Why don't you just look it up, or Google it? Plenty of stuff on cardinalities, countable and uncountable infinities, the diagonalization argument, Cantor ... — tom
It appears very obvious to me that you do not understand the accepted meaning of the word "countable" and, more fundamentally, the distinction between logical possibility and nomological possibility — aletheist
Your worldview is too small because it limits the real to the actual and the finite. — aletheist
OK, so you can count integers, but you cannot count the real numbers, even in a tiny subset. There is an uncountable infinity of reals within any subset - hence it is a continuum. The countable infinities do not have this property. They are different and one is at least infinitely bigger than the other. — tom
I think intention is inherent within life itself, as all living things tend to act with purpose.But, where does this intention come from? — TimeLine
Do you think you might be able to count a subset of the integers? — tom
Try counting the real numbers between 0 and 1. — tom
Countable infinities are precisely those which can be put into one-to-one correspondence with the integers. This is a definition, and no, no one expects you to count them all. — tom
Newton's laws concern mass, not substance, in the Aristotelean sense. Crucial distinction. — Wayfarer
I guess you must deny, then, that the integers are countable, since nothing and no one can actually count them all. — aletheist
I said that, also, the reason being that Galilean and Newtonian physics rejected Aristotelean physics, it didn't need the scholastic concept of 'substance' in order to do its work (and besides wanted to break from the 'dead hand of scholasticism'). — Wayfarer
No one is talking about doing anything. To say that something is infinitely divisible does not mean that a human being is actually capable of infinitely dividing it. It means that it is possible in principle to divide it infinitely. — aletheist
Space is actually infinitely divisible and potentially infinitely divided. — Michael
You're still making the same mistake. It is false to say that space is potentially infinitely divisible only if it actually is. — aletheist
What a philosopher would ask is a question that science will never address, but desperately needs an answer to (so it will not be so easily commandeered by mindless megalomaniacs), a question that we all need an adequate answer to, the Greatest of the Great Questions of Life: that of "Why Bother?"
Without an adequate answer to that Greatest of the Great Questions of Life (for you must admit, you must answer that question before you even begin to address the others), all will crumble in uncertainty. (I have the answer, by the way) (and no - it is not a smart-ass answer. so don't go there). — Numi Who
I’m not sure I’d agree. My understanding is that Aristotle ultimately argues that substance is the unity of matter and form or, more generally, of dunamis and energeia. This unity is the necessary and sufficient condition of being. In that sense hylomorphism fundamentally differs from modern substance dualism, which explicitly dichotomizes thought and extension into mutually exclusive categories of being. In the modern approach a thinking substance can exist entirely apart from extended substance and vice versa. — Aaron R
Either space is infinitely divisible or it is not. Whether anyone can actually divide space into infinitely many parts is completely irrelevant - only whether it could potentially be divided into infinitely many parts. — aletheist
Only the motion from one actual location (i.e., arbitrarily defined coordinate) to the next is a discrete event. We can only define a finite number of distance coordinates, so we can only measure motion in discrete units. — aletheist
Well, it's only that something like this must happen if motion is to be possible.
...
There are a finite number of coordinates for the object to pass through, "jumping" from one point to the next without passing through the space in between. — Michael
How can something "jump" from one discrete location to another without ever occupying the space in between? This is pure nonsense to me. — aletheist
It is not that I have incorrectly applied the term epistemological but rather you yourself have failed to understand the subconscious mind and the structural layers of the psyche; I fear you think that somehow the subconscious is distinct from the conscious mind. It is not, and as I said earlier, the subconscious mind is still a form of consciousness. — TimeLine
Neither seem satisfactory to me. I think that we definitely need both, and I see no need to prioritize one, let alone kill one with the other. I can't bridge the gap either, but oh well. — Wosret
It is really no different from philosophy in this regard; it all boils down to one's assumptions. To get us back on topic, Zeno's alleged paradox exploits this by smuggling in the idea that any finite interval of space consists of infinitely many individual points, such that one must somehow pass through them all in order to get from one place to another. Once we dispense with that misconception and recognize that space is continuous, and the only actual points are the ones that we arbitrarily define, the paradox dissolves. — aletheist
You are confusing actual possibility with logical possibility. Mathematics deals with the latter, not the former. It is indeed actually impossible to add infinitely many fractions, but it is not logically impossible. — aletheist
Mathematics is entirely a matter of necessary reasoning about hypothetical states of affairs. There is no falsity whatsoever in saying that if someone were to add infinitely many fractions in a particular series, then the result would be 1. The fact that no one can actually add infinitely many fractions is completely irrelevant. — aletheist
Not at all. We can reason about infinity without actually doing anything an infinite number of times. If someone (God, perhaps) were to add up Banno's infinitely many fractions or carry out my multiplication to infinitely many decimal places, then the result would be 1 in either case. — aletheist
Convert 1/3 to a decimal, then multiply it by 3. Is the result 1, or an infinitesimal fraction short of 1? — aletheist
You're overthinking it.
