Philosophy Now Forum

a. There is a totality of things.
b. This totality is one.
c. This one totality is without comparison, as it is everything, thus is indefinite.
d. This indefiniteness is the same as nothing, as there is no contrast, therefore 0.
e. 1=0 and A=-A.

Eodinhoj7, have you ever considered taking a Philosophy 101 course?

alan1000 wrote: ↑Sat May 14, 2022 1:20 pm XXX, have you ever considered taking a Philosophy 101 course?

No school of philosophy has been able to convince me that I would be getting my money; or my time's worth attending it.

Terrible at self-promotion; or terrible at persuasion. Either way - it reflects poorly.

Right. We obviously have a great deal of spadework in front of us. Please begin by outlining the set of axioms by which you advance your own arithmetical arguments. If you deny that formal axioms are necessary or appropriate, please supply arguments to support this position.

alan1000 wrote: ↑Sat May 14, 2022 1:59 pm Right. We obviously have a great deal of spadework in front of us. Please begin by outlining the set of axioms by which you advance your own arithmetical arguments. If you deny that formal axioms are necessary or appropriate, please supply arguments to support this position.

This request is a non-starter.

By what set of axioms do you determine whether any given argument supports; or doesn't support any position?
I wish to offer no argument whatsoever. I only wish to point to the field of reverse mathematics.

Perhaps, I shall even agree with Bertrand Russel who points out that the predicate 1+1=2 is sometimes useful; and expand upon his observation to point out that sometimes the predicate 1+1=1 is useful too.

Eodnhoj7 wrote: ↑Thu May 12, 2022 6:49 pm a. There is a totality of things.
b. This totality is one.
c. This one totality is without comparison, as it is everything, thus is indefinite.
d. This indefiniteness is the same as nothing, as there is no contrast, therefore 0.
e. 1=0 and A=-A.

NO.

It trascend the comparision, because it is the max homogeneus.

Is different to trascend the comparision because it is nothing.

CHNOPS wrote: ↑Sat May 14, 2022 9:31 pm

Eodnhoj7 wrote: ↑Thu May 12, 2022 6:49 pm a. There is a totality of things.
b. This totality is one.
c. This one totality is without comparison, as it is everything, thus is indefinite.
d. This indefiniteness is the same as nothing, as there is no contrast, therefore 0.
e. 1=0 and A=-A.

NO.

It trascend the comparision, because it is the max homogeneus.

Is different to trascend the comparision because it is nothing.

Listen to what you are saying....


If it, the totality, transcends the comparison then 1 and 0 do not compare and are thus equal as the comparison necessitates non-equality because of differences, an absence of comparison (thus difference) is equality. To transcend above comparison is to transcend beyond being thus resulting in nothing as there is only being; being transcending being is being as nothing.

alan1000 wrote: ↑Sat May 14, 2022 1:20 pm Eodinhoj7, have you ever considered taking a Philosophy 101 course?

Already did and level 400+...got A's in the ones I studied for, B's in the ones I didn't. Maybe you should be a bit more philosophical and question the axioms you blindly accept.

alan1000 wrote: ↑Sat May 14, 2022 1:59 pm Right. We obviously have a great deal of spadework in front of us. Please begin by outlining the set of axioms by which you advance your own arithmetical arguments. If you deny that formal axioms are necessary or appropriate, please supply arguments to support this position.

And what axioms are you postulating in determining which axioms are correct and which are not, which arguments are correct and which are not? You need axioms to justify axioms and this leaves "the axiom" as self-referential thus indefinite. You have no foot to stand on.

In quantifying "the totality" I already listed my axioms; numbers are inseparable from that which they point to as this act of pointing is a connection.

Eodnhoj7 wrote: ↑Wed May 18, 2022 11:42 pm

CHNOPS wrote: ↑Sat May 14, 2022 9:31 pm

Eodnhoj7 wrote: ↑Thu May 12, 2022 6:49 pm a. There is a totality of things.
b. This totality is one.
c. This one totality is without comparison, as it is everything, thus is indefinite.
d. This indefiniteness is the same as nothing, as there is no contrast, therefore 0.
e. 1=0 and A=-A.

NO.

It trascend the comparision, because it is the max homogeneus.

Is different to trascend the comparision because it is nothing.

Listen to what you are saying....


If it, the totality, transcends the comparison then 1 and 0 do not compare and are thus equal as the comparison necessitates non-equality because of differences, an absence of comparison (thus difference) is equality. To transcend above comparison is to transcend beyond being thus resulting in nothing as there is only being; being transcending being is being as nothing.

