A paradox is not a contradiction.

A paradox is indicative that you have an underlying logic error.

In the case of Cantor's paradox, Galileo's paradox, Hilbert's hotel, the Measure Problem, the underlying logic error is the assumption that actual infinity exists.

A paradox is indicative that you have an underlying logic error. — Devans99

Where are you getting your information from?

These are my opinions.

Start is depending on religion:
-In christianity in a start, according to Bible, you are born, and never die. Also if you end in hell, you still live.
-Budhism is different. Is like a circuit, when you come at the same point. Circle.
-Mathematicly said, could be both.

I hope to be able to definitively answer the question in the OP before long. I have been busy in the important exercise of observing everything and identifying for every single thing whether it has a start.

When I am finished, I will post the result here, and then we'll finally know for good and all.

When I am finished, I will post the result here, and then we'll finally know for good and all. — andrewk

You can answer the question without induction:

- Temporal. Would an object exist if its temporal starting point was removed? That would be like a human having the moment of conception removed. Remove the temporal start and everything else is undefined.

- Spacial. If an object has no identifiable start, it has no middle and no end. So it can't exist.

One can make those assertions, but one can't know them to be true or false without either observing whether they are the case, or making a deductive argument. I can't see how one would do either of those things without essentially assuming the conclusion.

Of course, one can hold an opinion that such things are true, or an opinion that such things are false, but there's not much discussion to be got out of a pure opinion.

One can make those assertions, but one can't know them to be true or false without either observing whether they are the case, or making a deductive argument. — andrewk

I am not making assertions, I am making deductions.

What you wrote here are not deductions. The first is an analogy. The second is a non-sequiteur.

What you wrote here are not deductions. The first is an analogy. The second is a non-sequiteur. — andrewk

Thats just plain not true:

- Something has no temporal starting point (time=0) in time
- then time=1 is not defined
- then time=2 is not defined
- etc..
- The object does not exist

- Something has no identifiable spacial start point (x=0)
- then x=1 does not exist
- or x=2
= etc...
= The object does not exist

A deduction is a sequence in which each statement is justified in terms of earlier statements, or accepted axioms, via a rule of inference. There is no rule of logical inference that justifies the second and subsequent lines in either of those sequences you wrote in terms of any of the lines that go before them. Hence neither is a deduction.

Lining up a bunch of statements in a sequence and putting 'therefore' in front of all except the first does not turn it into a deduction.

If a moment does not exist, the moment after it is undefined, so is the moment after that, etc... If all moments are missing then the object does not exist. So the fact that all moments are missing justifies the last deduction that the object does not exist.

Same logic for space.

There is no rule of logical inference that justifies the second and subsequent lines in either of those sequences — andrewk

1. PREMISE: Something has no temporal starting point (time=0) in time
2. DEDUCTION: Then time=1 is not defined

If an object does not exist at time=0, how can it exist at time=1? Thats a valid deduction.

Think about if your conception (time=0) was removed, would you exist at your birth (time=1)?

Time is a series of moments. Take away one moment and the following moments are undefined/cannot exist. Imagine Eternity, it has no starting moment, so none of it can exist. Think of the initial starting positions of all the particles in the universe. If that was removed, what is left? Something completely undefined. So eternity is rather like negative infinity; the start is undefined so the whole thing does not exist.

It is a very interesting question. I suggest to you a lecture: the first Antinomy(abut the beginning of the world or not) in the Critique of Pure Reason you may find pdf online in an accurate edition.

LOGIC AND PHYSICS

The reason why the infinite regress is rejected, in regard to the beginning of physical things, is not logical, but physical: to us the cognitive process involves a « discretion» of matter in unities which can be worked up until reflection let us have awareness of the distinction between ourselves and what is and object to us. This requires some kind of continuity in the physical process of working up data.

Now, if you think the data are selected THEN recognized, you recognize a structure of recognition as basing the process of selection. If you think the other way, you think that recognition is sufficient to elaborate data, but the elaboration is necessary to recognition and independent from it.

In the first case you can't say that the physical WORLD(as a whole) as a beginning whatsoever, because you must first account for the origin of the structure which made to you possible to distinguish two states at all, where a beginning would be the recognition of a thing in a certain state, within the recognition of the absence of any thing like that in a precedent state.

In the second case you can't say that something has or not a beginning, but just that something there is or not, or that something comes before or after(iff you recognize the indipendency of the data, though not existent, in the same form you attribute to them, independently); and this because you have no recognition at all until a certain thing make you recognize something at all. In this case the most accurate thing to say may be: about those data, that I recognized, I can establish a scale to measure them(let's call it: the complexity of them). Furthermore, assuming you know the somehow independent being of them, I can find which complexity is necessary to generate a being like myself(and finding such a correlation alone would be an heroic work).

REFERENTIAL TIME AND SPACE?

