If something is an abstract illusion, then by definition it is not a reality. — aletheist
Where have I ever said anything about "what is natural and an illusion"? I have consistently been discussing the distinction between existence and reality.@Relativist and myself are confused with your philosophy regarding what is natural and an illusion. — 3017amen
Where have I ever denied laws of nature? On the contrary, I have explicitly affirmed them, but suggested that they are not strictly exceptionless due to the reality of absolute chance.You are contradicting yourself when you say Pierce recognizes the laws of nature but when we talk about physics you are denying such phenomena. — 3017amen
I keep asking you to provide a succinct summary of the specific paradox that you have in mind, and you keep failing to do so.You also seem to be denying the paradox between what's reality and illusion — 3017amen
No, either time is a reality or time is an illusion. I hold that time is a reality, and you apparently hold that time is an illusion; so there is no paradox, we simply disagree.The reality of time is just an illusion. And therein lies your paradox. — 3017amen
Since I do value the conversation, I went ahead and watched the video more carefully, this time typing up a transcription so that I could study what was said and provide my own summary.If you care to continue the discussion, let's start with this basic understanding regarding time as an illusion, and you tell me what is wrong with this paradox(s): — 3017amen
Abstractions do not exist (not in the real world), they are mental devices that we create via The Way of Abstraction. They reflect types of objects that share some common properties. For example, the abstract object triangle does not actually exist (not in the real world) but triangular objects exist - they are instantiations of the abstraction.
Numbers are abstractions, some of which are instantiated in the real world.
I was referring to that fact that infinity is not a number that is mapped to. That fact doesn't entail an upper bound.As far as we can see integer numbers are instantiated or mapped to the real world, how do you find it reasonable to assume this relation abruptly stops above some very large number or below number one? — Zelebg
I was referring to that fact that infinity is not a number that is mapped to. That fact doesn't entail an upper bound.
Indeed the Way of Abstraction is grounded in the real world: first order abstractions are mental creations formed by considering several similar (actually existing objects) and omitting all features except for those held in common. Second order abstractions are formed by extrapolating from first order abstractions - they are abstractions of abstractions, and these are not grounded in existing objects (unless they can also be formed in first-order fashion).While it is true that abstract concepts only exist in minds as mental entities, minds themselves have no other source of information than the actuality of the external world, so they are all ultimately grounded or abstracted from the real world and are really only extrapolations and variations on the theme provided by the universe itself. — Zelebg
Setting aside the question of what quailia are, colors are first order - we consider objects that are red, and abstract redness from the memory of those perceptions. The geometrical figure "line" is second order - we may envision a drawing of a line on a page, which is imperfectly straight, and 3-dimensional, and imagine its ideal form as one dimensional. A similar process with 2 dimensional objects.I’m not sure if that article makes one interesting distinction about the abstraction algorithm called “visual perception”. There are colors, clearly an abstraction of who knows what order, but then, there are lines and shapes, and countable discrete things, not quite abstracted, but rather mapped kind of directly. — Zelebg
And yet, if space is finite, it's contents are finite - which would entail some upper bound. Current physics indicates that space, and its contents, extends in space through a temporal process (described here). This means the extent can only be unbounded if the past is unbounded (which the article also states). — Relativist
As for your conceptual anti-infinitist argument, this is an old and surprisingly persistent confusion. Quentin Smith had a nice analysis of this and several other such arguments in a 1987 paper Infinity and the Past.
Physics will never be able to prove the past is infinite, all it can possibly do is to show that no past boundary of time has been found.The article says quite clearly, and more than once, that we don't know whether the universe is spatially finite or infinite. We can estimate a lower bound on its size, but not an upper bound. The simplest topology consistent with our observations at large scales is an infinite, flat space; this is what the most common current cosmological model posits (so-called FLRW model). However, there are also closed topologies that are consistent with the same observations. — SophistiCat
Thanks for the article. I'd seen it a few years ago, but forgot about it. However, it does not address my argument.As for your conceptual anti-infinitist argument, this is an old and surprisingly persistent confusion. Quentin Smith had a nice analysis of this and several other such arguments in a 1987 paper Infinity and the Past.
If one apple exists on a table there is one apple. If zero apples exist on a table there are zero apples. zero exists. — christian2017
I'm not insisting that only physical objects have existence - I'm open to other possibilities, but I suggest we should be parsimonious in our assumptions of what actually exists in the world. I'd be fine accepting the existence of angels and devils despite being immaterial, if their existence is needed to explain some aspect of the world. I accept the existence of mental objects (exactly what they are depends on what the nature of mind is). On the other hand, abstract objects (all of them, not just infinity and zero) ostensibly exist independently of minds. Where are they? Why include them an an ontology? They aren't causally efficacious, and they can be accounted for without assuming they are components of the world. We need to treat them as existing when doing math, but this utility doesn't force us to treat them as actual, independent components of the world. Math works just fine even if they're just useful fictions.It depends on what you mean by exist doesn't it? From what I gather existence to you has to be physical - tangible and perceivable through the senses. Existence so defined implies nothing of the mind, let alone numbers, exists. The onus then is on you to show us why you're specifically concerned about infinity and zero. What about their nonexistence is nontrivial? — TheMadFool
I'm not insisting that only physical objects have existence - I'm open to other possibilities, but I suggest we should be parsimonious in our assumptions of what actually exists in the world. I'd be fine accepting the existence of angels and devils despite being immaterial, if their existence is needed to explain some aspect of the world. I accept the existence of mental objects (exactly what they are depends on what the nature of mind is). On the other hand, abstract objects (all of them, not just infinity and zero) ostensibly exist independently of minds. Where are they? Why include them an an ontology? They aren't causally efficacious, and they can be accounted for without assuming they are components of the world. We need to treat them as existing when doing math, but this utility doesn't force us to treat them as actual, independent components of the world. Math works just fine even if they're just useful fictions. — Relativist
The abstraction "triangle" that exists in your brain is spatially located in your brain, so it is not the identical object located in my brain. — Relativist
Abstractions do not exist (not in the real world).... — Relativist
Only in your mind, because you're considering the possible presence of apples on the table. Suppose there were oranges and bananas on the table. The negative fact (there are no apples on the table) provides no information about what DOES exist on the table.
There are no more truths than those entailed by the conjunction of all positive truths, so negative truths are redundant. — Relativist
You have described an uncomp!etable task,not an existent.Infinity exists for the simple reason that if you were to task me to write down all the natural numbers then that would be an instantiation of infinity in the real world. — TheMadFool
Negative facts do not establish what exists.If I had 5 pennies in my wallet and I gave you all of them then my empty wallet is a real-world instantiation of zero. — TheMadFool
As I see it, the concrete precedes the abstract, the latter being derived from the former. Doesn't it follow then that "all" abstract objects will invariably be instantiated in a concrete object? — TheMadFool
We can abstractly consider geometrical objects of 4 or more dimensions. That doesn't imply such things exist in the world.As I see it, the concrete precedes the abstract, the latter being derived from the former. Doesn't it follow then that "all" abstract objects will invariably be instantiated in a concrete object? — TheMadFool
Infinity exists for the simple reason that if you were to task me to write down all the natural numbers then that would be an instantiation of infinity in the real world.
Each TV has its own set of pixel producing devices, and while you and I may perceive nearly identical images, the images in my brain are in MY brain, not yours.The abstraction "triangle" that exists in your brain is spatially located in your brain, so it is not the identical object located in my brain.
— Relativist
It is no more ‘located in the brain’ than actors are located inside televisions. Rather a rational mind is able to recognize such concepts which however are not dependent on being recognized in order to be real. — Wayfarer
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