Abstract Objects
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Posted 12/12/12
Every entity, it is evident, falls into that which is abstract, and that which is concrete. Abstract objects are those that, like the concept of 'one' or Milton's Paradise Lost, which can be distinguished from the concrete, one apple or a copy of Paradise Lost, one can be seen as an 'idea' and the other as 'substance'. Yet, do these abstract object actually exist beyond the purely intellectual and noetic sense that they exist within our mind as an invention of our mind? Concrete objects, obviously, physically exist, for example, there is such thing as a tennis ball, a knife, a bed, a copy of a certain book, etc. Yet, the question must then be asked, does the idea of 'ball' exist independent of the human mind, does the idea of 'knife', of 'bed', or of 'book'- any non-spatial and non-temporal objects. On the one hand, one can say something like '3 is a prime number' as a matter of fact, as we can say of concrete objects, 'the moon is round', and it seems independent of what we think or would think, as some of the things in mathematics which does follow deductively do seem counter-intuitive, but, on the other hand, it would also seem as if the way we define of '3', 'prime number', multiplication, and other factors seem to create '3' into a 'prime number' by definitions.
wyrvan 
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Posted 12/14/12

longfenglim wrote:


Rakuin wrote:

We created designations for invented objects and otherwise, though I don't see the concept of each existing outside the human mind in a way that makes them have bearing on reality as universally acceptable by any/all minds. Numeric understanding seems simpler when processed by living things besides humans. A dog intent on fighting should know that it had best not take on several other dogs alone, and a wasp instinctively knows how many sides the polygons of their nests have.

There is an exact system to how everything works. We can be sure of that. I would say that abstract objects have no concrete existence, yet I can see the minimum of concrete explanations for what the abstract objects are. This doesn't really make abstract objects concrete.


Let's return to the example of Mathematics- we can demonstrate that, despite 3 is an abstract concept, we can clearly count that there are three apples, or that the universe does, at times, seem to confirm the Pythagorean Hypothesis, in that there seem to be a sort of mathematical ordering- we can use certain integral and derivative function, at the basic level, to calculate to a great degree of accuracy how certain things will behave, and, at higher levels of Physics, there is much more mathematics involved. These, it seems, points to a existence of Mathematics independent of our mind, and existing within the universe.


It might be useful to divide the abstract into two groups: Those that appear to be part of the function of the physical universe (mathematics, physcal laws) and those that seem to only be part of the mind (emotions, philosophy, politics).

Mathematics appears to be an abstract concept but one that is underpinning the concrete physical world. So abstract concepts in the first group might be more like an OS (operating system) for the universe (something that exists but that we cannot see or touch). Any idea that can be physically made would also be in the first group because they are based on principles already hardwired into the universe.

The second group is composed entirely of abstract concepts that only appear in the mind and not independently in nature. With out the mind they cannot exist.
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Posted 12/15/12 , edited 12/15/12

Rakuin wrote:


longfenglim wrote:


Rakuin wrote:

We created designations for invented objects and otherwise, though I don't see the concept of each existing outside the human mind in a way that makes them have bearing on reality as universally acceptable by any/all minds. Numeric understanding seems simpler when processed by living things besides humans. A dog intent on fighting should know that it had best not take on several other dogs alone, and a wasp instinctively knows how many sides the polygons of their nests have.

There is an exact system to how everything works. We can be sure of that. I would say that abstract objects have no concrete existence, yet I can see the minimum of concrete explanations for what the abstract objects are. This doesn't really make abstract objects concrete.


Let's return to the example of Mathematics- we can demonstrate that, despite 3 is an abstract concept, we can clearly count that there are three apples, or that the universe does, at times, seem to confirm the Pythagorean Hypothesis, in that there seem to be a sort of mathematical ordering- we can use certain integral and derivative function, at the basic level, to calculate to a great degree of accuracy how certain things will behave, and, at higher levels of Physics, there is much more mathematics involved. These, it seems, points to a existence of Mathematics independent of our mind, and existing within the universe.


