Answering Aron Ra’s Epistemic Claims Regarding His Criterion for Modal Evaluation

This article may result lengthy and arduous for the reader not used to read philosophical material.

 

INTRODUCTION

A few days ago I encountered, thanks to the Facebook page “Capturing Christianity”, a Youtube video showing the popular atheist Aron Ra discussing the nature of evidence with Christian philosopher Blake Giunta (also the author of the great website https://beliefmap.org).

What made me write this article after such a long break from blogging was a quite perplexing claim made by Aron Ra regarding the existence of God.

This is the link to the video I will be discussing: https://www.youtube.com/watch?v=d0pbKcGCHUk&t=473s

Around the 7th minute of the video, Blake Giunta asks Ra whether he thinks God exists. He answers that he regards God’s existence as impossible. Quite reasonably Giunta responds by asking if he reached that conclusion by, for example, assessing a contradiction/incoherency within God’s nature.

Ra replies that this position is based on the fact that “you can’t declare something is possible until you can show the precedent, parallel and verified phenomena indicating such a possibility exists” (minute 7:20).[1]

Let me now delve into what I want to focus on: the absurdity of this last claim. My critique towards his criterion used to asses the modality[2] of a proposition such as the one “God exists” will be divided into nine parts each corresponding to a different type of criticism. Let’s remember that the criticism doesn’t take in account only this proposition in itself, but also the fact that Ra uses it to assess God’s impossibility.

 

PRELIMINARY INFORMATION

When we are talking about the possibility, impossibility or necessity of the thing a proposition is referring to, we are within a field of philosophy called modality (or modal logic).

Such options (i.e. possibility, impossibility, and necessity) can be evaluated on a logical level and a metaphysical one. The logical modality of a proposition is more fundamental than the metaphysical one in the sense that it precedes it in the order of modal evaluation. This is the case because an object in order to be metaphysically possible has to be logically possible, but something to be logically possible doesn’t necessarily have to be metaphysically possible. It follows that usually logical possibility is assessed first and then metaphysical possibility is taken into account.

Another thing I want to mention is that I will use the terms criterion and principle interchangeably.

This  is what I hold to be the central argument by Ra: “you can’t declare that something is possible until you can show the precedent, parallel and verified phenomena indicating such a possibility exists”, which, when thought to entail God’s impossibility, entails also the truth of the proposition: “something is impossible until a parallel, precedent, verified phenomena indicates its possibility”.

Let’s see why this proposition, or this sum of propositions, is false.

 

CRITICISM 1

Ra’s argument implies that the default modal evaluation of something has to be the one of impossibility (given that he asserted that God is impossible unless proven otherwise). The problem with this position is that he is ignoring what impossibility actually is: as philosopher Richard Swinburne writes in his book  “The Coherence of Theism” (page 11,12), impossibility arises from a contradiction[3], not from a lack of positive evidence for possibility or necessity. The fulfilling/actualizing criterion[4] for impossibility is a contradiction[5], not absence of evidence of alternative modalities. I agree that if positive evidence were offered against the other modalities (i.e. necessity and possibility), then we would have an argument for impossibility. But the absence of positive evidence is not a positive proof against possibility and necessity when it comes to an entity studied, given our epistemic position which allows development of knowledge, especially when it is the existence of God which is addressed.

Impossibility cannot hence be assumed, for, by its own nature and definition, to be proclaimed, an assessment of the fulfillment of its own conditions of existence has to be made (i.e. a contradiction has to be found).

At this point, we can conclude that the lack of evidence for possibility does not entail impossibility.

Therefore, in the presence of absolute cluelessness regarding a modal status, a more honest position would be the one of agnosticism, ergo “I do not know it’s modal status”.

 

CRITICISM 2

His default position is arbitrary. Why should the default position, when the modality is not known, be the one of impossibility? Why impossibility but not necessity?

He gives us a clue to why his criterion would overcome this objection when he says that the default position of possibility is falsified by the fact that such presumed modal status is often shown to be false when something is discovered to be not possible (minute 7:40).