½ + ¼ + ⅛...=1 — Banno
I think these kinds of intuitions is what the 'myth of the given' is criticising. It is the belief that knowledge has a dimension which is given or self-evident, which philosophy then elaborates on, when in fact, critical philosophy is questioning the very thing which you're taking to be self-evident. — Wayfarer
Personally speaking, I really enjoy reading the metaphysics of the various historical cultures. Neo-Platonism is mysterious and esoteric, yet intriguing. A what if? - what if Neo-Platonism actually is true?! Simply wondering about that possibility is enough. — darthbarracuda
The difference may cut even deeper if, as Aaron R mentioned in another thread, true Aristotelian substances are unities of matter and form, of dunamis and energeia. In that case, the only true substances are living organisms, and also, arguably, pure chemicals or chemical elements (as argued by Aryeh Kosman in The Activity of Being: An Essay in Aristotle's Ontology). Artifacts and non-living objects like stones and mountains are substances only by analogy. — Pierre-Normand
It is a very specific sort of substance that strictly obeys Newton's first (or second) law. It's a substance that is either defined as the mereological sum of its material parts, or that consists in an essentially indivisible mass. Substances that can survives the loss of some of their massive parts, or maintain their identities though the accretion of new massive parts, such as plants, animals, most artifacts, and celestial bodies, don't strictly obey Newton's laws of motion precisely because of the principle of conservation of momentum (which is a consequence of those strict laws). Those laws only strictly apply to physical "matter", things that have invariant mass. When an ordinary substance gains or loses parts, conservation of momentum only applies to the unchanging mereological sum of this substance and of the parts that it either lost or gained. — Pierre-Normand
That's because those concepts, as used by Kant to investigate into the grounding of empirical knowledge, are revealed to be tied up with the concept of an enduring substance and such a formal concept doesn't fall under the purview of physical law. — Pierre-Normand
It's almost as if we expect judges to intentionally distort the facts to agree with personal views. E.g. a Democrat will try to make it seem like the Constitution forbids a state-ban on abortion and a Republican will try to make it seem like it doesn't. — Michael
The objector has not understood the fact that time is one of the forms of sensibility. — Wayfarer
But, what exists 'beyond perception'? And, what does 'duration' comprise? It might seem obvious, but in order for time to exist, there has to be sense of scale. Humans conceive of time in terms of the rotation of the earth around the sun, which gives them days and years - everything is measured by us in those terms. But what if you perceived it from the point of view of a being that lived for a million years? Or a being that lived for an infinitesmal instant? Those scales would be vastly different to the human scale - which is real? — Wayfarer
My argument is not that the world doesn't exist in the absence of any or all observers, but that whatever we can say we know about what exists, presupposes a perspective. Even if that is mathematicized, which effectively eliminates purely individual perspectives and gives a kind of 'weighted average' of all points of view, it's still an irreducibly human point of view, which is inextricably an aspect of whatever we say exists. — Wayfarer
This is a view of the "block universe" in which time just is another dimension akin to the three spatial dimensions. — Pierre-Normand
Such a view of the universe can't of course mesh with our view of the world as a source of possible objects of experience. Kant argues in the Analogies of Experience (in his CPR) that an empirical experience can't have an objective purport if it doesn't potentially rationally bear on other experiences. (Wilfrid Sellars also argued for this in his Empiricism and the Philosophy of Mind currently being discussed in another thread). And this is only possible if we can distinguish the successive experiences of a single thing that has changed from the simultaneous experiences of two separately existing things. — Pierre-Normand
I guess the point I am trying to make is that what is innate is relative to our experiences and that is why it is epistemological and not independently innate. It triggers emotional responses through memory and imagination, only sometimes we are just not aware at conscious level as to why. — TimeLine
The window to surfacing our memories caught in the subconscious realm is our imagination; that is innate, a universal translator of sorts to our emotional responses that are triggered by musical experiences. It is not the same as language acquisition, but I do wander whether it may be a product corresponding to semantic mechanisms, but even then meaning and development is wholly social. — TimeLine
Not necessarily. Ever had an extremely strange dream, cut up into multiple, unintelligible parts as you say that when you wake up think, 'what the heck?' and have a rather intense emotional response to it; but when you think about the dream, are able to piece the puzzle as to why some images were perhaps representations of certain fears or desires, it begins to make sense and the anxiety subsides. It is an intellectual sophistication that would enable one to decipher and relate, just the same as one would when listening to music. Indeed, for the most part a temporal arrow enables us to surface our emotions, but it is not essential. The sophistication itself being as you say: — TimeLine
So you mean ... exactly what I said then?
Ie: Holism is four cause modelling, reductionism is just the two. And simpler can be better when humans merely want to impose their own formal and final causality on a world of material/efficient possibility. However it is definitely worse when instead our aim is to explain "the whole of things" - as when stepping back to account for the cosmos, the atom and the mind. — apokrisis
1. Hylomorphic dualism provides an interesting and worthy counterpoint to the dichotomous substance dualism that undergirds the dialectic of modern philosophy since Descartes and Locke. Subdues the modern tension between realism and idealism by more-or-less eliminating the underlying cause of that tension. — Aaron R
I had the idea that the reason why Christianity engenders (which I prefer to 'secretes') atheism, is because of the compulsory nature of belief that it requires. Right from the outset of the early Church Councils, which thrashed out the Nicene Creed and the other articles, there was an emphasis on what belief is required of the professing Christian. 'Heresy' is derived from the greek word for 'choosing' or 'making a choice', the implication being that it is wrong to even have a view about what one ought to believe. As is well-known, the suppression or persecution of heresies gave rise to many of the darkest chapters in Christian history (not least the destruction of the Cathars). — Wayfarer