Is just the limit of knowledge, but I think you dont understand it, so, I say the contradition to trying to go beyond duality.

Some budists says that the Self is "empty". But how could you be "empty" when you are everything? and when you are being....

Eodnhoj7 wrote: ↑Thu May 12, 2022 6:49 pm a. There is a totality of things.

The proposition in math that comes closest to affirming a thing like that, is the axiom of infinity: the fully inducted set of natural numbers somehow exists.

The set of natural numbers is not considered a final totality.

According to the generalized continuum hypothesis, there would be a sequence of set cardinalities, where the next set is the power set of the previous one. It would just keep going on.

The idea is that there is no "totality of things" because such purported totality always belongs to a larger power set.

godelian wrote: ↑Wed May 25, 2022 2:40 am

According to the generalized continuum hypothesis, there would be a sequence of set cardinalities, where the next set is the power set of the previous one. It would just keep going on.

GCH is not needed. Cantor's theorem shows that there's an endless hierarchy of powersets, each with strictly larger cardinality than the previous. That's a theorem of ZF, don't even need the axiom of choice.

GCH says that 2^(Aleph_k) = Aleph_(k+1) for each k; that is, that the cardinality we get by taking each powerset is exactly the next Aleph.

In other words the cardinality of the natural numbers is Aleph_0. Its powerset has cardinality 2^(Aleph_0). The Continuum hypothesis says that this is exactly Aleph_1, and GCH says that this continues to hold true: that the cardinality of the powerset of each Aleph is just the very next Aleph.

wtf wrote: ↑Wed May 25, 2022 2:46 am

godelian wrote: ↑Wed May 25, 2022 2:40 am

According to the generalized continuum hypothesis, there would be a sequence of set cardinalities, where the next set is the power set of the previous one. It would just keep going on.

GCH is not needed. Cantor's theorem shows that there's an endless hierarchy of powersets, each with strictly larger cardinality than the previous. That's a theorem of ZF, don't even need the axiom of choice.

Yes, agreed.

I had never run into Cantor's theorem. Since I was aware of GCH, I thought that it was also the source of the infinite power set hierarchy. Thanks for pointing out that Cantor's theorem is sufficient for this purpose.

CHNOPS wrote: ↑Wed May 25, 2022 2:01 am

Eodnhoj7 wrote: ↑Wed May 18, 2022 11:42 pm

CHNOPS wrote: ↑Sat May 14, 2022 9:31 pm

NO.

It trascend the comparision, because it is the max homogeneus.

Is different to trascend the comparision because it is nothing.

Listen to what you are saying....


If it, the totality, transcends the comparison then 1 and 0 do not compare and are thus equal as the comparison necessitates non-equality because of differences, an absence of comparison (thus difference) is equality. To transcend above comparison is to transcend beyond being thus resulting in nothing as there is only being; being transcending being is being as nothing.

Is just the limit of knowledge, but I think you dont understand it, so, I say the contradition to trying to go beyond duality.

Some budists says that the Self is "empty". But how could you be "empty" when you are everything? and when you are being....

Everything is without comparison as there is only everything. As absent of comparison it is empty of definition. Definition requires distinction, distinction requires opposition thus contradiction. To be absent of definition is to be absent of contradiction thus contradiction self-negates. This self-negation is a further contradiction as the contradiction of contradiction.

godelian wrote: ↑Wed May 25, 2022 2:40 am

Eodnhoj7 wrote: ↑Thu May 12, 2022 6:49 pm a. There is a totality of things.

The proposition in math that comes closest to affirming a thing like that, is the axiom of infinity: the fully inducted set of natural numbers somehow exists.

The set of natural numbers is not considered a final totality.

According to the generalized continuum hypothesis, there would be a sequence of set cardinalities, where the next set is the power set of the previous one. It would just keep going on.

The idea is that there is no "totality of things" because such purported totality always belongs to a larger power set.

The totality belong to another totality then another totality is to make the phenomenon of "totality" ever-present thus there is a singular totality. Infinite regress/progress is a phenomenon existing in a continuous state thus unchanging.


An example of the above:

1. There is 1 line.
2. This line reduces to 2 lines.
3. Each line reduces to a further 2 lines.
4. So on and so forth.
5. The line is continuous as it is only measurable against itself.
6. The line relative to another line is just the line.

Dually this continuity requires time and space. The totality is above time and space as it contains time and space; one potentiality is a relative actuality from another time/space position, the totality is all that is, was or ever will be thus no regress or progress result.