Agriculture is a big part of the OP isn't it? — frank
Are you saying that you want this thread to only consist of "wailing and gnashing of teeth" about climate change? — Agree-to-Disagree
Or are we only allowed to talk about the negative consequences of Climate Change? — Agree-to-Disagree
And there's a 1-to-1 correspondence:
(1, 2, 3, 4, 5, 6, 7,...)
(2, 4, 6, 8,10,12,14,...) — ssu
OK, basically how Cantor showed that real numbers are uncountable is the way to do this.
Basically if you have a list where all the Moliere-numbers would be and then you show that there's a Moliere that differs from the first Moliere-number on the list, differs from the second Moliere-number on the list and so on. This way you show that there's a Moliere-number that isn't on the list. Hence there cannot be a list of all Moliere-numbers. The conclusion is a Reductio ad absurdum proof. — ssu
How does this enter into a discussion of these Zeno type paradoxes? Define the momentum of a point as it progresses to zero. Does the tortoise have momentum? Too much of a stretch for me. — jgill
Ok.
If you think so, then wouldn't there be more natural numbers (1,2,3,...) than numbers that are millions? Isn't there 999 999 between every million?
No, similar amount, because
(1,2,3,....) can be all multiplied by million
(1000 000, 2 000 000, 3 000 000,...)
And because you can make a list of all rational numbers (as above), the you can fit that line with the (1,2,3,...) line in similar fashion. That's the bijection, 1-to-1 correspondence. — ssu
If you think so, then wouldn't there be more natural numbers (1,2,3,...) than numbers that are millions? Isn't there 999 999 between every million? — ssu
Let's say you have a set of numbers, let's call them Moliere-numbers. As they are numbers, you can always create larger and larger Moliere-numbers. Hence we say there's an infinite amount of these numbers. The opposite of this would be a finite number system that perhaps an animal could use: (nothing, 1, 2, 3, many) as that has five primitive "numbers".
If we then say that these Moliere-numbers are countably infinite, then it means that there's a way to put them into a line:
Moliere-1, Moliere-2, Moliere-3,.... and so on, that you can be definitely sure that you would with infinite time and infinite paper write them down without missing any.
If Moliere-numbers are uncountably infinite, then we can show that any possible attempted list of Moliere numbers doesn't have all Moliere-numbers. — ssu
No. The measurement is true. Specifying the degree of error does not render the measurement untrue. The tank really does contain 25±1 litres. — Banno
Physical measurements are not infinitely precise, nor is such precision needed. — Banno
It's due to the way that time exists, in conjunction with the limitations of our capacity to measure. We are limited in our ability to measure time by physical constraints. If we had a non-physical way to measure time we wouldn't be limited in that way. — Metaphysician Undercover
There's that, and then there's the philosophically more interesting view expressed here:
Each measurement has a certain amount of uncertainty, or wiggle room. Basically, there’s an interval surrounding your measurement where the true value is expected to lie.
...the presumption that there is a true value; that given infinite precision we could set out the actual value as a real number. There is no reason to supose this to be true. — Banno
Actual measurements fail beyond Planck's constants. These paradoxes are all hypothetical involving motions of dimensionless points along rational number scales. — jgill
More or less in the case of Zeno. Mathematics is often said to resolve the paradox in terms of the topological continuity of the continuum, by treating the open sets of the real line as solid lines and by forgetting the fact that continuum has points, meaning that the paradox resurfaces when the continuum is deconstructed in terms of points. — sime
In my view, Zeno's arguments pointed towards position and motion being incompatible properties, but the continuum which presumes both to coexist doesn't permit this semantic interpretation.
As having difficulty choosing a topic, I do wonder if having a theme (or several) would have made the activity seem less daunting. At one point, I remember that I'magination' was suggested but I think it was dismissed. Anyone could choose to use it as a prompt although it may be seen as unimaginive to do so. — Jack Cummins
Kant wanted to disprove metaphysics as a science with Newtonian materialism. What do you think? — Gregory
I’d be surprised if you were not with the familiar 1783 passage regarding “dogmatic slumbers”. THAT….is the root of Kantian dualism, the unity of rational vs empirical doctrines prevalent in his time. The two-world or two-aspect-of-one world confabulation was the illegitimate, red-headed stepchild of a veritable PLETHORA of successors, except Schopenhauer, methinks to be the foremost immediate peer that actually understood wtf the noise was all about.
Noise. Including, but not limited to….whether or not that which can be treated as a science, actually is one. — Mww
In that case, I am not sure if Hegel was understanding Kant properly. Because from my view, it is not clear that Kant's world view was dualism. What Kant said was that our knowledge can only give us understanding to the point of our experience, and that is the limit our reason. — Corvus
I should preface by saying that I've never been all too enamoured with morality as a field of study quite frankly. Using obtuse thought experiments to parse what is good and bad simply always seemed like a rather pointless endeavour, and I personally feel it's more fruitful to investigate morality in specific terms rather than universal terms and evaluate morality more so from a personal and societal perspective than from a seemingly objective view-point. — Dorrian
But the question I wish to ask is, in some sense, aren't all universal moral systems inevitably going to be flawed in some way and therefore rendered futile? — Dorrian
Heidegger ends Being and Time on Hegel's analysis of time. — Gregory
a luxury not available to all. — Paine
For Hegel contradiction is the essential element in the changes and progress of the world. — Corvus
Reason itself is a faculty which analyses and finds truths, but if it is to employ transcendental logic for its operation, then does it not duplicate itself with another faculty of truth telling system? Does it imply that reason says true on X, but the logic says false on X at the same time? If both of them says true, then why does reason need the logic, and why logic needs reason?
Are they not rather actually the same faculty expressed in different terms? — Corvus
Can it be that it it is the concept of "beyond our grasp" that is beyond our grasp?
(My old friend Ludvic suggested this to me.) — unenlightened
What is Kant's one great idea? — Gregory
I, and others, do understand what it is to follow plus and quus and to choose which to enact. — Banno
I would encourage people to participate, especially if they enjoy philosophy. — Sam26
except I rather think contradiction is certainly a necessary part of logic. Or, maybe, if not a necessary part, then at least the fundamental ground for the validity of logical constructs. — Mww
was contradiction a necessary part of logic and/or reality in the worldview of Kant? — Gregory
If we can only see two sides of an idea, how do we know they unite at a highet level?
I agree, but feel like I shouldn't... — Banno
