Jun 11, 2012 -- 2:26PM, Jiwe wrote:

Jun 11, 2012 -- 2:04PM, Qwesam wrote:

Jun 11, 2012 -- 1:50PM, Jiwe wrote:

Jun 11, 2012 -- 1:39PM, Qwesam wrote:

Jun 11, 2012 -- 1:31PM, Jiwe wrote:

Jun 11, 2012 -- 10:26AM, Blü wrote:

Adelphe

p=(x,y,z)

Now please derive x=p from that, showing us all the steps.

I'll do it. Suppose that God is numerically identical to the father, the son and the holy ghost taken collectively, that is G = (F, S, HG).

Now we suppose for a consistency check that G = F (i.e. that God = the Father). Well, then by substitution:

F = (F, S, HG) which by a trivial contraction collapses into:

F = (S, HG).

Or for purely academic interest, it expands into:

F = (G, S, HG) = ((F, S, HG), S, HG) which then trivially collapses into F = F.

So it turns out that by a simple application of plural logic, everything is consistent. I guess a Trinitarian can have her cake and eat it too.

James

What kind of Math are you using?

 

 

Plural logic.

No wonder why it is pure contradictory: www.oysteinlinnebo.org/burgess.pdf 2 The Problem of Plural Parameters Although Burgess's account motivates the axioms of set theory in a natural and elegant way, I will now give two arguments that this account also motivates the view that every plurality forms a set. In a theory such as Burgess's with an unrestricted plural comprehension scheme (P-Comp), this view leads straight to contradiction. To see this, let rr be the sets that are not elements of themselves, and let r be the set that they form. Then r is an element of itself just in case it isn't. My ¯rst argument concerns the behavior of plural parameters under the reinterpretations that Burgess uses to motivate his re°ection principle. A \reinterpretation," in the relevant sense, is just a matter of restricting quanti¯ers: the reference of parameters and the interpre- tation of predicates (that is, their satisfaction conditions) are kept ¯xed. To make this clear, I will refer to such reinterpretations as quanti¯er-reinterpretations or q-reinterpretations for short. The domain associated with any q-reinterpretation of a formula © must thus contain the referents of all parameters occurring in ©. For instance, the domain associated with any q-reinterpretation of `Socrates is mortal' must contain Socrates. Likewise, the domain asso- ciated with any q-reinterpretation of `Socrates and Plato agreed' must contain both Socrates and Plato. This means that the motivation Burgess provides for his re°ection principle (Re°) also motivates a stronger re°ection principle. For simplicity, I will only state this stronger principle for a formula © whose only parameter is uu; the general case is an obvious extension. (Re°0) 8uu[© ! 9t(uu 22 t ^ ©t] But given this re°ection principle, we can easily prove that every plurality forms a set. Let aa be an arbitrary plurality, and let © be a formula containing a plural parameter referring to aa. © can then be q-reinterpreted as being about a domain that forms a set t. But this set must contain the referents of all parameters occurring in this formula, including the plural ones|as made explicit in (Re°0). It thus follows that aa must be contained in the set t. By Separation, we then get that aa form a set. Finally, since aa were arbitrary, it follows that every plurality forms a set. I will refer to this as the Problem of Plural Parameters. I will now consider three objections to this argument. Firstly, it may be objected that even if my argument works, this just shows that the re°ection scheme must be restricted to formulas that don't contain plural parameters. The most natural such restriction would be to limit the re°ection principle to sentences, that is, to formulas containing neither singular nor plural parameters. However, the resulting re°ection principle would be too weak for Burgess's purposes, as his account uses re°ection on formulas containing singular parameters.11 Consider the proof of the axiom of Pairing that Burgess adopts from Bernays. Given any two objects a and b, we have the following logical truth

Man, how unlucky can you get! I've both studied with and worked with Oystein . What he's addressing in that paper is a formal extension of ZFC set theory (the standard set theory in which math is represented) based on plural logic rather than second order logic, and in particular certain formulas called comprehension formulas or abstraction principles. Informally they say that every formula defines a set, or in this setting that every plurality defines a set. That leads to a contradiction analogous to Russell's Paradox. The problem is with unrestricted use of these comprehension formulas - not plural logic.

Duh!

Then, try again...

Use plural Logic to prove trinity...

James

Jun 11, 2012 -- 1:00PM, Jiwe wrote:

Jun 10, 2012 -- 8:01PM, Miguel_de_servet wrote:

... As I see it, without putting in question the logical aspects, there are (at least) two weaknesses in your image.

