Divine Propositions and Referential Opacity

The following thoughts occurred to me yesterday, and I wanted to jot some notes down before forgetting them, though I am far from endorsing them.  Just something to chew upon. Some philosophers reject Divine Simplicity and certain explications of the Doctrine of the Trinity because such doctrines seemingly involve contradictions. These contradictions arise when the attributes of God and/or Persons of the Trinity are related to one another by numerical identity. Here are some problematic Divine Propositions:

  1. God = the Triune Godhead
  2. The Son of God = God
  3. God = God’s Knowledge
  4. God = God’s Power

These are problematic, because (1) and (2) seem to suggest that the Son of God = the Triune Godhead, which no orthodox Christian wants to say. Likewise, it prima facie problematic to take (3) and (4) to mean that God’s Knowledge is identical to God’s Power. One solution to this latter problem is to appeal to the doctrine of analogy and say that God’s Knowledge and Power and not the same as the knowledge and power we commonly know about from our everyday experience, so they can be identical. This may be compelling for some, like myself, but for others, I suspect it comes off as appealing to mystery. That is, we don’t really know what we are saying when we say that God has power or knowledge. The former problem is more difficult to resolve. How can we say that the persons of the Trinity are identical to God, but not infer that they are identical to one another, or to the totality of the Godhead? A method to address this is to appeal to the Relative Theory of Identity, devised by Peter Geach. According to this theory, it is an incomplete expression to say that “x is the same as y”. Geach thinks we have to specify the sortal concept by which x and y are the same, that is “x is the same F as y”. This might help us to explain the “The Son of God is the same God as the Father” while also admitting “The Son of God is not the same Divine Person as the Father”.   The sortal terms prevent a direct contradiction. Of course, this may pose a problem for absolute simplicity, since it seems like a sortal is kind or type, and “The Son” or “The Father” are tokens of the type. Also, this solution does not seem to help with (1) and (2), since it seems that the same sortal term could be specified. That is “God is the same God (or Divine Substance) as the Triune Godhead” and “The Son of God is the same God (or Divine Substance) as God.” With the same sortals in place, it seems that Leibniz’s laws are in play again, and we should be able to substitute terms salve veritate. A recent discussion got me thinking of a possible solution to these puzzles. A person was arguing against the Identity of Indiscernibles by appealing to Max Black’s Spheres as possible counterexamples.  The other interlocutor noted that the issue really isn’t the Identity of Indiscenibles, but the Indiscernibility of Identicals. Just to be clear, the two principles are here:

  1. (∀x)(∀y)((x = y) ⊃ (∀φ)(φx ≡ φy)) [indiscernibility of identicals]
  2. (∀x)(∀y)((∀φ)(φx ≡ φy) ⊃ (x = y))[identity of indiscernibles]

The interlocutor seemed to be saying that while (6) may be controversial, it is irrelevant to his problem.  Rather, it is (5) which seems to imply that since the Son of God is numerically identical to God, and God is supposed to be Triune, the Son of God must be Triune, where “Triune” stands as some sort of property, attribute, predicate or description. This implies a transitivity among identicals, which I take to be the real underlying problem in these theological discussions. If the orthodox teachings of divine simplicity and the Trinity depend on a notion of numerical identity, and numerical identity is transitive, or admits of substitution, then certain untoward consequences and contradictions result. By transitivity, I mean the following formal expression:

  1. (∀x)(∀y)(∀z)(((x = y) & (y =z)) ⊃ (x = z)) [transitivity]

So my proposal is to consider whether there is a way to maintain the claim that all of God’s attributes and relations are strict identity claims (rather than relative identity claims, or mere predications) while avoiding untoward inferences. It occurs to me that the indiscernibility of identicals, identity substitution, and the transitivity of identity generally are disrupted in referentially opaque contexts.  So, for instance, consider the following:

  1. I believe that the Boston Strangler = Bobby Orr.
  2. The Boston Strangler = Albert DeSalvo.

We cannot infer from (8) and (9) that Bob Orr is Albert DeSalvo. Perhaps it is true that Albert DeSalvo has been living under a false identity of Bobby Orr, so “Bobby Orr” and  “Albert DeSalvo” refer to the same person. That’s possible, but it is not logically necessary, so truth would not be preserved. This is because “I believe” is a context that is referentially opaque. How does this help us in preserving orthodox theological claims? There are other referentially opaque contexts. One such context that Quine famously argued for is de re modality. In a de re modal claim, one asserts that a certain property, predication, or identity is necessarily predicated of an individual (or property). This is opposed to de dicto modal claims, in which propositions themselves are said to be necessary. So, for instance, a de re modal claim might be something like “Daniel is necessarily an animal” where as a de dicto claim might be something like “necessarily, Daniel is an animal.” Now it might not strike us immediately that de re and de dicto phrases are in any way different from one another, but consider something like this: “necessarily, a bachelor is an unmarried male” and “a bachelor is necessarily an unmarried male.” It seems clear that the de dicto expression is true, as it is positing a necessity between synonymous. The latter is clearly false, because many bachelors are not necessarily unmarried males, and many cease to be unmarried at some point in the future. Quine is suspicious of de re modality because of issues found in the above examples, but he makes his concern more explicit in the following:

  1. 9 = the number of planets.
  2. 9 is necessarily greater than 7.[1]

From (10) and (11) can we infer that the number of planets is necessarily greater than 7? It seems not, because the number of planets can change, and not just by scientific fiat (poor Pluto). A few planets could blow up, or fall out of orbit around the sun. There seems to be no logical or metaphysical necessity that the number of planets in our solar system is greater than 7. So Quine reasons that de re modality is referentially opaque. If this is so, then Divine Propositions expressed in contemporary logic, where modality is treated as an operator, may also be referentially opaque. Let’s stipulate that Divine Propositions are identity statements about God, the Persons of the Trinity, or the Divine attributes. So, I argue that they are not merely identity claims, but de re identity claims. Now some philosophers claim that de re necessity is not referentially opaque. David Wiggins, for instance, endorses the following argument, claiming that opacity is a problem that “no longer presses”:

