If I correctly understand you, you presume:
P1. A is identical to B and vice versa.
P2. A and B are different compositions.
P3. Relative identity is invalid.

However, P1 and P2 together exemplify relative identity.

Blessings,

Jim

These things are always interesting to me. You think Walls’ lecture is “devastating” while I found it very uninformed on some important issues and underwhelming overall. How people can have such diverse reactions is a strange phenomenon, touching on psychological matters as well as epistemological.

Anyway, on the consequence argument (CA) remark:

First, re: Mackie’s (LPoE) argument, you don’t need to believe in LFW, you need to believe it is *possible*, even if nonactual.

Second, the CA doesn’t get the conclusion that compatibilism about moral responsibility is false. That’s arguably a more important compatibility claim than the freedom claim, since the Bible speaks much about the latter but not much about the former. Of course, you can argue that LFW is necessary for moral responsibility, but the point I’m making is that the CA doesn’t show it.

Third, by ‘compatible’ I assume you mean

COMP = There does exist a model on which ‘determinism’ is true and someone is ‘free’ in the model. Put differently, there is *at least one* determined worlds that contain a single free person (or choice, or act, etc.).

I take it by ‘compatibilism is false,’ you mean the negation of COMP. The negation of COMP is incompatibilism:

INC = There does *not* exist a model on which ‘determinism’ is true and someone us ‘free’ in that model. Put differently, there are *no* determined worlds that contain a single free person (or choice, or act, etc.).

But how could the CA show *that*? In fact, the CA you cite is modally fallacious if the conclusion is INC. It employes an essential premise that is a *contingent* premise, and then concludes INC.

As incompatibilist Ted Warfield notes,

“Most incompatibilists, to be precise, seem unaware that in order to get the incompatibilist conclusion that determinism and freedom are strictly incompatible (that no deterministic world is a world with freedom), their conditional proofs must not introduce or in any way appeal to premises that are merely contingently true in between the assumption of determinism and the step at which the “no freedom” conclusion is reached.”

What’s the contingent premise? The premise that “If determinism is true then all of our actions are the consequences of the laws of nature and facts about the remote past.”

Recently, Joseph Campbell has exploited this fact. He asks us to consider ‘Adam’, a being who exists at the first instant of a determined world and does an action in the first instant. Adam has no remote past, and so the CA can’t show he’s unfree. Some have responded that you can’t do an action at an instant. This response requires one to buy some controversial metaphysical theories about time, actions, belief-desire complexes, etc. So the argument will depend on controversial metaphysical assumptions, and let’s face it, incompatibilists have expended *loads* of a metaphysical capital to make their theory remotely plausible. But suppose you’re committed to the necessary truth of this theory of action. Campbell has presented ‘oscillating’ Adam. This Adam lives in a cyclical universe, where time operates in a cycle, with Adam growing old then becoming you, etc. His has no “remote past”, and thus the CA can’t show that he’s unfree. If these are *possible*, then COMP is true.

Some have tried to respond by making the argument employ a premise about the laws of nature conjoined with *any* time (a la PVI’s “The Second Argument”). But of course, other Adam’s can be constructed. Adam who live in a world where anti-realism about laws is true and yet is determined to do some free action by a fact about their nature. Or we might think of a timeless Adam, who’s nature determines that he freely think about the Pythagorean theorem. You’ll balk that they’re not free. But the CA can’t show that.

Finally, one can keep laws and times yet deny that the laws of nature plus the facts about a time do the determining. Perhaps it’s the ‘fates’, the ‘laws of logic’, or ‘God’s will’. In these determined worlds, someone can do a free action if they meet the compatibilist criteria. You will object that they aren’t free; but of course, the point is that *the CA doesn’t tell you that*.

So, the CA doesn’t get INC.

Did that one too.

@ James Goetz [# 35, May 17, 2013 at 11:52 pm] Given that physical entities including biological entities constantly change over time, I see no basis for your presumption that A is absolutely identical to B unless you are referring to a paradoxical essence that is absolutely identical over time.

