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If A=A, how does A become B?

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I am having problem with thinking how things seem to change or evolve, and I will appreciate a lot your help.

There are things that change in such a clear-cut events, that we can say they have dissapeared and another thing has emerged from a rearrangement of the "parent" thing's elements.

For example, if A = a protein, we can imaging that protein breaking down into many aminoacids by the action of a digestive enzyme.

In that moment, A (our protein) ceases to exist, and B, C, D, E, F... etc. which are the aminoacids, begin to exist.

Or was it that A was just a concept encompassing B, C, D, E, F... etc but A never existed as an object?

In cases of less well defined, slow transformations, like a rock becoming sand, what is what happened?

If A= a rock, and B= sand, did A become B? Or did A disappeared and B appeared out of its elements? And when could we say that A ceased to exist and B appeared?

If the difference in A and B is only difference of attributes, then, wouldn't we conclude that all objects in the universe be just one single object, manifested in different "clusters" of matter and attributes? What if the clouds, and stones and men and man-made objects are just like the ears, tail and legs of a single elephant (i.e. the universe)?

When we say A = A do we actually mean: "existence is existence", "the universe is the universe", or are we meaning "a chair is a chair", or even more, "that chair is that chair"? Or are we saying all of the above?

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A is A, is the proper expression for the Law of Identity. It states that a thing is itself.

A = A is a mathematical expression, and has no relevance to the philosophy of O'ism.

Didn't Ayn Rand once say that in the future, someone could expand upon ideas in Objectivism by applying her methods to the philosophy of mathematics?

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In that moment, A (our protein) ceases to exist, and B, C, D, E, F... etc. which are the aminoacids, begin to exist.

Or was it that A was just a concept encompassing B, C, D, E, F... etc but A never existed as an object?

A did exist as a real object. A's metaphysical nature is quite complex (thank god we're not talking about much more complex things like fish), so that you can say that the potential for B C D E F exists as part of that nature. Since I don't know how proteins are digested, I'll substitute beer ingredients where I think I know more about what goes on. An amylose molecule with 1000 glucose units can be attacked by alpha amylase and break a random 1-4 link, so that one physical object becomes two different physical objects. This can result in two much shorter-length polysaccharides, or a marginally-shorter polysaccharide and a molecule of maltose (or glucose). Thus maltose potentially exists within an amylose molecule; the amylose molecule actually exists (at an initial time).

At each stage, the "input" molecule has a definite nature, and the output molecules have definite natures. The concept "amylose" includes very many physical types (branchings and numbers of glucose units); "maltose" is much more specific, as is "glucose". These latter two concepts are extremely important (maltose and glucose are very different from each other and everything else whereas a G1000 amylose molecule is functionally like a G1001 amylose molecule.

I think the only difference of substance from sand-creation is that the breakdown of a rock is so slow that it's way beyond human detection, and also more of the intermediate stages do correspond to distinct concepts, viz 'rock', 'cobble', 'granule', 'pebble', 'sand', 'silt'. There are scientific criteria for classifying something as 'sand', and these correspond to ordinary language meaning (i.e. you wouldn't classify something the size of an aspirin as 'sand'). The scientific criteria are derived from a physical fact -- go to a beach and grab some naturally-occurring sand to determine how big "sand" is.

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You can consider that both letters attempt to represent the same thing. Consider "A" as two lines diverging from a specific point of origin, with a division in the center representing the absolutism of their divergence. Contrary to this, the lines would not go "forever" out into space but eventually the angle would become so great that they would circle back around and intersect. So "B" represents that principle with a line permanently dividing two circles at their threshold of being at the angle that would otherwise be leading them back to intersection (180 degrees). "CD" :o

Based on the nature of the universe, you can therefore say A never becomes B. :o

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Things can change due to their nature into other things, but those other things can still be described - they have identities. For identity to be violated, you would have to say, "the protein breaks down and turns into infinity amino acids" or "the protein breaks down into fthargns" where "fthargns" have some contradictory description, as would be the case with "God".