  1. Hesperus is necessarily identical to Hesperus.
  2. Hesperus is identical to Phosphorus.

So,

  1. Hesperus is necessarily identical to Phosphorus.[2]

I remain completely unconvinced that this argument is valid. While it might be the case that the object to which Hesperus and Phosphorus refer, the planet Venus, is necessarily self-identical, it doesn’t seem to me that there is any logical or metaphysical necessity that Hesperus and Phosphorus could not have been two distinct objects. So even though these are co-referring terms, it seems to me that de re identity is an intensional context, i.e. it is referring to the intension of the terms and relating them to one another by a necessity of identity. I find this tantamount to the following:

  1. I necessarily believe Hesperus is Hesperus.
  2. I believe Hesperus is Phosphorus.

So,

  1. I necessarily believe Hesperus is Phosphorus.

Let’s say that (16) is true, that I am a consistent thinker. It seems odd though, that (17) should follow. Of course, those who think that de re contexts are not opaque will remain unconvinced. To me, this is one of the major shortcomings of contemporary modal logic, and is a primary motivator for seeking out a modal logic that avoids the opacity problem. In my estimation, Aristotelian modality has the advantage of making de re-like modal claims, but without being opaque. Aristotle achieves this by treating modality as a copula modifier rather than a predicate modifier, or movable operator. But this is a tangent that I will have to explore in later posts. Now let us re-examine Divine Propositions:

  1. God is necessarily identical to the Triune God.
  2. The Son of God is necessarily identical to God.

These are de re identity claims, and if these claims are referentially opaque, it unclear whether we can now infer from (18) and (19) the the Son of God is necessarily identical to the Triune God. So, if all identity relations said of God are de re identity claims, then substitution of identity cannot occur. This does not mean that certain substitutions will not happen to preserve truth, but that we simply cannot assume to make such substitutions.  That is, the identity relation in Divine Propositions will not guarantee the preservation of truth when terms are substituted.  This gives some philosophical reason to appeal to a certain mystery regarding God’s nature. That is, God’s nature cannot be fully comprehended, at least in part, because Divine Propositions are referentially opaque de re identity claims. Now one might object that if it is true that God is necessarily identical to the Triune God, then God is identical to the Triune God, and so we can reduce out the referential opacity so that the substitution problem arises. One response to this would be to say that it is simply false to assume that the reduction from de re modality is truth preserving for Divine Propositions. For if we assume that Divine Propositions are, at the very least, always based on identity, then a certain problem arises with Divine Identity itself.  That is:

  1. God’s identity to the Triune God is identical to God’s necessary identity to the Triune God.

If God’s identity to the Triune God is identical to necessary identity, then we must ask whether the identity relation that relates the two sorts of “God’s identities” is itself referentially opaque. If we grant that “identity” is not referentially opaque in (20), then by transitivity “God’s identity” on the left side is referentially opaque as it is on the right side. Alternatively, we might deny that such a transitive relation exists in (20), but that must be because it is an opaque context despite being explicitly de re.  And this is precisely what we are arguing.  So the conclusion seems unavoidable. Another objection one might make is that referential opacity disappears if the same intensional context is used throughout an argument. So, for instance:

  1. I believe that the Boston Strangler = Bobby Orr.
  2. I believe the Boston Strangler = Albert DeSalvo.

From this, it seems that I can validly infer that:

  1. I believe that Bobby Orr = Albert DeSalvo.

Is this true? Well, not if I am an inconsistent believer. We have to make certain doxastic assumptions about me, in addition to these premises, to reach that conclusion. What about in the case of de re modality?

  1. 9 is necessarily identical to the number of planets.
  2. 9 is necessarily greater than 7.

Does the following follow?

  1. The number of planets is necessarily greater than 7.

Can we make this inference? I suspect not without making certain assumptions about the kinds of necessity at play. Even then, it is ambiguous as to which sort of “necessity” is found in the conclusion. So, I don’t think including the same opaque context throughout an argument transforms the premises into something transparent. For instance, it may be  that (24) is about metaphysical necessity, nomological necessity, physical necessity, or some other sort of necessity? Is the same sort of de re necessity used in (25)? I think most of us would see (25) as some sort of logical, or arithmetic necessity. What about in the case of Divine de re claims? Well, we would have to have a clear sense of the univocal way in which God’s attributes and persons are related to one another by de re identity. I suspect that our own understanding of the ways in which these relations are described will vary from logical necessity, to metaphysical necessity, to necessities that are contextualized by our understandings of specific attributes. For instance, there is a sense in which the Father is unbegotten and necessarily exists a se, and a sense in which the Son is begotten, but still necessarily existing in that the divine relation from the Father to the Son is a necessary because of the metaphysics of subsistent relations, or because of some necessity in the nature of perfect love and community. So the Son is necessary, but begotten of the Father, which doesn’t seem to be exactly the same sort of necessity.  Is there an overarching sense in which the Father and Son are both necessary, sure, but that sense may be beyond our immediate comprehension. Consequently, I find it dubious that we can settle on one opaque de re context in all of our discussions of God. And even if we could, it is not likely that opacity can be remedied by maintaining the same context throughout an argument. Therefore, I think we must conclude that Divine Propositions, i.e. propositions about God, the Persons of the Trinity, and Divine Attributes that are linked together by de re identity relations can be strict, opaque, and not admit of transitivity.  Thus, God’s nature can be described through the Divine Propositions, but God’s nature prevents inferences about His nature and so preserves mystery.  This is not a fallacious appeal to mystery though, but one that has philosophical motivation.  If this is so, it represents one way that orthodoxy can be intellectually defended. [1] W.V.O. Quine. 1966. “Three Grades of Modal Involvement” in The Way of Paradox and other Essays. New York: Random House. pg. 161. [2] See David Wiggins. 2001. Sameness and Substance Renewed. New York: Cambridge University Press. pp. 114-115.