I would reverse what you call a “paradox”: while the simplest objects, elementary particles, according to Quantum Theory, “cannot be regarded as individual objects”, or anyway, “such objects are indistinguishable in a sense which leads to the violation of Leibniz’s … Principle of the Identity of Indiscernibles” (see SEP > Identity and Individuality in Quantum Theory), it is the identity of complex, living conscious beings to themselves (in spite of some sophistications on Personal Identity) that I find more intuitively obvious …

… at least until someone can reproduce two identical individual humans in a superposition of quantum states …

MdS

Per comment 34 part 2:

Thank you for clarifying those points about your model of continuity of identity over time.

Given that physical entities including biological entities constantly change over time, I see no basis for your presumption that A is absolutely identical to B unless you are referring to a paradoxical essence that is absolutely identical over time.

Blessings,

Jim

By the way, I heard of some college students going through phases worse than Calvinism

Jim

[# 32, May 17, 2013 at 4:23 pm]

[m] All cases of mammalian bodies with multiple heads (human or non-human) are identical siblings who/that never completely separated unlike normal identical siblings. By the way, term “identical” in the case of normal identical siblings means they existed as an identical zygote (fertilized egg) or up to an identical early embryonic stage. In some cases of conjoined twins, some organs are identical. For example, the Hensel twins have an identical reproductive system.

[n] Some of the substance of the Cerberus is undivided, and that undivided substance is a good comparison to the Trinity. But the heads and necks of the Cerberus and most real multi-headed mammalian bodies are divided, and that divided substance is a misguided comparison to the Trinity that many social Trinitarians nonetheless appreciate.

[m] Mine was not a question on the embryology of Siamese twins and/or (more specifically) on “mammalian bodies with multiple heads”. The whole point, once again, is that Cerberus is a dog with three heads, IOW a monster, which is not inconceivable, in fact it is even possible and there are even real cases of such monsters. Likewise the “trinitarian god” is a (well, yes) monster (yikes!), but it is not inconceivable. Personally (beside finding it inconsistent with the Scripture), I sincerely hope that such monster, the “trinitarian god” is not real, that it is not the case.

[n] See my comment #31 for Jaco, in particular his quoted b and my comment b. Briefly, when speaking of the “trinity”, the word “substance” (which is the direct translation of the Greek ousia) is NOT a “mass term”, does NOT mean “stuff”, or “continuous substance”, BUT either “particular entity belonging to a class” (primary substance) or the “class (=universal) to which the particulars belong” ” (secondary substance). In the case of God (be it the God of Scripture or the “trinitarian God”), because there is only one, the “particular entity belonging to the class God” coincides with the “class (=universal) to which the particular entity, God, belong”.

Having clarified the above, whichever of the three heads you consider, it is always the same Cerberus. Likewise, whichever “person” you consider, it is always the same “trinitarian god”.

Finally, and once again, the only parallels that are missing from the Cerberus-analogy, when compared with the Nicene-Constantinopolitan (and traditional-orthodox) model of the “trinity” are the s.c. “processions” (respectively “generation of the son” and “spiration of the spirit”), but then, Calvin was quite ready to minimize/ignore them, so as to insist on the absolute equality (aseity, autotheotes) of the three “persons” (see his Institutes, Book I, Chapter 13).

[# 33, May 17, 2013 at 4:37 pm] Does A(t)=B(t) and t1 < t < t2 imply some type of simultaneous existence of t1 and t2?

No, it means considering A and B (which is presumed absolutely identical to A, that is one and the same as A) at every single instant t included between t1 (beginning of existence) and t2 (end of existence).

MdS

Does A(t)=B(t) and t1 < t < t2 imply some type of simultaneous existence of t1 and t2?

Blessings,

Jim

Per comment 22:

MdS said:
And how, pray tell, would a dog with three heads (or a human with three heads, for that matter) be discernible from triplet sharing the same body, and having only three separate heads? (Other than by mere verbal convention, I mean.)

My reply:
All cases of mammalian bodies with multiple heads (human or non-human) are identical siblings who/that never completely separated unlike normal identical siblings. By the way, term “identical” in the case of normal identical siblings means they existed as an identical zygote (fertilized egg) or up to an identical early embryonic stage. In some cases of conjoined twins, some organs are identical. For example, the Hensel twins have an identical reproductive system.