Goes deep when we think of the precise amount of objects making up one object, and how it is likely not exactly the same. Molecules of the example apple, molecules made of atoms, atoms made of nucleus, protons, electrons, and photons. The atoms have their own exact characteristics due to different elements.

It's almost convincing that there may be the truth of grand design substantiating all things as concrete. If we could think of it, so could an entity in the form an omniscient deity. The will of the deity exercised as a power over existence making all things concrete in nature. Still, there has been no physical evidence supporting the existence of deities, making them plausibly abstract objects, so we are best off searching for other lifeforms with mental capacities like our own. Those also remaining abstract until proven to exist from the human perspective.

If we look at the definition of what an object is, then maybe everything is concrete. Thought processes are chemical reactions and electricity, so there is the substantiated physical evidence rendering the concept of all objects as concrete. If it can be perceptible by senses, it is, by definition, concrete, as thinking has its own perceptible experience.



While the universe may be mathematically structured, it does not follow that there exist a deity, I don't think, because a deity presupposed intentional design, which should be differentiated from structure, which seems to be the case of the relationship between the universe and mathematics. I think an example of this would be Natural Selection- there is no need for intentional design in Natural Selection (unless you take the Catholic Church's view of 'Guided Natural Selection') in these natural processes do not seem to work to a grand purpose, the Neanderthals didn't die out because of some pre-designed plan or some divine ordination, nor did Mammal return to the sea because a higher order of being commands it to, so that there may be whales and dolphins. There is however, a structure which governs all this- that whose characteristics, born from mutations of genes, is most adapted to an environment are more likely to survive to pass on its genes to the next generation, whilst those that do not have such favourable characteristics are less likely to survive and do the same.

So, if the universe is mathematically structured, we do not necessarily have to say that it is mathematically designed, as design implies a intentionality not found in structure. Thus, if it is mathematically structured, we can think of the concept of maths as 'existing' beyond the concrete and 'structuring' the same.

Finally, while I agree broadly that, in a sense, thoughts can be considered physical, in the sense that the working of the mind are made of physical processes, I disagree that that would make them concrete, in that what I think must have some existence beyond me to exist, just as a ball, though I perceive it with my senses, exist beyond me physically. For abstract objects to have existence, it should, I think, be a thing beyond the human mind.
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Posted 12/17/12 , edited 12/17/12
At the risk of sounding inarticulate;

Going back the OS example. A PC would have a hard-drive or other physical storage in which the OS resides. We created it, therefore we have means to measure its size and identify every byte's purpose. It exists as bumps etched on by the reading arm inside the enclosure (that is how hdd tech works right? It's late.). Does a file not exist? A better example, an audio CD. A music track can skip or struggle to play when there is wear physically located on a specific part of the disk.

My point being, we still lack the means to properly measure human thought. We yet don't fully understand how our brains function Although i argue that to be frightening knowledge for us to possess. We may not have to means to find the location of specific thoughts, but they are very much contained within our heads.

My point is best simplified with a question. Does a proton exist?


But the harp back on the mathematics abstraction thing, do you not know of Pi? Irrational numbers? How do you measure infinite?

*edit for mi bad grammarz*
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Posted 12/18/12

wyrvan wrote:


Both actually.

Mathematics is a creation of the human mind is describe and represent an underlying aspect of the universe. But the universe appears to be mathematically structured (both before and after the existence of humans), so something exists separate from mathematics but appears to mathematical.

The problem is that language is an abstract concept itself depenedent on the human mind. That means we have to use a human mind abstract to describe a universal abstract.

So, mathematics is a human mind language description abstract AND an independent universal abstract. But it can be used as a tool to better understand the concrete universe. To do this it has to use both abstracts together. So that means mathematics has a third abstract state between the two.

(Did I just argue that mathematics as an abstract is in a quantum state? I think I feel a headache coming on.)



I don't quite follow- so mathematics exist independently of the human mind, but the language and the way we express mathematics and mathematical formulas are human inventions?
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