Richard Carrier and γίνομαι

Richard Carrier believes that Jesus Christ never existed.  His theory is that Christ was initially a celestial being and later received historical biographies.  Part of Carrier’s case is that he claims that Paul never makes mention of Christ in any way that would indicate that he was a historical flesh and blood person.  He has a video where he puts together his argument here: At about the 31:50 mark, Carrier addresses a criticism of his argument, and it is his response that I would like to address here.  The criticism is that Paul does indeed indicate that Christ was a flesh and blood individual, who is a born member of the human race.  The significant passages are Romans 1:3 and Galatians 4:4. That is:

…concerning His Son, who was born of a descendant of David according to the flesh (Romans 1:3, NAS).

In Greek, is says, “περὶ τοῦ Υἱοῦ αὐτοῦ τοῦ γενομένου ἐκ σπέρματος Δαυεὶδ κατὰ σάρκα…” (Romans 1:3, emphasis mine). Likewise, Galatians 4:4 says,

But when the fullness of the time came, God sent forth His Son, born of a woman, born under the Law… (Galatians 4:4, NAS).

The Greek says, “ὅτε δὲ ἦλθεν τὸ πλήρωμα τοῦ χρόνου, ἐξαπέστειλεν ὁ Θεὸς τὸν Υἱὸν αὐτοῦ, γενόμενον ἐκ γυναικός, γενόμενον ὑπὸ νόμον…” (Galatians 4:4, emphasis mine).

Carrier’s argument is to focus on γενόμενον or γενομένου, which are the accusative and genitive forms of the aorist participle of γίνομαι.  According to Carrier, this is an odd form of the verb to use for “born”, and indicates that Paul was trying to make a specific point, namely that Christ was directly made or manufactured by God.  Thus, these passages don’t actually conflict with the idea that Christ was a celestial being.  Carrier makes the point that this is the same word used in the Septuagint to describe the creation of Adam.  Presumably he has Genesis 2:7 in mind:

Then the LORD God formed man of dust from the ground, and breathed into his nostrils the breath of life; and man became a living being (Genesis 2:7, NAS).

“…και έπλασεν ο θεός τον άνθρωπον χουν λαβών από της γης και ενεφύσησεν εις το πρόσωπον αυτού πνοήν ζωής και εγένετο  ο άνθρωπος εις ψυχήν ζώσαν…” (Genesis 2:7, emphasis mine).

In this verse we see the aorist indicative form of γίνομαι, which is related, though not precisely the same form of the verb that Paul uses. [Updated comment] Another important point is that the verb being used to describe the moment of divine manufacture is not εγένετο, but έπλασεν, the third person aorist indicative of the verb πλάσσω, which means “to form” or “to mould”.  The verb εγένετο is used in the context of saying that when God breathed life into Adam, he “became” a living man.  So here, the verb is being used more broadly to discuss a change of state or coming to be of life from the non-living clay that God had formed.  So it isn’t exactly correct to say that γίνομαι means “divine manufacture”.  At best, πλάσσω could take that meaning.  Instead, γίνομαι can mean “become”, but in this context it is the coming to be of life in the body of Adam, which is γίνομαι + a predicate (living) rather than γίνομαι + a person, in which the proper translation is “born”.  So, context always rules over these situations.  I makes sense to say that Adam came to be living, but in Romans 1:3 and Galatians 4:4 we are talking about γίνομαι + a person, not a property, predicate, event, or state of affairs.  Citing Adam in Genesis just won’t do.

Carrier notes that Paul doesn’t use the word γίνομαι to refer to a human birth.  This is somewhat question-begging since, he must assume that these two instances are really meant to indicate “to happen, become, or be made” but not “to be born”, which is precisely the question he is raising.  Consequently, he precludes instances where Paul seemingly does use the word because he already assumes that it has a different meaning than “born”.   This is not entirely fair since the word specifically does mean “to be born” in the context of persons, as I’ve mentioned in my analysis of Genesis 2:7.  So it does have broad meaning for a general “coming to be” but Greek relies on context to shave down the meaning.  One need only check Liddell and Scott’s Intermediate Greek Lexicon to see that, of persons, it means to be born, as I have said.  Carrier points out that Paul uses another verb for being born in Romans 9:11 and Galatians 4:23,29.  It is true that Paul also uses γεννάω, but that just means that Paul is willing to use synonyms of a word, it does not not imply that Paul was trying to make a careful distinction.  Carrier then makes a big deal about the fact that some scribes switched verbs in certain manuscripts (indicating for Carrier some grand conspiracy to make Jesus appear historical rather than mythic-celestial). It could be just a substitution error.  They put in the synonymous word by accident.

There is a major flaw in Carrier’s argument.  He cites the Septuagint as evidence that γενόμενον means divinely manufacture rather than born, since it is used to describe the creation of Adam.  Well, how is this verb used elsewhere in the Septuagint? I started to check and only made it through the rest of the book of Genesis, but I am almost certain there will be more examples, if I had the time an patience to research the entire Septuagint.  Here, I am searching out the precise aorist participle form of the verb γίνομαι to see how it is used in those context.  We might ask if “divine manufacture” to “born” would be better translations in these passages.