MdS said:
Don’t forget that Cerberus is an analogy for the “trinity”, but, AFAIAC, it is a very strong one, as I have already suggested at the above comment #21 (body “substance”; heads “persons”; Cerberus “trinitarian god”).

My reply:
Some of the substance of the Cerberus is undivided, and that undivided substance is a good comparison to the Trinity. But the heads and necks of the Cerberus and most real multi-headed mammalian bodies are divided, and that divided substance is a misguided comparison to the Trinity that many social Trinitarians nonetheless appreciate.

MdS said:
The only parallels that are missing from the Cerberus-analogy, when compared with the Nicene-Constantinopolitan (and traditional-orthodox) model of the “trinity” are the s.c. “processions” (respectively “generation of the son” and “spiration of the spirit”), but then, Calvin was quite ready to minimize/ignore them, so as to insist on the absolute equality (aseity, autotheotes) of the three “persons” (see his Institutes, Book I, Chapter 13).

My reply:
See my previous sentence.

probably the answer is somewhere in Dr. Wall’s presentation but, as it is over an hour long, I thought it would be quicker to ask you, who have presumably examined it in detail: what is philosophically (rather than biblically) problematic with Calvin’s doctrine of the “trinity”?

Thanks.

MdS

P.S. My question, BTW, ties up with my comments on Calvin at thread White vs. Navas – Does the New Testament teach “the deity of Christ”?

@ James Goetz [May 17, 2013 at 7:31 am] I understand that “A” and “B“ is the entity; “t1? and “t2? are time coordinates, but I am not sure what you mean by “A(t)=B(t)” and “t1 < t < t2." Also, what specifically does "<" mean?

“t1? and “t2? are two instants in time, respectively the beginning and the end of the history of A (presumed identical to B).

A(t) means “entity A at the (generic) instant in time t”

The symbol “<" means "less than", so “t1 < t < t2" means "time included between the beginning and the end (of the history of A)”

MdS

@ Jaco [#26, May 17, 2013 at 6:25 am]

[a] Why do you say it [the Cerberus analogy] [i]s a strong analogy? I just think it’s a different version of the same picture painted throughout history. You might want to be clearer on what you make of the analogy. I’m interested to hear your thoughts.

[b] The issue I have with it [use of the correspondence: body of Cerberus = = “substance” of the "trinity"] is that a numerical modifier (=”body”) is used as a mass term (=”substance”). Since substance is unrelated to number, then three distinct persons and beings chained at the ankle would still be “one substance.” I think the necessity of a one-bodied mythological character would then be unnecessary…

[c] I have no reason to consider it [“self”] otherwise [than “person”]. The second part of the question [what (other than mere verbal convention/decision) distinguishes the phrase “one body/self/substance with three heads/consciousnesses/persons” from “three heads/consciousnesses/persons sharing the same body/self/substance”?] had me thinking a bit. While I don’t see any conceptual difference between the two clauses (…), I find it hard to understand how you understand “body” to be synonymous to “self” synonymous to “substance.” Identical twins have identical genomes but distinct bodies, distinct selves but identical substance. Grafting the two bodies will reduce the number of bodies to one, but there would still be two selves.

[d] I just wonder how many seemingly contradictory constructs could be thought out and centuries spent on trying to reconcile the contradiction at some level. It could be an amusing exercise for logicians. But what’s the use?

[e] What forces us to understand “God” as a mass term (=”substance”) and not a numerical modifier (=”a god”).

[f] Wouldn’t “spirit” be a substance too? (I know in that case all kinds of other members would share in that substance…)

[g] What do you think about that summary on Cartwright’s book?