The first thing to say is that such falsifications would bring us to conclude that all a priori default modal claims ought to be avoided. A simple ‘reductio’ shows how his position is clearly defeated by his reason to avoid possibility as a default modal claim: all types modal assessments (possibility, necessity, and impossibility) can be falsified and corrected.

This tells us nothing on which modal claim is the less presumptuous that is the one which less warrant or fulfilling conditions are needed (besides the fact that the fulfilling conditions besides being less, would have to be more probably true that their rival hypothesis) and hence is more justified in being a default position.

By his own reasoning, impossibility should not be taken as default because it is often falsified.

 

CRITICISM 3

The position of “possibility” is actually the most modest position, therefore the less presumptuous and therefore the best candidate for a default position (if one is ever to be taken). This can be seen from the nature of the entailments of the respective definitions of necessity, possibility, and impossibility. Such entailments, because definitional, are necessary and therefore, when they are shown to be false, disprove the theory (in this case, the modal status) from which they arise.[6]

So let’s see the entailments of the three modal claims we are addressing:

-Impossibility asserts/entails that the proposition/entity is “false in all possible worlds”.

-Necessity asserts/entails that the proposition/entity is “true in all possible worlds”.

-Possibility asserts/entails that the proposition “true in at least one possible worlds”.[7]

Given these entailments, it seems evident that the claim of possibility is the most modest among the three. The least pretentious claim is the least probably false (given the least need for warrant which implies the least possibility of falsification).

The modal status of possibility, in fact, possesses (given its entailments) the least amount of defeaters (that is, incompatible propositions that falsify the proposition in question) when compared to the other modal statues.

For this reason, “possibility” deserves, if such a thing exists, to be the default and most prudent modal assumption.

 

CRITICISM 4

His modal claim is an ontological claim while his argument is epistemic in nature. His argument claims to reach ontological conclusions: i.e. God does not exist, while his argument in potency has only the power to reach conclusion regarding justified belief, an epistemic concern, and not regarding existence, which is an ontological concern. Let me develop.

Instead of concluding, given his argument, that God’s existence is impossible (ontological claim) he should have deemed the belief in God as irrational (epistemic claim).

A sentence consistent with his argument would have been, for example, “we should not believe in him because we cannot know whether his existence is even possible”. Giunta realized this very clearly and in fact he stated in reply to Ra, starting from minute 8:33 of the video: “you presumably mean it’s irrational to say that a proposition is possible unless [you can show the precedent, parallel and verified phenomenon]”.

The nonsensical ontological pretension of Ra’s claim is shown by the absurd entailments of his criterion when interpreted ontologically. Let’s remember that his argument is not simply the truth of the criterion, but the fact that this principle entails God’s impossibility. As already mentioned, such thing implies that he believes in the proposition that: “something is impossible until a parallel, precedent, verified phenomena indicates its possibility”.

Here are the absurdities:

a) an object would not exist (because impossible) before discovering a parallel object. Subsequently, your discovery would somehow bring about the existence of the object (or the idea of the object) you were trying to find a parallel of. This is clearly absurd! But this is even more absurd once you realize that the object which you were trying to find a parallel of, not only was precedently not existent, but had a modal status of impossibility, that is, it could not.  So an object which you believe cannot exist then starts to exist! And this is different from the person who mistakenly attributes a false modal status to then recognize the real one. Here the person determines somehow the modal status to a degree in which he can bring about a contradiction (i.e. mysteriously making exist, that means therefore making possible, something impossible). Here it is not the subject that conforms to the object, but the object that conforms to the subject in the most radical way conceivable, beyond the imagination of even the most radical German idealist!

