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This is the principle used in classical mathematics that is created by presuming the Law of the Excluded Middle. Whatever does not lead into contradiction must already exist, and can be used as needed. Its existence does not need to be further defended or derived in any way.

The primary use is to let us generalize more freely about things that we cannot enumerate or identify, so we can imagine what kinds of combinations those imaginary things might participate in. We can imagine different configurations of infinities or spaces by starting from what they would have to be like if they existed, without feeling silly about it, because we have already decided that they exist.

This is very convenient -- until it isn't. It leads directly into traps like Russell's paradox and other confusing aspects of negation. Does 'nothing' exist.? Well, it must, unless that would be impossible, and the impossibility seems unlikely. But what is it like? This, this absolute nothing.? It verily seeths with internal contradictions, and we would like to be rid of it, except we have accepted that whatever is not impossible is already real.

Lifting this principle from Platonic mathematics and transplanting it into other kinds of philosophy has the same effect. It broadens our horizon, but threatens to confuse us.

This is the principle used in classical mathematics that is created by presuming the Law of the Excluded Middle. Whatever does not lead into contradiction must already exist, and can be used as needed. Its existence does not need to be further defended or derived in any way.

The primary use is to let us generalize more freely about things that we cannot enumerate or identify, so we can imagine what kinds of combinations those imaginary things might participate in. We can imagine different configurations of infinities or spaces by starting from what they would have to be like if they existed, without feeling silly about it, because we have already decided that they exist.

This is very convenient -- until it isn't. It leads directly into traps like Russell's paradox and other confusing aspects of negation. Does 'nothing' exist. Well, it must, unless that would be impossible. But what is it like? This absolute nothing. It verily seeths with internal contradictions, and we would like to be rid of it, except we have accepted that whatever is not impossible is already real.

Lifting this principle from Platonic mathematics and transplanting it into other kinds of philosophy has the same effect. It broadens our horizon, but threatens to confuse us.

This is the principle used in classical mathematics that is created by presuming the Law of the Excluded Middle. Whatever does not lead into contradiction must already exist, and can be used as needed. Its existence does not need to be further defended or derived in any way.

The primary use is to let us generalize more freely about things that we cannot enumerate or identify, so we can imagine what kinds of combinations those imaginary things might participate in. We can imagine different configurations of infinities or spaces by starting from what they would have to be like if they existed, without feeling silly about it, because we have already decided that they exist.

This is very convenient -- until it isn't. It leads directly into traps like Russell's paradox and other confusing aspects of negation. Does 'nothing' exist? Well, it must, unless that would be impossible, and the impossibility seems unlikely. But what is it like, this absolute nothing? It verily seeths with internal contradictions, and we would like to be rid of it, except we have accepted that whatever is not impossible is already real.

Lifting this principle from Platonic mathematics and transplanting it into other kinds of philosophy has the same effect. It broadens our horizon, but threatens to confuse us.

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source | link

This is the principle used in classical mathematics that is created by presuming the Law of the Excluded Middle. Whatever does not lead into contradiction must already exist, and can be used as needed. Its existence does not need to be further defended or derived in any way.

The primary use is to let us generalize more freely about things that we cannot enumerate or identify, so we can imagine what kinds of combinations those imaginary things might participate in. We can imagine different configurations of infinities or spaces by starting from what they would have to be like if they existed, without feeling silly about it, because we have already decided that they exist.

This is very convenient -- until it isn't. It leads directly into traps like Russell's paradox and other confusing aspects of negation. Does 'nothing' exist. Well, it must, unless that would be impossible. But what is it like? This absolute nothing. It verily seeths with internal contradictions, and we would like to be rid of it, except we have accepted that whatever is not impossible is already real.

Lifting this principle from Platonic mathematics and transplanting it into other kinds of philosophy has the same effect. It broadens our horizon, but threatens to confuse us.