[a] I assume that by the expression “same picture painted throughout history” you are referring to (one of the many versions of) the s.c. “shield of the trinity”. Now, while the “shield of the trinity” is geometrically accurate, it doesn’t really clarify what are, respectively, the “substance” and the “persons”. In fact, with the central circle marked as “God” (or Deus), it seems to suggest a “quaternity”, rather than a “trinity”. OTOH, and once again, if you establish these correspondences …

• Cerberus = = “trinitarian god”

• whole body of Cerberus (including the 3 heads) = = whole “substance” [NOTE] of the “trinity” (including the 3 “persons”)

• 3 heads of Cerberus = = 3 “persons” of the “trinity”

… you have a model of the “trinity”, whose only limit is that it doesn’t account for the “processions”. But then, again, neither does the “shield of the trinity”.

[NOTE] For the problem you seem to have with the use of the word “substance” (Greek ousia), see next.

[b] The problem, here, is that you are assuming that the word “substance” used in the “trinitarian god” is a “mass term”, as though the “substance” of the “trinity” was some sort of “continuous substance” (like oil or soap), somehow “filling” the “persons”. But in the Greek language, in which the doctrine of the “trinity” was originally formulated, the word ousia, in its philosophical, metaphysical use, in particular in Aristotle, can mean two rather different things (see his Categories):

1. Primary substance is that which cannot be predicated of anything or be said to be in anything. Hence, this particular man or that particular tree are substances. Later in the text of hisCategories, Aristotle calls these particulars “primary substances”, to distinguish them from …

2. … secondary substances, which are universals (= classes) and can be predicated.

For example, Socrates is a primary substance, while man is a secondary substance. Man is predicated of Socrates, and therefore all that is predicated of man is predicated of Socrates.

So, what is the “trinitarian god”? Well, it is, at the same time, a “primary substance” (because it is a concrete instance of the category “god”), AND/BUT also a “secondary substance”, because the class “god” is constituted by one and only one instance.

In the Cerberus analogy, Cerberus is a “primary substance” (because it is a concrete instance of the category “three-headed-dog”). IF we make the further assumption that Cerberus is unique, then Cerberus is also a “secondary substance” (because the class of “three-headed-dogs” has only one concrete instance: Cerberus).

So, once again, the “Cerberus analogy” is a good model of the “trinity” (except for the “processions”)

[c] First, I trust (hope …) that my answer [b] above will have clarified the ambiguous meaning of the word “substance”, while excluding once and for all its use in the sense of “mass term” (or “continuous substance”), when applied to the “trinity”.

Second, I take good note that (as apparently Dale does, BTW) you use the word “self” as synonym of “person”. Let me remind you that the “Cerberus analogy” is what it is: an analogy. Therefore it should be rather obvious that, while it is legitimate to attribute to a spiritual entity like God (and even to the “trinitarian god”) consciousness and person(s), nobody (I hope) would attribute consciousness and/or person(s) to a dog, whether with one or three heads. So, for the sake of clarity, let’s omit “selves” and “consciousnesses”, and consider ONLY the correspondences indicated at my above reply [a].

[d] My point is precisely that the “Cerberus model” is NOT a “contradictory construct” of the “trinity”, BUT is logically valid and sound. I leave it to you (or someone else) to prove otherwise (once again, with the caveat that the “Cerberus analogy” does NOT satisfactorily model the “divine processions” of the “trinity”.

As for the “use”, I consider a rather relevant consequence of the validity and soundness of the “Cerberus model” of the “trinity” that the problems with the “trinity” are NOT logical/conceptual, BUT rather lack of scriptural support.

[e] Once again, I trust (hope …) that my answer [b] above will have clarified the ambiguous meaning of the word “substance” (primary vs secondary), while excluding once and for all its use in the sense of “mass term” (or “continuous substance”), when applied to the “trinity”.

[f] If one believes in the possibility/existence of “spiritual substances” (once again, in the Aristotelian sense of ousia, NOT in the sense of “mass term” or “continuous substance”), then the God of the Scripture (and even the unscriptural “trinitarian god”) belongs to that class. (But I have no idea what your parenthetical comment would mean …)

[g] See my relative comment #29 of May 17, 2013 at 10:17 am

MdS

@ Jaco [#24, May 17, 2013 at 4:24 am] … check out this article: “A summary of Richard Cartwright’s On the Logical Problem of the Trinity [by L.M. Geerdink]

The “Cerberus analogy” is perfectly compatible with the first 7 propositions (“doctrine [of the "trinity"] in narrow sense”) quoted at page 1 of the above essay. More, it is perfectly apt to illustrate them. Check.