If this position (the ontological interpretation of Ra’s criterion) wants to be defended, the almost comical proposition “things are always contingent to their similar and their existence is dependent on the knowledge on the similar” has to be proven.

b) Not only the objects possibility would mysteriously depend on the subject’s cognition[8], but it would also be somewhat dependent on this parallel object/phenomenon. Let’s say for example that to assess the possibility of point mutations you had to witness another point mutation (which would be the verified parallel phenomenon that confirms the first). For some reason, the existence and hence possibility of the first mutation is ontologically connected and dependent on the second. This weird connection among object and, more generally, this weird metaphysics, I believe, argues against Ra’s claim.

c) A further problem that this principle seems to entail, is that it is impossible for a first fact/thing/event to be true/exist. I say this in light of the ontological dependence that the phenomenon has to have on another phenomenon and in light of the clause “precedent” present in the formulation of Ra’s principle, for there is nothing precedent to a first fact/thing that verifies this. In other words, according to this absurdity, the first thing of a certain type of things cannot possibly exist for no parallel thing/phenomenon is to be found. Is it possible for example for an illiterate person to become literate? If so, how could it have been possible for the first illiterate to become literate not having any parallel phenomenon that can ground and verify that possibility? Such thing, therefore, implies that he who wants to defend the ontological interpretation of the criterion has to believe that the parallel phenomenon is always concomitant (that is, it exists and came into existence at the same time).[9]

Now a person may say: “it is obvious that the criterion simply had epistemic pretensions”. Well, if so, Ra misspoke because he was answering an ontological question: “does God exist”, not whether the belief in God is rational; and he answered that God’s existence is impossible (minute 7:14 of the video).[10]

Giving the benefit of the doubt, and assuming he simply didn’t express himself correctly, I hold that this criticism (Criticism 4) would fall if, at least in the intention, if not propositionally, the argument was an epistemic and not ontological claim. Therefore, if the claim is ontological, all my objections in this article will apply to his criterion (9 out of 9), if the claim is epistemic all the objection expect most of this one will apply to his criterion (8 out of 9).

 

CRITICISM 5

For a complete understanding of this following argument, I advise reading also the note section (in particular note 15, 16, and 17).

The criterion is self-defeating. This is the answer offered by Blake Giunta during the conversation (minute 7:53). Let me develop upon his briefly mentioned insight.

A criterion/principle has the presumption to be comprehensive in the context which it addresses, if not, there has to be a reason for such restriction.[11] For example, if a restriction where to be made on the criterion itself, given the counterintuitivity of such thing[12], a reason has to be provided. In the absence of such a reason, a counterexample to the principle acts as a defeater[13] to the principle itself. The restriction cannot simply be “it applies in every case except to itself because this is what happens”, this would be a circular argument in which the criterion is assumed to be true. Reasons have to be given in order to justify a limited restriction to a criterion, in particular, why it shouldn’t be falsified when applied to itself.

So how does the principle “you can’t declare something is possible until you can show the precedent, parallel and verified phenomena indicating such a possibility exists” apply to itself? Which means: “what is the precedent, parallel and verified phenomenon that verifies this criterion?”

Before answering this question let me make an important clarification: It can be conceded that a precedent, parallel and verified phenomenon may be an indicator of possibility. I believe that this criterion could have maybe an aspect of argumentative sufficiency, but not necessity. In fact, the big issue I have with Ra’s criterion is not the more plausible alternative formulation of the principle which is: “something is shown to be possible if a precedent, parallel and verified phenomenon is provided”; rather, I have a problem with the clause (which Ra affirms) “you can’t declare something to be possible unless a parallel etc”. Clearly, he didn’t simply misspeak and intended the second version, for he concluded God’s impossibility from this principle[14].

Therefore, according to Ra’s formulation, all things have to pass this criterion in order to be possible.

So now let’s apply Ra’s criterion to itself. What parallel phenomenon verifies this criterion? Another criterion presumably (for something parallel in this case has to be a criterion), but this other criterion is impossible until a precedent, parallel and verified phenomenon is shown. This would create an endless chain of needed verification.
Clearly the first criterion, for example Ra’s principle (let’s call it C1), which needs verification, cannot sustain the criterion (C2) which ought to verify it. C1 cannot sustain C2 while C2 is sustained by C1, because C1 is not verified until C2 is provided, but the C2 provided is not yet verified so it cannot be used by C1, and C1 is still not verified (it cannot be verified by an unverified principle like C2) therefore it cannot be used to verify C2.[15] Because of how Ra’s principle is formulated, an “a priori” assessment of what is true is not allowed (because truth depends at least on possibility, if not necessity) and something can be said to be possible only after this other parallel phenomenon is provided.[16] Consequently, we have fallen into an infinite regress which is not only ontological in nature but, above all, epistemological!