Edited by brian0918
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A is A, is the proper expression for the Law of Identity. It states that a thing is itself.

A = A is a mathematical expression, and has no relevance to the philosophy of O'ism.

The relationship of concepts to their constituent particulars is the same as the relationship of algebraic symbols to numbers. In the equation 2a = a + a, any number may be substituted for the symbol "a" without affecting the truth of the equation. For instance: 2 X 5 = 5 + 5, or: 2 X 5,000,000 = 5,000,000 + 5,000,000. In the same manner, by the same psycho-epistemological method, a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes.

Let those who attempt to invalidate concepts by declaring that they cannot find "manness" in men, try to invalidate algebra by declaring that they cannot find "a-ness" in 5 or in 5,000,000.

Granted, it is not the equivalent to the Law of Identity - but the relationship between the proposition A is A, and the proposition that A=A: both state that A is whatever A is, epistemologically, and in mathematics which is the language which the universe is written/read.

The crux of the illustration that was being made is - there is the law of identity, and the law of causality. Invoking the law of identity - an answer was provided to a question containing the expression A=A.

Causality - reviewing my response and observing the oversighted commas to separate the thought A is A, or A=A (as stated above) . . . acted as a causal agent (identity=post 3) bringing about post 8.

Entities do act according to their nature.

Edited by dream_weaver
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A did exist as a real object. A's metaphysical nature is quite complex (thank god we're not talking about much more complex things like fish), so that you can say that the potential for B C D E F exists as part of that nature. Since I don't know how proteins are digested, I'll substitute beer ingredients where I think I know more about what goes on. An amylose molecule with 1000 glucose units can be attacked by alpha amylase and break a random 1-4 link, so that one physical object becomes two different physical objects. This can result in two much shorter-length polysaccharides, or a marginally-shorter polysaccharide and a molecule of maltose (or glucose). Thus maltose potentially exists within an amylose molecule; the amylose molecule actually exists (at an initial time).

At each stage, the "input" molecule has a definite nature, and the output molecules have definite natures. The concept "amylose" includes very many physical types (branchings and numbers of glucose units); "maltose" is much more specific, as is "glucose". These latter two concepts are extremely important (maltose and glucose are very different from each other and everything else whereas a G1000 amylose molecule is functionally like a G1001 amylose molecule.

I think the only difference of substance from sand-creation is that the breakdown of a rock is so slow that it's way beyond human detection, and also more of the intermediate stages do correspond to distinct concepts, viz 'rock', 'cobble', 'granule', 'pebble', 'sand', 'silt'. There are scientific criteria for classifying something as 'sand', and these correspond to ordinary language meaning (i.e. you wouldn't classify something the size of an aspirin as 'sand'). The scientific criteria are derived from a physical fact -- go to a beach and grab some naturally-occurring sand to determine how big "sand" is.

Thank you very much, David, and N/A as well, to help me in understanding this.

Please let me know if I understood this correctly.

When we say that A becomes B we mean that A as an actuallity dissapeared and B as an actuallity appeared. By the Law of Identity, in no moment A was B.

In the same way that amylose is a definite object that can break down in glucose units were are themselves definite objects, the stone is breaking down into smaller pieces minute after minute. However, since these slow changes are beyond human detection, we have not developed concepts for "semi-semi-semi-semi-rocks" or words for them.

The rock acts as a gigantic amylose molecule losing one molecule of glucose per minute, until years later all we have is a pile of separate glucose molecules (the sand).

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I am having problem with thinking how things seem to change or evolve, and I will appreciate a lot your help.