Even proposition no.11 (“What [the] Father is, such is the Son and such the Holy Spirit”) can be modelled with the “Cerberus analogy”:

“What Cerberus1 is (a dog with three heads), such is Cerberus2 and such Cerberus3”

Once again, the “Cerberus analogy” is NOT suited to model the additional 3 propositions (no. 8 through no. 10) that make up the “doctrine in wider sense” and that, as can be easily seen, are essentially the Nicene-Constantinopolitan (and traditional-orthodox) model of the “trinity” (directly derived from the Nicene-Constantinopolitan Creed), viz. the s.c. “processions” (respectively “generation of the son” and “spiration of the spirit”). But then, as already remarked, Calvin was quite ready to minimize/ignore them, so as to insist on the absolute equality (aseity, autotheotes) of the three “persons” (see his Institutes, Book I, Chapter 13).

I will add here that the Nicene-Constantinopolitan formulation (NOT the “one ousia in three hypostases” of the Cappadocians) retains some subordinationist “flavor”, which was NEVER eliminated in EO Christianity, whereas it was forced out of the doctrine of the “trinity”, in Western Christianity, ONLY with Peter Lombard …

“For since one and most high certain thing is the Divine Essence, if the Divine Essence has begotten the Essence, the same thing has begotten its very self, which entirely cannot be; but rather the Father alone has begotten the Son, and from the Father and the Son the Holy Spirit proceeds.” (Sentences, Book 1, Distinction 5, Chapter 1)

… eventually sanctioned (in even more “essentialist” and “egalitarian” form that Peter Lombard himself had) by the 4th Lateran Council (1215):

“But we, with the approval of the holy and general council, believe and confess with Peter (Lombard) that there is one supreme entity, incomprehensible and ineffable, which is truly Father, Son, and Holy Ghost, together (simul) three persons and each one of them singly.” (The Canons of the Fourth Lateran Council, 1215, Canon 2 (“On the error of abbot Joachim”, @ fordham.edu)

Calvin, who so thoroughly attacked the Roman and “popish” doctrine in nearly all aspects, with his radically egalitarian “trinity”, peculiarly and unreservedly retained the most scholastic product of the Medieval Church, viz. the doctrine of the “trinity” of Peter Lombard and of the 4th Lateran Council.

MdS

Per comment 19:

John said:
But doesn’t ‘three consciousnesses’ denote three persons?

My reply:
Yes.

John said:
Are not the conjoined legs and organs no more than common user facilities?
Isn’t it something like a computer connected to several facilities -
-i.e. printers, scanners etc.?
Am I being over-simplistic?

My reply:
That sounds correct to me as long as the facilities are integral to the persons.

Blessings,

Jim

Per comment 20:

Sometimes I am slow to understand equations. I understand that “A” and “B“is the entity; “t1″ and “t2″ are time coordinates, but I am not sure what you mean by “A(t)=B(t)” and “t1 < t < t2." Also, what specifically does "<" mean?

Blessings,

Jim

[a] The Cerberus analogy is, once again, an analogy, but a strong analogy. See my comment #22. Why don’t you take issue with my comment, if you have problems with it?

Why do you say it’s a strong analogy? I just think it’s a different version of the same picture painted throughout history. You might want to be clearer on what you make of the analogy. I’m interested to hear your thoughts.

[b] How is this an objection to the “Cerberus analogy”? A human (or a dog, for that matter) “with with no arms and legs” still has a body (= “substance”) and a head (= “person”).

The issue I have with it is that a numerical modifier (=”body”) is used as a mass term (=”substance”). Since substance is unrelated to number, then three distinct persons and beings chained at the ankle would still be “one substance.” I think the necessity of a one-bodied mythological character would then be unnecessary…

[c] It all depends whether you use the word “self” in the same sense as “person” or not. Again what (other than mere verbal convention/decision) distinguises the phrase “one body/self/substance with three heads/consciousnesses/persons” from “three heads/consciousnesses/persons sharing the same body/self/substance”?