Abraham called the name of his son who was born to him, whom Sarah bore to him, Isaac (Genesis 21:3, NAS)

The Hebrew word translated into “was born” is “yalad”, which means “to bear, bring forth, or beget”.  The translators of the Septuagint render the passage this way:

“καὶ ἐκάλεσεν Αβρααμ τὸ ὄνομα τοῦ υἱοῦ αὐτοῦ τοῦ γενομένου αὐτῷ, ὃν ἔτεκεν αὐτῷ Σαρρα, Ισαακ” (Genesis 21:3, emphasis mine).

Notice that γενομένου, used in Genesis 21:3 is precisely the same word used in Romans 1:3, right down to the same case and number.  So are we to interpret this as “divinely manufactured”?  In the context, we are talking about Abraham, not God.  It doesn’t make sense to translate this any other way.  Surely Paul would be familiar with this passage, if he was familiar with the Greek word used in Genesis 2:7. Also, let us consider this passage:

and the sons of Joseph, who were born to him in Egypt were two; all the persons of the house of Jacob, who came to Egypt, were seventy. (Genesis 46:27, NAS).

Again the Hebrew word that is translated as “were born” is a form of the verb “yalad”.  Let’s see how the Septuagint translated the passage:

“υἱοὶ δὲ Ιωσηφ οἱ γενόμενοι αὐτῷ ἐν γῇ Αἰγύπτῳ ψυχαὶ ἐννέα. πᾶσαι ψυχαὶ οἴκου Ιακωβ αἱ εἰσελθοῦσαι εἰς Αἴγυπτον ἑβδομήκοντα πέντε” (Genesis 46:27).

Here we have the same aorist participle, but this time it is the nominative plural form of γίνομαι. Clearly we are seeing a translation pattern here.  And again, consider whether “divine manufacture” makes sense when we are talking about the sons of Joseph! My last example is:

Now your two sons, who were born to you in the land of Egypt before I came to you in Egypt, are mine; Ephraim and Manasseh shall be mine, as Reuben and Simeon are (Genesis 48:5, NAS).

Again, the Hebrew verb translated to “were born” is “yalad”.  And the Septuagint is as follows:

“νῦν οὖν οἱ δύο υἱοί σου οἱ γενόμενοί σοι ἐν Αἰγύπτῳ πρὸ τοῦ με ἐλθεῖν πρὸς σὲ εἰς Αἴγυπτον ἐμοί εἰσιν, Εφραιμ καὶ Μανασση ὡς Ρουβην καὶ Συμεων ἔσονταί μοι…” (Genesis 48:5).

Again, this is the aorist participle of γίνομαι, which comes from the older form γίγνομαι.  It is a word that is commonly translated as born when set within the context of the “coming to be” of humans.  Clearly Paul would have had access to these examples from the Septuagint.  He would have known that it is a common way to translate “yalad”, which means “to beget”.  So Romans 1:3 and Galatians 4:4 are very strong evidence that Paul thought Jesus was actually born of the seed of David, and of a woman, just as the Gospels report.  This is compelling evidence against the thesis that Paul thought Christ was a celestial being who never walked the Earth. So, my assessment of Carrier is that he really did not do a careful analysis of γίνομαι.  I think it is clear that Paul uses the word to mean “born” and that he would have been quite familiar with the verb as one which can mean “born”.  That Paul uses a synonym occasionally does not mean that he wants to use γίνομαι in some technical sense with Adam’s “divine manufacture” in mind.  In fact, there are plenty of instances of the Septuagint where the exact same verb-form is used and “born” is the only reasonable way to translate.  I don’t see how Romans 1:3 or Galatians 4:4 could be about “divine manufacture” like Adam since they specifically mention the involvement of humans in both cases.  Why mention David’s seed or that He will be from a woman at all?  Carrier says that the latter instance is an allegory.  [Updated comment] Undoubtedly, he has Galatians 4:21-31 in mind, where Paul tells us that Abraham had two sons, the first born to a slave woman and the second was of a free woman.

This is allegorically speaking, for these women are two covenants: one proceeding from Mount Sinai bearing children who are to be slaves; she is Hagar (Galatians 4:24, NAS).

So Carrier wants to say that “being born of a woman” is “being born of a covenant” and so Galatians 4:4 really just means that Jesus was born of a covenant, not that he was actually born of a human.  But is this a fair assessment?  Paul makes the point that his discussion of Hagar and Sarah are “allegorizing” of what was said before.  This does not mean that Paul did not think it was true that Jesus was born of a woman. Rather, a straightforward reading is that he made the statement in Galatians 4:4 quite plainly and then adds an allegorical dimension to it by referencing Hagar and Sarah as a way to draw out a deeper dimension of what the birth of the Jewish messiah, whose lineage traces all the way back to Isaac, means.  But, let us suppose this was meant to be allegorical even in Galatians 4:4.  If so, then Carrier’s claim that it would be odd or incorrect to translate γενόμενον as “born” utterly falls apart.  For it must be translated that way, though allegorically.  That is, Paul would not use γενόμενον if he intended it to have a different meaning than “born” if the allegory in which it is employed depends upon us understanding the word to mean “born”.  Otherwise, it would not be much of an allegory.  But if that is the proper translation in Galatians 4:4 (though allegorical), then Romans 1:3 is the clincher.  For there is no “allegorizing” going on there.  This means that Carrier must recognize that Romans 1:3 is saying that Christ Jesus, who was promised by the prophets, was  indeed “born of the seed of David according to the flesh.”  Without the excuse of saying that this was “divine manufacture”, Carrier has no retreat.  So, insisting that the woman in Galatians 4:4 is allegorical is not actually helpful to Carrier in the least.  It only shows that Paul is willing to use synonymous terms for “born”, as I suggested.  So, this is not an extra argument that he can add to his thesis that γίνομαι shouldn’t be translated as “born”, but directly contradicts it.  Perhaps if Galatians 4:4 were the only instance where Paul uses a derivation of γίνομαι, Carrier could simply insist that it is only an allegorical birth.  However, there is also Romans 1:3, a thorn in the side of Carrier’s argument.

