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rossum
Guest
Agreed, as with my example of an odd perfect number.
More in the sense of “imprecisely defined concept”. Mathematics uses very precise definitions; philosophy less so.
rossum
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rossum
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GEddie
Guest
What if it were expressed with a bar over the last two 3s?
Are you maintaining that one cannot divide by 3??
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JuanFlorencio
Guest
It is not philosophy nor mathematics: it is us who are more precise or more imprecise. And the kind of foundation that we have at the basis of every field of our thought is of the “philosophical” type.
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JuanFlorencio
Guest
It would be the same, Geddie. It would indicate the same thing that we want to express with the three dots (a process that goes on with no reason to stop).
Of course we can divide one by three. And if we used, for example, a numerical system consisting of three symbols (a ternary positional system), we would be able to represent one third in a very simple way: It would be 0.1
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lmelahn
Guest
Well, I think I agree with you 90%. (Not a precise measure, of course
.)I mean that an immense (immeasurably large) body is not repugnant to reason. But I think that even in such hypothesis, there is not exactly an “actual infinity,” but only a potential infinity. (I.e., you would be able to measure an arbitrarily long portion of the body, but you could never measure the whole body.)
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PseuTonym
Guest
How about the following?
(0/3) = 0.00000…
Do you consider that to be an equation?
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JuanFlorencio
Guest
What does 0.0000… mean, Pseu Tonym? I am not aware of any convention about that chain.
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Jaaanosik
Guest
One can be divided by three in mathematics.
It cannot be divided in physics once units of measure are associated with numbers representing quantities of UOMs. The equation is false in physics with UOMs.
1/3m=0.33333…m is false, we can not go past the Planck length.
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PseuTonym
Guest
Yes, I agree that the popular appeal to so-called “linear spatial measure of separation of two space-time points” in the 4-dimensional space-time continuum – and also the more Newtonian concept of "taxicab distance assuming no zig-zagging in space-filling curve or Brownian motion paths, but instead assuming something like the time it takes for light to travel the path, or perhaps sound rather than light, given the failure of Galileo’s attempt to measure the speed of light and subsequent hypothesis that light …
Anyway, what about angular measure? In radians, it is a pure number, because the least upper bound of the set of chords generated via selecting arbitrary finite subsets of the set of points on the perimeter of the circular disk, and also the length of the radius are associated with linear spatial measure in the Newtonian apparatus. The metres or inches or whatever cancel out, and we get a pure number in so-called “radians.”
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Jaaanosik
Guest
Well, let us assume a radius of 1 Planck length.
What is the circumference of the circle? Is it 2*pi or it’s 6 of Planck length?
Are we dealing with a circle or hexagon?
The speed of light is media dependent. It’s different for the air, vacuum, water, glass, …
Even outer space vacuum is not ‘empty’.
How could Galileo possibly do anything reliable with his approach about measuring speed of light at his time?
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Neildown
Guest
**
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
Amounts or values of themselves are always finite, but an “infinite amount” can be thought of as a rate or flow of finite amounts compiling without end.
2. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.
An actual infinite quantity can be defined as a distinct quantity because an actual infinite fits within its predisposed criteria of being an irrational number (and therefore subject to at least some sort of scrutiny as a given). An infinite cannot, however, be an actual number: it is just an “increasing” finite.
Whether or not there is an actual infinite quantity is ultimately impossible to determine, given the subjectivity of the question in and of itself: where exactly would we look for such a number?
Under the assumption that there is an actual infinite quantity, the answer must inherently remain in a state of limbo simply due to the fact that it is an unending number - you can’t be sure of what it is unless it ends.
Which in my opinion opens up a lot of interesting musings - maybe that’s why we’re all so unsure of life itself. Or, alternatively, maybe everything is finite, but the scale of time that we live compared to that of other things is so huge that the mere concept of infinity is impressed on human consciousness. Just as well, even if it were an impression, it wouldn’t necessarily be in vain.
This is why I want to write science-fiction. :compcoff:
- Any actual quantity of something is a distinct quantity - it is an actual number no greater or smaller than the distinct units of which it is comprised.**
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
Amounts or values of themselves are always finite, but an “infinite amount” can be thought of as a rate or flow of finite amounts compiling without end.
2. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.
An actual infinite quantity can be defined as a distinct quantity because an actual infinite fits within its predisposed criteria of being an irrational number (and therefore subject to at least some sort of scrutiny as a given). An infinite cannot, however, be an actual number: it is just an “increasing” finite.
Whether or not there is an actual infinite quantity is ultimately impossible to determine, given the subjectivity of the question in and of itself: where exactly would we look for such a number?
Under the assumption that there is an actual infinite quantity, the answer must inherently remain in a state of limbo simply due to the fact that it is an unending number - you can’t be sure of what it is unless it ends.Which in my opinion opens up a lot of interesting musings - maybe that’s why we’re all so unsure of life itself. Or, alternatively, maybe everything is finite, but the scale of time that we live compared to that of other things is so huge that the mere concept of infinity is impressed on human consciousness. Just as well, even if it were an impression, it wouldn’t necessarily be in vain.
This is why I want to write science-fiction. :compcoff:
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