Time is, indeed, a definition: it defines the interaction between us and the world insofar we distinguish the property of irreversibility(the infamous example of the egg which breaks but not unbreaks). This is due to the fact that the parameter indexed by the Boltzmann constant designates something the physical effect is enough big to us, that it results in a certain mode of perception of events. Thus time isn't properly a reference, being a reference that indicates any beginning, through the reference of which distinguish a before and an after.

It remains space. Space, in general, presupposes just homogeneity. But, as we perceive, we presupposes other properties, which may varies within our evolution. At now, we perceive the (macro)world as euclidean, whatever the reason may be. There is, however, a book titled "Twelve examples of illusion" (I liked it) in which there is a reference to the work of a mathematician, which disposed a set of exercises to learn to perceive the world in more than 3d..

Hence, not even space has that referential structure that we were searching for: homogeneity alone it is not sufficient to distinguish any beginning(different parts of space are in a relation of difference(or identity) but not of succession).

DEFINITIONS

As Poincaré said somewhere: that the light travels in straight lines is a definition of straight line. That is to say: definitions presupposes a criteria of identifying objects. But in order to do so, we perceive them in space and time. But space and time are not referential, i.e. those alone do not let to identify more than a ordered multiplicity, and not an object for a subject. Therefore, the definitions too rely on a referential structure which does not identify with the criteria of perceiving object, and even less with the actual modes in which they are perceived.

INFINITY

It is a well known topic in mathematical logic and in analysis. Let's just say: Infinity it is not a number, it is a relation: infinity means that no matter how many units you add(how many times you apply an operation): you will never obtain a result, such that the operation can not recur on it. Of course, if the operation is not recursive there is no such problems of establish an end or not to its application through a series. Infinity is, in this sense, a relation between a unit and a correlative operation.

In analysis it is a concept used to establish a hierarchy in respect to the set of natural numbers. I hope nobody thinks a hierarchy has a beginning, just as the laws that regulate the behavior of waves has none.

HAVING NOT A BEGINNING

As in the last analogy, with all its limits, I tend to consider beginning as relative, insofar as it depend on a referential structure which imply a certain mode of recognition. That is: x has begun equals I recognized x and y in respect to z.

It may be the case, that having a scale to measure the complexity of matter, we could establish a necessary(and perhaps sufficient in some respect) value of complexity to the possibility of such beings to become a form of life.

In the first case you can't say that the physical WORLD(as a whole) as a beginning whatsoever, because you must first account for the origin of the structure which made to you possible to distinguish two states at all, where a beginning would be the recognition of a thing in a certain state, within the recognition of the absence of any thing like that in a precedent state — Ikolos

The physical world (=universe) must have a temporal beginning. How can something exist without a temporal beginning? If you take away the Big Bang, the universe no longer exists. So deductively its impossible for the universe to exist without a temporal start.

I hope nobody thinks a hierarchy has a beginning, just as the laws that regulate the behavior of waves has none. — Ikolos

I would argue that everything real has a start, so a real world hierarchy has a start (eg the left leaf node). The laws of the universe, their start and end coincide with the start and end of the universe.

The physical world (=universe) must have a temporal beginning. How can something exist without a temporal beginning? If you take away the Big Bang, the universe no longer exists. So deductively its impossible for the universe to exist without a temporal start. — Devans99

Do you agree that without change there is no time?

If so, the temporal beginning of the universe would be the beginning of change.

That beginning of change could have been arbitrarily far in the past, but before it there was no change and thus no time.

We could say there was something that had the ability to bring change to itself. And when it used that ability is when the universe began to change, what you call its temporal start.

It's difficult to conceive, but then again it's not something we see every day.

What troubles you about that?

Do you agree that without change there is no time? — leo

I see time as fundamental to the universe: The speed of light speed limit (speed = distance / TIME) is obeyed by every particle in the universe and exists independently of change. To be a normally functioning universe, a speed limit is required. Else it's possible to accelerate objects to infinite velocity and thus straight out of the universe. So time is not emergent; it is fundamental to the universe.

We talked about that on the 2nd page of this thread, I thought I had convinced you, I addressed all your points regarding that.

I remain convinced of the Special Theory of Relativity.

Then look into the Lorentz ether theory, it is empirically equivalent to Special Relativity, no experiment distinguishes between the two, yet in the former one light can go arbitrarily fast. But we measure its velocity to remain constant because all we are able to measure empirically is its round-trip average speed. Look it up. You are basing your reasoning on assuming Special Relativity is true, but it's just one out of several possible theories that match experiments equally well. So you're saying if Special Relativity is true, then time is fundamental to the universe. But at least one other theory is equally accurate as Special Relativity and does not imply that time is fundamental to the universe. So why keep assuming that time is fundamental to the universe? If you stopped assuming that I think you would find some intellectual peace on that matter.

Time is fundamental because we can't have stuff flying around at infinite speeds in a sane universe. There has to be a speed limit so the universe must be time-aware. And all experimental evidence points to that speed limit.