How can we keep providing parallel phenomenon without an end (the principle does not allow a stopping point) to show something is possible (even if such phenomena were to actually exist)? This infinite regress shows ultimately that no actual phenomenon can be ontologically and/or epistemically possible. The ontological impossibility of any phenomenon would entail that nothing exists (because impossible), while the epistemic one would entail that we cannot say that anything exists (because everything has to be deemed impossible).[17]

Now a careful reader might ask if this objection (Criticism 5) may be overcome by W.L.Craig’s plausible principle that “in order to recognize that explanation (x) is the best, you don’t need an explanation of the explanation”[18]? In this sense, it could be said that the parallel phenomenon counts as the explanation for the possibility of a phenomenon without the need to find the further explanation (parallel phenomenon) of the second parallel phenomenon. The answer to whether this overcomes the problems previously highlighted is a definitive “no”! The reason is that if Ra’s criterion is true, Craig’s criterion is clearly false, for the “best” explanation provided, until a further explanation is provided, is an impossible explanation! And, clearly, an impossible explanation is not an explanation!

To conclude Ra’s criterion ultimately will never find a possible precedent, parallel and verified phenomenon (criterion) in order to be deemed possible! Ra’s principle, therefore, demonstrates its own impossibility.

 

CRITICISM 6:

His criterion excludes from existence entities that can exist and actually do exist.

In order for Ra’s criterion to be true, several contrasting seemingly true propositions have to be denied by the person who wants to defend Ra’s principle. The absurd denial of these contrasting propositions will represent a strong “reductio ad absurdum” against Ra’s principle.

Ra’s principle (which we call here for simplicity RP) in fact denies that:

1) “Things that do not have a parallel (or that do not show to have) a parallel phenomenon can exist or be said to exist.” (we shall call this proposition DFR, that is “Defeater of Ra’s principle)

Let’s see now how this proposition acts as a defeater towards Ra’s claims, which signifies showing how the contradiction of the two propositions is resolved in the denial of Ra’s principle.

a) The ontological version of Ra’s principle is contrasted by the fact that there is no reason to believe that something unique can’t actually exist (that is, things that do not have a parallel phenomenon). Therefore the intuitive trustworthiness of DRP reveals the falsity of RP.

b) The epistemic version of Ra’s principle is contrasted by methods that assess existence of something in and of itself independently from any parallel phenomenon. Such methods will constitute a further defense for DRP.

Therefore “something can be shown to be possible even without showing a ‘precedent parallel and verified phenomenon indicating such a possibility exists’” is confirmed by:

the empirical method (something can be said to exist, hence be possible, simply by empirically assessing its existence),

deductive reasoning in which conclusions are based on self-evident principles (and therefore principle not based on something else to be verified) which are believed to be true (and therefore also possible). We intuitively know the truth of these principles without the need of a parallel. We know that “good ought to be done” in and for itself, we know that “mutually exclusive propositions cannot both be true” given the inherent meaning of the proposition itself.
Further, all sound and valid arguments for the existence of God not founded upon the RP qualify as a strong defeater for Ra’s principle.

extrapolation and abstraction in which a phenomenon is assessed not thanks to something “parallel” but something different which simply points to a conclusion beyond itself, usually something bigger. Something also cannot be postulated as a purely explicatory device. For example, in standard Big Bang cosmology, dark matter and dark energy are postulated and regarded as true given entailments of the theory and their theoretical power to explain things. Clearly, these things are not counted as true or possible through verification, but rather through their theoretical capability to explain the observable data.

abductive reasoning in which an explanation is said to be the best explanation (which implies also its possibility) on grounds that go beyond it having a verified parallel (ex. Explanatory power, explanatory scope, ad hocness, plausibility, simplicity).

any “a priori” arguments which claim to reach truth/existence (both of which entail possibility) apart from any a posteriori investigation (which RP entails). The conceptual impossibility on an a priori argument has yet to be proven and therefore they currently act as evidence for DRP.