The mythicists demand that we throw away all context and instead imagine some grand conspiracy was afoot.  I just can’t buy it.  And Carrier’s efforts to pretend that γίνομαι is inappropriately translated as “born” is either extremely ignorant or dishonest.  Combines with his attempt to allegorize Galatians 4:4, I find his case to be contradictory and confused.

None More Actual

1579 drawing of the Great Chain of Being from Didacus Valades, Rhetorica Christiana (Wikipedia, Great chain of being)

Whenever I discuss the ontological argument with my atheistic friends, I find that they always get hung up on the same word, “greater”. They want to infuse it with moral or aesthetic meaning, and so suspect that it is subjectively defined. They don’t think there is any objective way to determine that one thing is ontologically greater than another (a flea is no greater than a child and the fact that you would swat one and not the other is just based on speciesist opinions). Indeed, to fully explain what Anselm meant by the definition, we would have to develop the neo-platonic notion of the Great Chain of Being, which is far more central to the argument than most contemporary philosophers of religion realize. Nonetheless, that requires some metaphysical assumptions from which many atheists will shy away. I want to sidestep that whole discussion by using something other than “greater.” My proposal is to run the ontological argument on a “more actual” relation. I think you can still derive the traditional divine attributes from this term, but it doesn’t suffer from seeming subjective (what is more actual is an objective question).  Nonetheless, understanding what is meant by “actual” will require some metaphysics.  When discussing proofs for God, metaphysics is inescapable.

What do I mean by “more actual”? I am appealing to the distinction between act and potency in the Aristotelian-Thomistic sense of the word. For Thomas, God is the only being that is purely actual. This is because God’s essence is His existence. God is “I am”. The distinction between act and potency is an important one in the history of philosophy. It is that distinction, which allowed Aristotle to provide a response to the Eleatics, who denied change. The Eleatics argued that change was impossible because it would have to involve being arising from non-being. Since nothing comes from nothing, change cannot arise from non-being.  Instead, Aristotle said that change occurs when a potential is actualized. So, a seed can become a plant because it is potentially a plant. And it undergoes that change when it is acted upon by actual things like water, soil, heat, etc.  We see change happen all around us, and it is rooted in the nature of things.  For instance, I am potentially bald, a potential that I am slowly actualizing with every lost hair follicle.  So, while act and potency are metaphysical concepts, they are fairly close to our commonsense.  The log is potentially fire, smoke, and ash.  The log is actually hard and damp.

An ontological argument that exploits the notion of actuality is a bit odd and perhaps shocking for my Thomistic friends. It is commonly thought that Thomas Aquinas did not accept the soundness of such arguments, a point that I am not going to discuss here. Nonetheless, I think the premises of such an argument could be defended. The argument would run like this:

1. God is that than which none more actual can be conceived (definition).
2. If God exists only in the mind, something more actual than God can be conceived (premise).
3. If something more actual than God can be conceived, something more actual than God can be conceived (tautology).
4. If something more actual than God can be conceived, something more actual than ‘that which none more actual can be conceived’ can be conceived (from 1 and 3).
5. Nothing more actual than ‘that which none more actual can be conceived’ can be conceived (premise).
6. Therefore, it is not the case that God exists only in the mind (from 2,4,5).
7. If it isn’t the case that something exists only in the mind, then it exists in reality (premise).
8. Therefore, God exists in reality (from 6 and 7).

Now, there are a few premises and a definition. The definition, I think, is fair. Aquinas takes great pains to show that whatever is pure actuality has the divine attributes. So a being than which none more actual can be conceived would be purely actual, and so simple, a se, necessary, immutable, eternal, omnipotent, omniscient, and good.

Furthermore, I think (2) is defensible. Generally that which exists merely as a conception is less actual, in some way, than its counterpart in reality. You can’t be cut by the thought of a knife.  Also, (5) seems plausible. For if something more actual than ‘that than which none more actual can be conceived’, a contradiction arises. Lastly, all that is meant in (7) is that if something doesn’t just exist in the mind, that means it exists independently of our minds, which is to say that it exists in reality.  I suspect someone might say that it is a false dichotomy to insist that if something doesn’t just exist in the mind, then it must exist in reality, but I can’t think of any alternative.  And if an alternative could be found, I am sure the argument could be adjusted in the relevant ways.

One last note is to consider whether this argument is susceptible to parody.  I think it is less susceptible.  Consider Gaunilo’s island.  Could we define an island than which none more actual can be conceived?  Well, every island is a composite of act and potency by nature.  So no island can be maximally or purely actual.  One can admit that islands that exist in reality are more actual than islands that exist in the mind, but this does not mean that ‘an island than which none more actual can be conceived’ would necessarily exist, since there is no such thing.  There are, at best, islands that are more actual than other islands, but that doesn’t lead to parody.

Article in Sci Phi Journal: Issue #1

Sci Phi Journal: Issue #1 is out in ebook format on Amazon and Smashwords.  Here is the description:

Sci Phi is an online science fiction and philosophy magazine. In each issue you will find stories that explore questions of life, the universe and everything and articles that delve into the deep philosophical waters of science fiction universes.

This month we have,

An original Novellete from author John C. Wright, The Ideal Machine, a tale of aliens from a distant star come to visit an old country church and offer our world a chance for the future.