Time is fundamental because we can't have stuff flying around at infinite speeds in a sane universe. There has to be a speed limit so the universe must be time-aware. And all experimental evidence points to that speed limit. — Devans99

In the Lorentz ether theory light does not travel at infinite speeds, but can travel arbitrarily fast depending on the direction. Again, absolutely zero experiment is able to measure the speed of light in a single direction. All we ever measure is its average speed on a round-trip. You can assume light goes at whatever speed in a given direction so long as its average is equal to c, and that contradicts zero experiment. In many aspects the Lorentz ether theory is more intuitive than Special relativity, there are no apparent paradoxes in it such as the twin paradox.

I could go into length explaining how it is that we cannot measure the speed of light in a single direction, how all we ever measure is its round-trip speed, how the Lorentz ether theory is more intuitive than special relativity, but if you accept the possibility that this is the case then what remains of time besides a tool we use to measure change?

but can travel arbitrarily fast depending on the direction — leo

But the universe is finite so we cannot have anything traveling at an infinite speed else it would not be in the universe.

But the universe is finite so we cannot have anything traveling at an infinite speed else it would not be in the universe. — Devans99

Arbitrarily fast is not infinite, and the universe can expand arbitrarily fast too.

If an object does not exist at time=0, how can it exist at time=1? Thats a valid deduction. — Devans99

Really? What rule of inference does it use? Modus Ponens? Modus Tollens? Double negative elimination?

Time is a series. You can't just arbitrary remove points from a series and the rest of the series remain intact. That's just common sense. Take away any moment in an object's life and the following moments are undefined.

Every moment must have a moment before it else its not valid. That's a self-evident axiom, and it implies time is circular.

It ties in with the physical evidence: The only place in the universe to get enough energy for the Big Bang is the Big Crunch so time must be circular.

Imagine an eternal being; he would have no start in time so could never exist. Being is possible we therefore conclude Eternal is not.

Well, I would say: if you think beginning as a l o c a t i o n in a certain instant, and not of a recognized difference in reference to an identified state, then there is no reason to think there is a beginning of the world as a whole, because the whole is a mere concept, through which we think a complete regress.

But it is wrong to say: « Time is a series» for a mathematical series is n o t characterized by an o r i e n t a t i o n: you can go back and forth just the same. We do not, as a fact, perceive time this way: we see irreversible event(because of the effect called time, i.e. interaction with is designed by the Boltzmann parameter), t h e n we determine this perception causally, i.e. we consider it as an effect, and a cause is to found. Otherwise, we presuppose a referential structure, i.e. recognition of meaning as Kemp Smith call it, to have the possibility itself to distinguish, in time, what is changed but still was there in other form, and what is present in a certain instant and was not before. With time alone you can n o t establish if you see the same sun every time you look at it, nor you can say there is at all if you are not perceiving it. Hence, time presupposes, as to be meaningful, and not a brutal sequence of events unconnected, a structure(an a priori, as Kant called it).

You are too smart to think that there is an absolute beginning in time, since 1 there Is no difference between mere instant and then no reason to distinguish a beginning instant from others and 2 we perceive time just because of certain constitution of ourselves: time is the effect of our interaction with the physical world insofar as we were capable of describing it in terms of thermodynamic: just because the parameter indexed by the Boltzmann Constant is big enough we perceive an irreversible direction of events. This means: time is relative as it implies a certain perceiving of things. If you by 'Time' mean a law of increasing complexity a n d some kind of correspondence between certain degrees of complexity(however it is to be measured is a interesting and hard problem) and the p o s s I b I l I t y of certain configuration as forms of life, welcome on the ship. If you do I advise you to read Reichenbach, the first to present a clear account of time as an effect(causal theory of time).

The fact that there is an hypothesis, i.e. Big Bang, to explain the actual development of the universe, does not mean that the universe itself begun at that point, but only that just so far our knowledge has been capable of establish an explicative hypothesis.

I think this is implicitly a definition of beginning similar to that of Kant in the Dialectic: «Beginning of a thing is the recognized difference between a time in which a thing does not exist and a time in which it exists.»

Yet, Kant is more precise elsewhere: this definition leaves out the cases in which we perceive the S a m e thing as changed( to perceive such a thing we need a structure of identification which 1 presupposes the permanent 2 it must be referential, because we perceive change from a certain point of view, which is given).

But it is wrong to say: « Time is a series» for a mathematical series is n o t characterized by an o r i e n t a t i o n: you can go back and forth just the same. — Ikolos

Time is a series: Now (t=0) only exists because t=-1 had existence. t=-1 only exists because t=-2 had existence. So all moments must have a moment prior to them. The only topology that fits is a closed loop IE circular time.

Actual infinity, if it existed, would be a quantity greater than all other quantities, but:

There is no quantity X such that X > all other quantities because X +1 > X

The non-existence of actual infinity implies negative actual infinity does not exist. Negative actual infinity has the same structure as past eternal (in time):

{ …, 2015, 2016, 2017, 2018 }
{ …, -4, -3, -2, -1 }

IE past eternal (in time) is impossible. IE time had a start. The start is coincidental with the end; IE Circular time.

How else can you explain the Big Bang except the Big Crunch?