I have no reason to consider it otherwise (i.e. “self” in the same sense of “person”). The second part of the question had me thinking a bit. While I don’t see any conceptual difference between the two clauses (unless you might want to show where you do see a difference), I find it hard to understand how you understand “body” to be synonymous to “self” synonymous to “substance.” Identical twins have identical genomes but distinct bodies, distinct selves but identical substance. Grafting the two bodies will reduce the number of bodies to one, but there would still be two selves.

[d] This is a perfectly legitimate question, but it has nothing to do with the logical validity and soundness of the “Cerberus model” of the “trinity”. (BTW, my personal opinion is that the “trinity” has no foundation in the Scripture, but is a projection on the Scripture).

Sure. I just wonder how many seemingly contradictory constructs could be thought out and centuries spent on trying to reconcile the contradiction at some level. It could be an amusing excercise for logicians. But what’s the use?

Just a question. What forces us to understand “God” as a mass term(=”substance”) and not a numerical modifier (=”a god”). Wouldn’t “spirit” be a substance too? (I know in that case all kinds of other members would share in that substance…)

Jaco

What do you think about that summary on Cartwright’s book?

[a] I do not see how the Cerberus analogy will bring us any closer to solving the logical problems with the Trinity.

[b] If physiological composition numerically alter ontology, then is someone with no arms and legs less human than someone with all their limbs, while still being fully personal?

[c] I am of the contention that multiple, distinct consciousnesses are actually distinct ontologies and distinct selves. No degree of relational arrangement can change this numerical distinction.

[d] And finally, are these analogies compatible with what we are presented in the bible? Are these true or false analogies? And if we talk about GOD in the trinitarian sense and refer to the biblical God, are we or are we not equivocating?

[a] The Cerberus analogy is, once again, an analogy, but a strong analogy. See my comment #22. Why don’t you take issue with my comment, if you have problems with it?

[b] How is this an objection to the “Cerberus analogy”? A human (or a dog, for that matter) “with with no arms and legs” still has a body (= “substance”) and a head (= “person”).

[c] It all depends whether you use the word “self” in the same sense as “person” or not. Again what (other than mere verbal convention/decision) distinguises the phrase “one body/self/substance with three heads/consciousnesses/persons” from “three heads/consciousnesses/persons sharing the same body/self/substance”?

[d] This is a perfectly legitimate question, but it has nothing to do with the logical validity and soundness of the “Cerberus model” of the “trinity”. (BTW, my personal opinion is that the “trinity” has no foundation in the Scripture, but is a projection on the Scripture).

MdS

“To clear up all ambiguity: just as Cerberus is a single dog with three consciousnesses, so God is a single spiritual substance or soul with three self-consciousnesses.”

And taking the analogy of human triplets sharing some vital body part: how are the individuality or the ontological distinction of three distinct humans chained by the heels any different from a conjoined triplet? Since, according to the trinity, there are fewer beings than persons, can we say that there are fewer humans in the case of a conjoined triplet than there are persons? And if so, does physiological composition numerically alter ontology? If not, then a conjoint triplet will be three humans and three persons nevertheless. If physiological composition numerically alter ontology, then is someone with no arms and legs less human than someone with all their limbs, while still being fully personal?

I am of the contention that multiple, distinct consciousnesses are actually distinct ontologies and distinct selves. No degree of relational arrangement can change this numerical distinction.

And finally, are these analogies compatible with what we are presented in the bible? Are these true or false analogies? And if we talk about GOD in the trinitarian sense and refer to the biblical God, are we or are we not equivocating?

Just my thoughts.

O yes, check ou this article: http://leongeerdink.nl/wp-content/uploads/2009/09/Summary-Cartwright.pdf

@John [#19, May 17, 2013 at 1:37 am]… Isn’t it something like a computer connected to serveral facilities …

A more accurate model would be a network of three computers such that the system requires (“essentially”) all three computers.

MdS