Original Science Fiction stories from
Joshua M. Young – Domo – A story of a Robot who wonders if he has a soul
David Hallquist – Falling To Eternity – Can a Blackhole help you get away with murder?
Frederick Best – Cosmic Foam – What is beyond the visible world
Jane Lebak – Abandoned River, Dry Water – What do you do when life throws you a curve ball?

Original Essays by
David Kyle Johnson – In Defense of the Matrix Saga: Appreciating the Sequel through Philosophy
James Druley – Star Trek’s Prime Directive : Moral Guidelines, Exceptions and Absolutes
Stephen S. Hanson – Personhood in H.Beam Piper’s Little Fuzzy
Daniel Vecchio – “I am Groot”: An Aristotelian Reflection on Space Aliens and Substance
Ruth Tallman – Endangered Species: Exploring Transhumanism, Genetic Engineering and Personhood Through the World of Sweet Tooth

And a book review by Peter Sean Bradley, Monster Hunter International by Larry Correia.

I’m very excited to be a part of this first edition along side some great philosophers and science-fiction writers.  My article, “‘I am Groot': An Aristotelian Reflection on Space Aliens and Substance”, is a popular level piece that uses the characters from the blockbuster smash hit, Guardians of the Galaxy, as a springboard to explain the Aristotelian notion of substance.  I consider the peculiar case of Groot, a sentient and lovable humanoid plant, and also whether an artificial life form like Rocket Raccoon could be considered a substance.  There are some spoilers, so I recommend that you check out the film first, if you plan on seeing it at all.  Also, I recommend the movie.  It’s a lot of fun and has an excellent soundtrack.  Nonetheless, I think you will be able to appreciate the article even if you are not familiar with Guardians of the Galaxy.

I haven’t had a chance to read the other short story and article contributions.  Once I have a chunk of my dissertation completed, I am hoping to take a moment to read the issue under a palm tree in my local park.  So, if you are looking for some fun and thought provoking reading materials for those crisp autumn evenings, take a look.  And please consider leaving a kind review! :-D

A Video on the Modal Epistemic Argument

[H/T Inspiring Philosophy]

The above video presents the following argument:

1. For all p, if p is unknowable, then p is necessarily false (premise).

2. The proposition “God does not exist”, is necessarily unknowable (premise).

3. Therefore, the proposition “God does not exist”, is necessarily false.

I find this argument interesting, especially since (1) is very similar to a crucial premise in my knowability argument for omniscience. So my premise states: (∀p)(p ⊃ ◊(∃x)Kxp), or for all p, if p is true, then it is possible that p is known by someone.  The modal epistemic argument above tells us something like: (∀p)(~◊(∃x)Kxp) ⊃ □~p). It would be interesting if one could derive the existence of omniscient mind, and the existence of God from two independent arguments that utilize the same knowability premise.  This means that knowability really stands against the naturalist, and I think some good arguments can be made to support it.  My ears perked up when the narrator mentioned some of the realists and idealists who would be willing to grant the knowability premise: Aristotle and Hegel.  I’ve noticed that anti-realists like Dummett and realists like Aquinas also endorse the knowability premise.  So, it is something to consider.

Beg Your Pardon, What is Begging the Question?

VQ:

Here is my recent contribution to Attack of the P-Zombies. Enjoy!

Originally posted on Attack of the P-Zombies:

We’ve all met them. Usually they are fresh off of a critical thinking, or informal logic course. They are the fallacy mongers. Taught to identify informal fallacies in headlines and textbooks, they begin to “see” fallacies at every turn. And suffering them in any conversion is nearly intolerable. For those unfamiliar, I am talking about people who behave like this. Now, I am not saying that it isn’t important to be able to know and be able to identify informal fallacies. It is. But it can also become a hammer that turns all arguments into nails. This is especially dangerous because informal fallacies tend to be vaguely defined, and often resemble perfectly good methods of reasoning. Pro-tip: When you encounter such people, inform them that it is not sufficient to merely burp up fallacies at you. Ask them to explain to you what the fallacy means, and specifically how…

View original 2,153 more words

The Sacred and the Sacrilegious: the Real Presence and a Black Mass

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I was very disheartened to learn that a Satanic group has managed to get their hands on a consecrated host and planned to desecrate it during a black mass service in Oklahoma this September.  Supposedly the latest news is that the Satanists have returned the Host and the Archbishop has dropped his suit:

The lawsuit was ultimately resolved this week without having to go to court, as Daniels agreed on Thursday to return the wafers in exchange for the lawsuit being dropped. But the incident is still noteworthy, as it is but the latest in a growing number of “tests” to America’s understanding of religious liberty, and questions linger about what action, if any, police would have taken had the suit been put before a judge (J. Jenkins August 24, 2014: How Satanists are Testing the Limits of Religious Freedom in Oklahoma, Think Progress).

Of course, the Black Mass is still moving forward, and who really knows if they actually returned the consecrated Host.  Perhaps equally infuriating is how breathless some in the secular left have become over recent rather brazen activities of the Satanists: see here, here, and  here.  They see the Satanists as joining the cause of protecting the separation between Church and State.

One thing to note is that when Satanists really want to offend and commit blasphemy, the target is almost always the Catholic Church. Now there may be historical reasons that they target the Catholic Mass to blaspheme, but to those who believe that they are influenced by demonic forces, it should, perhaps ironically, stand as a witness to the sacredness of the Holy Mass.

Those who believe that Catholics are, themselves, guilty of a grave sacrilege by the sacrifice of the Mass must wonder why Satanists are drawn to make a sacrilege out of a sacrilege. One answer is that Satanists are merely interested in mocking and ridiculing that which others take to be sacred.  So the issue is not whether the Mass is objectively sacred, but whether it is taken to be sacred by a significant number of people. If so, I think this would strongly count against the position that Satanists are influenced by the demonic in these matters. For, why would the demonic waste its time trying to get people to make a sacrilege out of a sacrilege?