First, when we describe tri-dimensional space, the chosen set of co-ordinates axes (x, y, z) is entirely arbitrary, so much so that the description of a point (or, more in general, any Euclidean geometrical object) in terms of (x, y, z), can be transformed in its perfectly equivalent description referred to another set of co-ordinates (u, v, w). It is totally unclear what would be equivalent —or even if at all possible— to this "change of co-ordinates" for the "trinity".

Second, it is not very clear to what the three co-ordinates of a point (or, more in general, any Euclidean geometrical object) would correspond in the case of God. [#] One thing, though, appears compellingly, from your image: far from being distinct from each other (like three persons would be, in the usual sense of the word "person"), the three "co-ordinates" of God (whatever they may be), would be like mere "projections" of the same "point" on three normal axes. The overwhelming impression that one derives from all this is that of modalism.

[#] Perhaps one may speculate fantasize (as some have done) that the three "axes of God" are "unbegottenness", "begottenness" and "procession". I am happy to leave this sort of overwrought fantasies to theologians ...

Don't take the geometry analogy to far. I never claimed isomorphism. It's just a familiar case of plural identity. 1km = 1000m is another.

First, that p = (x,y,z) [a point in the Euclideans is identical to its Cartesian co-ordinates] is same type of identity as 1km = 1000m [a distance measured in one unit is identical to the same distance measured in another unit] is at least dubious.

Second, while the former associates a tern with one ojject, the latter certainly doesn't, and is therefore totally inappropriate as an analogy for the "trinity".

Third, if p ≈ God, in what sense (x, y, z) ≈ (Father, Sone, Holy Spirit), OIOW, if the point is the analog of God, what is the analogue of its Cartesian co-ordinates?

[James] And no, it's not modalism. This solution allows that there are literally speaking three divine persons. Not three modes of being of one God.

Yours is a mere claim. 

OTOH, from your analogy, its even too obvious to draw

co-ordinates of p = projections of p along x, y, z ≈ modes of God

MdS

Jun 11, 2012 -- 3:10PM, Miguel_de_servet wrote:

First, that p = (x,y,z) [a point in the Euclideans is identical to its Cartesian co-ordinates] is same type of identity as 1km = 1000m [a distance measured in one unit is identical to the same distance measured in another unit] is at least dubious.

Second, while the former associates a tern with one ojject, the latter certainly doesn't, and is therefore totally inappropriate as an analogy for the "trinity".

Third, if p ≈ God, in what sense (x, y, z) ≈ (Father, Sone, Holy Spirit), OIOW, if the point is the analog of God, what is the analogue of its Cartesian co-ordinates?

You are spectacularly missing the...point (no pun intended.)

Yours is a mere claim. 

OTOH, from your analogy, its even too obvious to draw

co-ordinates of p = projections of p along x, y, z ≈ modes of God

MdS

Three coordinates x,y,z combine to form a point "p."

x can exist alone, y can exist alone, z can exist alone.

This doesn't result in modalism.

On the contrary.

Jun 11, 2012 -- 12:53PM, Adelphe wrote:

Jun 11, 2012 -- 12:43PM, Miguel_de_servet wrote:

... The question, here, is that there are two different and irreconcilable statements:

"YHWH is actually the SON" [Dave, #201]

"YHWH is {Father, Son, Holy Spirit}" [Adelphe, everywhere]

... why should I care that there "are two different and irreconcilable statements." 

Obviously because it means that it is precluded for Adelphe to hop from her "YHWH is {Father, Son, Holy Spirit}" to Dave's "YHWH is actually the SON": NOT ONLY they are obviously different statements, BUT, MOST OF ALL, they are incompatible, so she (the same person ...) cannot (shouldn't ...) subscribe to both.

Are you numb to the "two different and irreconcilable statements" that are de rigueur for this board--indeed any of the debate forums here?

That different people subscribe (on this and other boards) to different, even irreconcilable statements (like "the trinity is scriptural" or "the trinity is NOT scriptural" is obviously altogether different, if she can appreciate the difference ...

MdS

Jun 11, 2012 -- 3:16PM, Adelphe wrote:

Jun 11, 2012 -- 2:43PM, Qwesam wrote:

Then, try again...

Use plural Logic to prove trinity...

 

Plural logic isn't needed "to prove the Trinity."

That's already been done a long time ago here.

James has taken it a step beyond--this is just icing on that cake.

In the statement "God=Father, Son, Holy Spirit", plural logic has now demonstrated that the Father=God.

Right?

At least that it's all consistent. You can have both that God = the father, the son, the holy ghost and God = the father.