You are having a problem with causality because we do not live in a static universe, we live in a dynamic universe. The concept of "identity" does not say that a thing will remain what it is no matter what or that it is immutable. We live in a universe in which things change -- i.e. wood burns to ash or ice melts into water. The proper formulation of such changes is that an entity is what it is and does what it does do to the fact that it is what it is. It's really all one concept, but causation is a derivative of identity. A thing is what it is and does what it does due to the fact that it is what it is and not something else. Where you draw the line and say, the wood is burnt or the ice is melted depends on the accuracy of your measurements -- can you measure that there is still some wood there or that there is still some ice there? However, concept formation is measurement omission, so the exacting measurements of when the wood is ash or when the ice is water is not relevant to the concept -- we just note in the concept that wood burns or that ice melts. A concept includes everything about the item, so "wood" includes the possibility of burning and "ice" includes the possibility of melting. It is not as if one thing goes out of existence whereas another thing comes into existence, this is an ancient mistake, but rather that something being what it is includes its potential to change according to its nature.

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Didn't Ayn Rand once say that in the future, someone could expand upon ideas in Objectivism by applying her methods to the philosophy of mathematics?

Philosophy is certainly meant to be applied to all areas of life. :P But this does not change the fact that the verbs "is" and "equals" have different meanings.

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You are having a problem with causality because we do not live in a static universe, we live in a dynamic universe. The concept of "identity" does not say that a thing will remain what it is no matter what or that it is immutable. We live in a universe in which things change -- i.e. wood burns to ash or ice melts into water. The proper formulation of such changes is that an entity is what it is and does what it does do to the fact that it is what it is. It's really all one concept, but causation is a derivative of identity. A thing is what it is and does what it does due to the fact that it is what it is and not something else. Where you draw the line and say, the wood is burnt or the ice is melted depends on the accuracy of your measurements -- can you measure that there is still some wood there or that there is still some ice there? However, concept formation is measurement omission, so the exacting measurements of when the wood is ash or when the ice is water is not relevant to the concept -- we just note in the concept that wood burns or that ice melts. A concept includes everything about the item, so "wood" includes the possibility of burning and "ice" includes the possibility of melting. It is not as if one thing goes out of existence whereas another thing comes into existence, this is an ancient mistake, but rather that something being what it is includes its potential to change according to its nature.

Thank you very much, Thomas.

Your response is very helpful.

Is then the universe something like a single huge object, (like a single elephant) out of which we can tell separate parts (the ears, legs, belly or trunk) that we call "objects"? By calling the universe a single object, we are still recognizing that A is A.

No matter how interconnected are the ears, legs, belly or trunk of an elephant, they are what they are. They exist.

This reminds me a bit about the gnostic concept of Unity.

They say we are all oneness, and separate beings at the same time.

When I observe the universe, it is the universe observing itself through me (through my mind).

Different people see the universe slightly different, since it is the Universe seeing itself from different angles.

The fact that there are so many "angles" only confirms that reality is what it is, and that existence exists.

What do you think about this?

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Is then the universe something like a single huge object, (like a single elephant) out of which we can tell separate parts (the ears, legs, belly or trunk) that we call "objects"? By calling the universe a single object, we are still recognizing that A is A.

No matter how interconnected are the ears, legs, belly or trunk of an elephant, they are what they are. They exist.

The law of causality does not inventory the universe; it does not tell us what kinds of entities or actions are possible. It tells us only that whatever entities there are, they act in accordance with their nature, and whatever actions there are, they are performed and determined by the entity which acts.

The universe is an abstraction for everything which exists. Just as animal is an abstraction which subsumes elephants, tigers, cats and dogs. A single huge object would be any specific entity which can be isolated and identified, such as an elephant, or the empire state building, or the planet jupiter. We cannot perceive the universe in its entirety. Epistemologically, as an abstraction, we can reduce it mentally to a single huge object, yet it continues to be comprised of entities, specifically, every existent which does, has, or will exist.

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The universe is an abstraction for everything which exists.

Right. It would be a mistake to say that the universe is one (which it is) but then say that because this is true then entities do not really exist in the universe. Entities that we normally encounter, such as tables, dogs, rocks, and other entities exist qua entities. The universe being one is more of an abstraction to say that everything that exists exists; it does not render the universe as one big glob of something such that ordinary entities do not exist and are not what they are. It's better to think of the universe being one as everything is interconnected somehow, rather being really one big glob and our observations of entities is somehow an illusion.

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