A paradox is something that is neither true nor false. e.g. This is false. If that statement were false then it must be true.
If it were true then it must be false. Both ways around it contradicts itself. It is neither true nor false it is in fact the
simplest paradox.
Mathematicians know Russell's paradox means you cannot have a Universal set of everything in mathematics. Otherwise it causes paradoxes.
According to naive set theory, any definable collection is a set.
Let R be the set of all sets that are not members of themselves.
If R is not a member of itself, then its definition dictates that it must contain itself.
If it contains itself, then it contradicts its own definition and so cannot be contained in the set R.
This means the set R is invalid in mathematics, which as a search for consistent truth excludes paradoxes. This is why mathematicians use a more complicated definition of sets called ZFC set theory which includes the axiom of choice. This theory enforces the exclusion of paradoxes and in the process excludes the Universal set that is the naive set U that contains everything, even itself
Mathematics restricts itself to all the self consistent beliefs to provide some very useful tools such as counting and fractions and percentages that can be relied on to give consistent results every time.
So the Universal set is quite correctly excluded from mathematics because if mathematics allowed paradoxes it would not be at all useful in science or accounting or the running of our daily lives.
From a philosophical point of view it is hardly surprising that the Universal set includes paradoxes, because the naive set of everything that exists has to include paradoxes because paradoxes exist. Paradoxes are just as real as numbers and as easily logically defined.
However, both mathematics and philosophy are based in words. Words do include paradoxes and Russell's Paradox as a part of the naive philosphical Universal set which is a philosophical not mathematical concept.
The Universal set may not be useful in mathematics but it is useful in finding an abstract definition of God.
The Universal set Contains everything so it is omnipresent.
The Universal set Contains all knowledge so it is omniscient.
The Universal set contains all possible outcomes even the ones we might call fictional or paradoxical. So it is omnipotent.
The Universal set Contains the creation of time and the whole of time until beyond the end of the Universe. So it is eternal.
The Universal set Contains the foundation of the Universe and can be called the foundation of everything if not the creator.
The Universal set contains all life and so it is alive in the same way a city is alive or a snail with hard lifeless shell and lively hiddden body. If you take extremes as Issac Asimov did it leads to Gaia, Galaxia and on a much bigger scale the whole of existent abstract and physical being alive.
The Universal set is a paradox. Paradoxes are based in words not numbers. Words are symbols used to share meaning.
Words are only useful if you have some knowledge and know some one to share it with.
Lying is abusing the symbols to not share meaning. This effectively stops lies from being words.
The fact that the Universal set shares meanings implies that it is by and large benevelont. However be aware of the anger of God if you know of his word and do not respect it, the Bible repeats over and over the stories of various kings and cultures that have died and disappeared because they did not fear God.
Yet another paradox of the God of Love. If you love him and let him lead you in life you find love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness and self-control. These can help you even through illness, imprisonment torture and death. It is inside you, mind and soul.
The Universal set is a paradox. It shares the meaning that the Universal set cannot be contained by mathematics.
The Universal set also defines all the primordial features of God. It is omnipresent, omniscient, the creator, eternal, omnipotent, it is alive.
On the positive side of this This does have an effect on the laws on Thermodynamics. As we can build sand castles so may God. It may be that he just has not yet or we have not recognised them as his work. Although that is one of the promises of the second coming. We get to live in heaven or hell for all eternity.
Mathematicians know Russell's paradox means you cannot have a Universal set of everything in mathematics. Otherwise it causes paradoxes.
According to naive set theory, any definable collection is a set.
Let R be the set of all sets that are not members of themselves.
If R is not a member of itself, then its definition dictates that it must contain itself.
If it contains itself, then it contradicts its own definition and so cannot be contained in the set R.
This means the set R is invalid in mathematics, which as a search for consistent truth excludes paradoxes. This is why mathematicians use a more complicated definition of sets called ZFC set theory which includes the axiom of choice. This theory enforces the exclusion of paradoxes and in the process excludes the Universal set that is the naive set U that contains everything, even itself
Mathematics restricts itself to all the self consistent beliefs to provide some very useful tools such as counting and fractions and percentages that can be relied on to give consistent results every time.
So the Universal set is quite correctly excluded from mathematics because if mathematics allowed paradoxes it would not be at all useful in science or accounting or the running of our daily lives.
From a philosophical point of view it is hardly surprising that the Universal set includes paradoxes, because the naive set of everything that exists has to include paradoxes because paradoxes exist. Paradoxes are just as real as numbers and as easily logically defined.
However, both mathematics and philosophy are based in words. Words do include paradoxes and Russell's Paradox as a part of the naive philosphical Universal set which is a philosophical not mathematical concept.
The Universal set may not be useful in mathematics but it is useful in finding an abstract definition of God.
The Universal set Contains everything so it is omnipresent.
The Universal set Contains all knowledge so it is omniscient.
The Universal set contains all possible outcomes even the ones we might call fictional or paradoxical. So it is omnipotent.
The Universal set Contains the creation of time and the whole of time until beyond the end of the Universe. So it is eternal.
The Universal set Contains the foundation of the Universe and can be called the foundation of everything if not the creator.
The Universal set contains all life and so it is alive in the same way a city is alive or a snail with hard lifeless shell and lively hiddden body. If you take extremes as Issac Asimov did it leads to Gaia, Galaxia and on a much bigger scale the whole of existent abstract and physical being alive.
The Universal set is a paradox. Paradoxes are based in words not numbers. Words are symbols used to share meaning.
Words are only useful if you have some knowledge and know some one to share it with.
Lying is abusing the symbols to not share meaning. This effectively stops lies from being words.
The fact that the Universal set shares meanings implies that it is by and large benevelont. However be aware of the anger of God if you know of his word and do not respect it, the Bible repeats over and over the stories of various kings and cultures that have died and disappeared because they did not fear God.
Yet another paradox of the God of Love. If you love him and let him lead you in life you find love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness and self-control. These can help you even through illness, imprisonment torture and death. It is inside you, mind and soul.
The Universal set is a paradox. It shares the meaning that the Universal set cannot be contained by mathematics.
The Universal set also defines all the primordial features of God. It is omnipresent, omniscient, the creator, eternal, omnipotent, it is alive.
On the positive side of this This does have an effect on the laws on Thermodynamics. As we can build sand castles so may God. It may be that he just has not yet or we have not recognised them as his work. Although that is one of the promises of the second coming. We get to live in heaven or hell for all eternity.