I mentioned to my friend, Joel, that the devil would have no interest in mocking a Catholic Mass if it truly were a sacrilege, since he would be pleased by the fine job we are doing ourselves. There is no point in making a blasphemy of a blasphemy, since the devil might as well direct his Satanists to follow the Catholic faith as an effective and idolatrous way to imperil their souls. Joel made the interesting connection to Christ’s claim that a house divided cannot stand:

Then a demon-oppressed man who was blind and mute was brought to him, and he healed him, so that the man spoke and saw. And all the people were amazed, and said, “Can this be the Son of David?” 2But when the Pharisees heard it, they said, “It is only by Beelzebul, the prince of demons, that this man casts out demons.” Knowing their thoughts, he said to them, “Every kingdom divided against itself is laid waste, and no city or house divided against itself will stand. And if Satan casts out Satan, he is divided against himself. How then will his kingdom stand?  And if I cast out demons by Beelzebul, by whom do your sons cast them out? Therefore they will be your judges. But if it is by the Spirit of God that I cast out demons, then the kingdom of God has come upon you (Mt 12:22-28 ESV).

If Satan directs people to mock that which are a sacrilege to God, then he seems to be divided against himself. So here, we find something of an argument for the Real Presence of the Eucharist, and the sacredness of the Catholic Mass. Here is my reasoning:

  1. If the Real Presence of the Eucharist is a false doctrine, then the Catholic Mass is a form of idolatry, sacrilege, and blaspheme (premise).
  2. The Catholic Mass is a form of idolatry, sacrilege, and blasphemy, and Satanists are directed by Satan to mock and blaspheme the Mass, only if Satan is divided against himself (premise).
  3. If Satan is divided against himself, his kingdom will not stand (premise).
  4. Satan’s kingdom will stand (premise).1
  5. Satan is not divided against himself (from 3 and 4).
  6. It is not both the case that the Catholic Mass is a form of idolatry, sacrilege, and blasphemy, and Satanists are directed by Satan to mock and blaspheme the Mass (from 2 and 5).

Now, given that I think that there are demonic forces in this world, I think it is reasonable that those who invoke the very name of Satan, Satanists, are influenced by him with regard to their Black Mass in its form and ritual. I think this is so, even if they explicitly claim to be atheist or reject the supernatural.  One may still be influenced by the demonic even if one claims not to believe in it.  So:

  1. Satanists are directed by Satan to mock and blaspheme the Mass (premise).

So,

  1. It is not the case that the Catholic Mass is a form of idolatry, sacrilege, and blasphemy (from 6 and 7).

Therefore,

  1. The Real Presence of the Eucharist is a true doctrine (from 1 and 8).

I pray that this group repents and finds more productive ways to fight for religious freedom and tolerance in this country.  I hope they find their way back to God.
[Update 9/7/2014]: Eye of the Tiber, a satirical site, makes an insightful point that relates to my reflection.  We just don’t see Satanists mocking denominations that take the Eucharistic meal to be a symbolic ordinance.

PAX

 

1Satan is said to have dominion over the Earth for the time being. His kingdom, though evil, is clearly not divided against itself, if Christ’s enthymeme has any merit.

Unsharing Poster

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Think of “sharing” as a form of efficient causality that brings the potentiality of a posted article on one’s social media page into the actual shared article. Intuitively, we know that a proper explanation of an article is always going to include an author and/or original poster, who did not share the article from someone else’s page. That is, the existence of the article cannot be explained by some endless chain of sharing. Likewise, our contingent universe cannot be explained by an endless chain of efficient causers that “share” their actuality so as to change potential effects into actual effects. There must be an original author, an uncaused causer, and an unsharing poster. And when it comes to the universe, everyone calls this “God”.

“Nothing”

😜

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Nothing = not anything

The Horse Head Argument

After developing three figures of the categorical syllogism, Aristotle bombastically claims, in Prior Analytics A23:

It is clear from what has been said that the deductions in these figures are made perfect by means of the universal deductions in the first figure and are reduced to them. That every deduction without qualification can be so treated, will be clear presently, when it has been proved that every deduction is formed through one or other of these figures (40b17-22, emphasis mine).

Contrary to this, Augustus De Morgan argues that there are deductions that cannot be reduced to a syllogism.

There is another process which is often necessary, in the formation of the premises of a syllogism, involving transformation which is neither done by syllogism, nor immediately reducible to it. It is the substitution, in a compound phrase, of the name of the genus for that of the species, which the use of the name is particular (FL, p. 114).

The most notorious example is, the horse head argument (HHA): ‘horse is animal, therefore the head of a horse is the head of an animal’. I should clarify that De Morgan uses ‘man’ rather than ‘horse’  in his example, but otherwise, the argument is the same. Now, our predicate logic is quite powerful and can handle compound substitutions ably. Here is an indirect proof that seems to comport to the demands of HHA:

