The real is that which is as it is regardless of what any individual mind or finite group of minds thinks about it. The actual (or existent) is that which reacts with other like things in the environment. Hence reality and actuality are not coextensive--besides real actualities (e.g., individual events), there are also real possibilities (e.g., qualities) and real conditional necessities (e.g., laws of nature) that cannot be reduced to collections of their actual instantiations....and the difference between "real" and "actual" is...? — Pattern-chaser
Assumption 2: Every physical process can be expressed mathematically.
Then it follows:
The logical framework that underpins a theory of everything must be based on natural numbers. This means, by the incompleteness theorem, that this system cannot be complete and consistent at the same time — Karl
No, time is not an independent "thing" that changes, it is the (fourth) dimension of space-time that corresponds to spatial change. As I keep pointing out, motion through continuous space-time is a more fundamental reality than discrete positions in space or moments in time, which we arbitrarily mark for the sake of measurement and analysis.There is some measurable quantity we call time that changes. — Devans99
Exactly--time is not composed of durationless instants, and space is not composed of dimensionless points. Those are human constructs, which are very useful for certain purposes, but not real.I don't see how you can have a 'durationless instant' surely a contradiction in terms? — Devans99
What changes to make ‘now’ ‘then’? There is some measurable quantity we call time that changes. So it is reasonable to discuss the duration of 'now'. — Devans99
Exactly--time is not composed of durationless instants, and space is not composed of dimensionless points. Those are human constructs, which are very useful for certain purposes, but not real. — aletheist
Who can deny that the natural numbers are infinite. — TheMadFool
Exactly--time is not composed of durationless instants, and space is not composed of dimensionless points. Those are human constructs, which are very useful for certain purposes, but not real — aletheist
We describe time as continuous--it is not composed of discrete instants or very short durations. Likewise, we describe a line as continuous--it is not composed of discrete dimensionless points or very short line segments. "Now" is an arbitrary human construct that separates what we call "the past" from what we call "the future," but time itself does not really include any such discontinuity.How do we describe time then? The only models of a continua I've seen have used points or line segments to model it. In both cases its valid to discuss the length of the point or line segment representing 'now'. — Devans99
But that is not what I am saying. Time is real and continuous; a durationless instant is an arbitrary human construct.You can say time is a human construct ... — Devans99
Measurement is a human construct. We indeed mark two instants as "then" and "now," and measure the non-zero interval of time between them by comparing it to an arbitrary unit--e.g., one second as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom."There was ‘then’ and there is ‘now’ and there is a non-zero distance between them measured in units of what we call time. — Devans99
We describe time as continuous--it is not composed of discrete instants or very short durations — aletheist
Measurement is a human construct — aletheist
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist) — Devans99
Exactly what I said before--not composed of discrete parts. If we were to "zoom in" on a continuous line, we would never "see" anything other than a continuous line.What do you mean by continuous? — Devans99
Who said anything about "constructing" a continuum? It is the more fundamental reality.How on earth would you ever construct a continuum? — Devans99
Who said anything about such an alleged property?By what magic processes do you construct something with the property 'each part is equal to its whole'? — Devans99
Who said anything about "constructing" a continuum? It is the more fundamental reality. — aletheist
Who said anything about such an alleged property? — aletheist
"Construct" implies building something up from discrete constituents, which cannot be done in the case of a true continuum. I have never claimed that true continua exist, only that they are real. I have already given a specific example of a true continuum in geometry--a line.Geometry reflects reality. If we can't construct it geometrically, its probably does not exist. — Devans99
Who (besides you) has attributed any such property to a continuum? What I said was that if we were to "zoom in" on a continuous line, we would never "see" anything other than a continuous line.If you sub-divide a continuum you get two continua identical to the one you started with - the parts are equal to the whole. Thats a unique and illogical property of continua. — Devans99
Mathematical infinity is an abstract concept. It doesn't claim any physical representation, does it? — TheMadFool
Is it real (then your argument works) or is it too an abstract concept (your argument is faulty)? — TheMadFool
Who (besides you) has attributed any such property to a continuum? What I said was that if we were to "zoom in" on a continuous line, we would never "see" anything other than a continuous line — aletheist
But nature is logical so maths can explain it because it is logical also. Actual infinity is not a logical concept so does not fits in maths or nature. — Devans99
Thats the question. We can measure time, does that make it real? I can't think of anything we can measure that is not real. — Devans99
You mean a physical line, which is not the same thing. If you were to "zoom in" on space-time itself--not any physical object within space-time--you would never "see" anything other than continuous space-time.If we were to try that with a real line, we'd see discrete atoms. — Devans99
Continua are perfectly logical, just not in strict accordance with the logic of discrete quantity. It straightforwardly begs the question to insist that the latter is the only version of logic that corresponds to reality.Continua are illogical, reality is logical, hence continua don't exist in reality. — Devans99
Infinity is counterintuitive, is the comment I usually encounter. That it's illogical may not be true. How many natural numbers are there? — TheMadFool
Looks to me like we're just counting the rhythmic beats of the pendulum or the Caesium atom. There's nothing like an object to which we put a measuring scale and say it's x cm/inches long. — TheMadFool
But nature is logical so maths can explain it because it is logical also. Actual infinity is not a logical concept so does not fits in maths or nature. — Devans99
If we were to try that with a real line, we'd see discrete atoms. — Devans99
If we start with the common sense notion that there must be more points/intervals in a large line compared to a small line then a continua immediately violates this with ∞ = ∞. Continua are illogical, reality is logical, hence continua don't exist in reality. — Devans99
Whats logical about ∞ + 1 = ∞ (implies 1 = 0)? In fact infinity is invariant under all arithmetic operations; what's logical about something that when you change it, it does not change? — Devans99
If you were to "zoom in" on space-time itself--not any physical object within space-time--you would never "see" anything other than continuous space-time. — aletheist
Nature isn't 'logical' — MindForged
A line is an abstract object, you have to investigate it's properties mathematically. And in basically any geometry you like a line is not finitely divisible. — MindForged
Can you give an example of something illogical from nature/reality — Devans99
Yes but you cannot actually infinitely divide a line - it would take forever. So thats a potential infinity rather than an actual infinity you can describe at best geometrically. It's impossible to describe actual infinity geometrically, mathematically or otherwise so/as it does not exist. — Devans99
But we know mathematically that the cardinality of the continuum is such that it can be put into a one-on-one correspondence with a proper subset of itself. — MindForged
But the one-on-one correspondence procedure yields nonsense like Galileo's paradox — Devans99
And the continuum does not have a cardinality... Cantor should never have made such numbers up. It's down to a deficiency in the core of set theory; the polymorphic definition of set supports two different object types: finite sets and descriptions of set. The first have a cardinality, the 2nd do not. They are different kinds of objects with different properties and need to be treated differently. Cantor tried to shoe-horn both objects into a common facade and ended up making up magic numbers for cardinality - definitely not the right approach. — Devans99
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