may call this the Principle of Chronological Precedence, or CP. As can be seen, it presupposes the Principle of Retarded Action discussed in Chap. 4, according to which every physical process takes a finite quantity of time to be completed.Note that so long as CP holds for the propagation of any physical influence, it will not matter whether light or anything else actually travels with the limiting velocity.41
As Robb showed in 1914, this means that—restricting temporal relations to these absolute relations only—a given event can be related in order of succession to any event in its future or past light cones, but cannot be so related to any event outside these cones (in what came to be called the event’s “Elsewhere”).There are therefore pairs of events that are not ordered with respect to (absolute) before and after, such as the events happening at the instants A and B on Robb’s “Fig. 6.1" The event B, being too far away from A for any influence to travel between them, is neither before nor after A.
For example, B could be the event on some planet in the Andromeda Galaxy that Paul Davies asked us to imagine, in the Elsewhere of me at the instant A when I am considering it. It is true that by walking this way and that I could describe that event as being in the past or in the future according to the time coordinate associated with the frame of reference in which I am at rest. But that event is not present to me in the sense of being a possible part of my experience. It bears no absolute temporal relation to my considering it...
All the events I experience, on the other hand, will be either before or after one another, and therefore distinct. In fact, they will occur in a linear order.They will lie on what Minkowski called my worldline.
There is nothing unique about my worldline, however. On pain of solipsism, what goes for me goes for any other possible observer (this is the counterpart in his theory to Putnam’s “No Privileged Observers”).42 Thus if we regard time as constituted by these absolute relations, time as a whole does not have a linear order: not all events can be ordered on a line proceeding from past to future, even though two events that are in each other’s elsewhere (i.e. lying outside each other’s cones) will be in the past of some event that is suitably far in the future of both of them. In this way, all events can be temporally ordered, even if not every pair of events is such that one is in the past or future of the other. This is Robb's "conical order." In the language of the theory of relations, it is a strict partial order, rather than a serial order.
In a paper of 1967 the Russianmathematician Alexandrov showed how the topology of Minkowski spacetime is uniquely determined “by the propagation of light or, in the language of geometry, by the system of the light cones”, noting the equivalence of this derivation to Robb’s derivation on the assumption of chronological precedence.
Thus the initial conditions of a deterministic universe 'contain' all the information of every moment of its evolution, and time is the running decompression algorithm that 'expands' the initial equation.
One is tempted by the analogue with a strange attractor, after ↪Count Timothy von Icarus, but even a strange attractor is rhythmic and predictable compared to the path of even a simple institution, or with the unpredictable events of a lifetime.
Take any pivotal life decision, be it moving to a distant city or committing to a partner or accepting a job offer. Everything changes, unpredictably, as a result of the decision. Because of this, while there may be a pretence of rationality, ultimately the decision is irrational. Not in the sense of going against reason, but in the sense of not being rationally justified. It is perhaps an act of hope, or desperation, or sometimes just whim.
And this not only applies to big choices, but to myriad small choices. Whether you have the cheese or the ham sandwich had best not be the subject of prolonged ratiocination.
Most of our choices are not rationally determined; and this is usually a good thing, lest we all become Hamlet