Let

Hx – x is a horse
Ax – x is an animal
Cxy – x is the head of y

1. (∀x)(Hx ⊃ Ax) (premise)
2. ~(∀y)(∀x)[(Hx & Cyx) ⊃ (Ax & Cyx)] (IP)
3. (∃y)~(∀x)[(Hx & Cyx) ⊃ (Ax & Cyx)](2 QN)
4. (∃y)(∃x)~[(Hx & Cyx) ⊃ (Ax & Cyx)] (3 QN)
5. (∃x)~[(Hx & Cux) ⊃ (Ax & Cux)] (4 EI)
6. ~[(Hv & Cuv) ⊃ (Av & Cuv)] (5 EI)
7. ~[~(Hv & Cuv) ∨ (Av & Cuv)] (6 Impl)
8. ~~(Hv & Cuv) & ~(Av & Cuv) (7 DeM)
9. (Hv & Cuv) & ~(Av & Cuv) (8 DN)
10. Hv & Cuv (9 Simp)
11. Hv (10 Simp)
12. Hv ⊃ Av (1 UI)
13. Av (11, 12 MP)
14. ~(Av & Cuv) (9 Simp)
15. ~Av ∨ ~Cuv
16. ~~Av (13 DN)
17. ~Cuv (15, 16 DS)
18. Cuv (10 Simp)
19. Cuv & ~Cuv 17, 18 Conj)
20. (∀y)(∀x)[(Hx & Cyx) ⊃ (Ax & Cyx)] (2-19 IP)

So, the inference seems to be valid, given the rules of first order predicate calculus. Is it really the case, though, that a parallel proof cannot be rendered in a Categorical syllogism? A categorical syllogism has three terms, and two premises, yet the above argument has one premise, which leads directly to the conclusion. So we need to identify the terms that would operate in a syllogistic version of HHA. And we need to allow that the reduction will contain two premises.

We must be cautious in how we articulate this syllogism, as Aristotle warns:

It is not the same, either in fact or in speech, for A to belong to all of that to which B belongs, and for A to belong to all of that to all of which B belongs; for nothing prevents B from belonging to C, though not to every C: e.g. let B stand for beautiful, and C for white. If beauty belongs to something white, it is true to say that beauty belongs to that which is white; but not perhaps to everything that is white. If then A belongs to B, but not to everything of which B is predicated, then whether B belongs to every C or merely belongs to C, it is not necessary that A should belong, I do not say to every C, but even to C at all. But if A belongs to everything of which B is truly said, it will follow that A can be said of all of that of all of which B is said. If however A is said of that of all of which B may be said, nothing prevents B belonging to C, and yet A not belonging to every C or to any C at all. If then we take three terms it is clear that the expression ‘A is said of all of which B is said’ means this, ‘A is said of all the things of which B is said’. And if B is said of all of a third term, so also is A; but if B is not said of all of the third term, there is no necessity that A should be said of all of it (APr 49b14-31).

So we don’t want to say that because all horses are animals, everything that a horse has, like a head, is something that every animal has. Some animals, after all, could be headless! And what we really mean to say is that, since ‘animal’ is the genus of ‘horse’, and since a horse has a head, an animal has a head. Perhaps, then, we should formulate the argument as follows:

21. All horses are animals.
22. All horses are those that have heads.
∴23. Some of those that have heads are animals.

By making the conclusion particular, we do not run the risk of affirming that all animals have heads to the consternation of amoebas and sponges. The preceding argument is Darapti, and it is a valid syllogism, barring any objections on the grounds of existential import.1 However, it is not quite what HHA demands. Recall that we need to conclude that ‘the head of a horse is the head of an animal’, since ‘horse is animal’. To approximate the conclusion more closely, we might use repetition. Aristotle mentions the use of repetition in the syllogism, but stipulates how it is to be used. We find in Prior Analytics A38:

A term which is repeated in the propositions ought to be joined to the first extreme, not to the middle. I mean for example that if a deduction should be made proving that there is knowledge of justice, that it is good, the expression ‘that it is good’ (or ‘qua good’) should be joined to the first term. Let A stand for knowledge that it is good, B for good, C for justice. It is true to predicate A of B. For of the good there is knowledge that it is good. Also it is true to predicate B of C. For justice is identical with a good. In this way an analysis of the argument can be made (APr 49a11-18).

So, Aristotle sets down that A is ‘knowledge that it is good’, B is ‘good’, and C is ‘justice’. Formally, the proof would be:

24. AaB (Knowledge, that it is good, belongs to all good.)
25. BaC (Good belongs to all justice.)
∴ 26. AaC (Knowledge, that it is good, belongs to all justice.)

Let us set down that D is ‘animal, qua horse’, E is ‘horse’, and F is ‘head’. Still making use of Darapti, the argument would then be:

27. DaE (Animal, qua horse, belongs to all horse.)
28. FaE (Head belongs to all horse.)
∴29. DiF (Animal, qua horse, belongs to some head.)

Or, in a more readable English prose:

30. Every horse is an animal in virtue of being a horse.
31. Every horse is that which has a head.
∴32. Some of those which have heads are animals, in virtue of being horses.

Now one might protest that the conclusion reached here is particular, whereas in predicate calculus one reaches a universal conclusion. But what does that universal conclusion really say? It says that, for all things x and y, if x is a horse and y is the head of x, then x is an animal and y is the head of x. In effect, it is not saying that the head of a horse is an animal head, but that if something is a horse and it happens, also, to have a head, then it is an animal that happens to have a head. Is this the same as HHA? There is no real sense in which the deduction formed by predicate logic has anything to do with the relationship between genus and species, as De Morgan indicates. But the categorical syllogism that we have formed does have this information, in that a horse belongs to its genus in virtue of belonging to its species.

I grant that the conclusion of the categorical syllogism is syntactically divergent from HHA. Nonetheless, I think it captures a similar, if not the same, sense.  Perhaps this is the best we can do.

1For those who are particularly bothered by the “existential fallacy”, we could run a similar argument on Datisi.

References:

Aristotle. 1995. “Prior Analytics.” In The Complete Works of Aristotle: The Revised Oxford Translation. Trans. A.J. Jenkinson. Ed. J. Barnes. Vol. I. Princeton, New Jersey: Princeton University Press.

De Morgan, A. 1847. Formal Logic. London: Taylor and Walton Booksellers and Publishers.

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