Ra’s criterion, therefore, allows only a specific type of inductive reasoning (which I call inductive comparative reasoning) excluding all other sound ways to reach a true conclusion. Such entailment of RP disproves RP given the validity which these methods of inquiry posses.

2) “Ultimately comprehensive entities can be said to exist.” (proposition which we I will call DRP2).

I define an ultimately comprehensive entity as something that includes in its entirety its subspecies in such a way that a parallel entity phenomenon cannot be possibly said to exist. For example, according to Ra’s principle, we cannot say that the universe exists. If we define “universe” as the “totality of physically existing things” the totality of physically existent things has no parallel, precedent and verified phenomenon given the fact that all possible purported things are included within the universe and therefore cannot be considered a verificatory parallel entity/phenomenon.

In other words, we can say that RP excludes the existence or belief in anything that is ultimately unique, such as the universe, and possibly even God. But Ra has yet to show why something unique which seemingly can exist, actually cannot exist , rather than being a defeater to his principle.[19] Given this assessment, proposition DRP2 reveals a further case for the falsity of RP.

In fact, Ra’s principle entails that “all possible things have a parallel phenomenon” but this claim has to be proven for Ra’s statement to be considered believable.

Even if Ra’s criterion is only epistemic, in order to work, there has to be an underlying ontology (reality) which allows this epistemic criterion to reach true conclusions. And what explanation if not the ontological fact that all possible things have a parallel phenomenon would show why this criterion works? It seems clear to me that this epistemic method entails that reality is made of things which all have a parallel phenomenon. While this state of affairs seems to be possible, why should it be true or actual? Is this just a brute fact? Is this a metaphysically necessary condition of existence? If so, why?

To conclude, this is my question: “Why does the proposition previously just mentioned have to be true?” In absence of a meaningful answer, the whole debate becomes worthless.

 

CRITICISM 7:

Swinburne’s case for metaphysical possibility via conceivability disproves Ra’s criterion.

Ra ignores what possibility is. Possibility, in fact, is 1) not ontologically dependent on a parallel phenomenon but, most of all 2) is not mainly shown to be true by showing a parallel phenomenon. Possibility is in fact assessed in the field of logic and epistemology on other grounds. In particular, possibility is assessed via conceivability[20].

Swinburne writes in his book “The Coherence of Theism”:

“[…] [A] conceivable proposition is one that it makes sense to suppose could be true[…]. To ‘conceive’ some proposition is to suppose that proposition, which does not entail a contradiction, to be true. To suppose a proposition to be true is not the same as to imagine it to be true, in the sense of visualizing it in one’s mind. Humans cannot (in this sense) imagine a figure having a thousand sides or a block of iron being solid, in that we cannot have a mental image of a thousand sides or of the solidity of the iron. (A block of iron with holes inside it would look the same as a solid block.) But we can conceive there being such things, because we can suppose there to be such things, without that supposition entailing a contradiction. It makes sense to suppose that there could be such things as a thousand-sided figure or a solid block of iron. What we can conceive is conceivable. But a proposition that some particular person cannot conceive, because he or she does not fully understand what it would be like for it to be true, may be conceivable because any person who does fully understand this can suppose it to be true without contradiction; but what is inconceivable cannot be conceived by anyone.” (page 12,13)

Therefore what is conceivable is logically possible because it does not entail a contradiction. What entails a contradiction is not conceivable (a squared triangle cannot be conceived) and hence ought to be regarded as impossible

Subsequently, Swinburne demonstrates in Chapter 3 of his book, that the metaphysical possibility of a proposition is assessed by substituting from the original logically possible proposition (that is, a proposition without an internal or entailed contradiction) co-referring informative designators for any of its uninformative designators (paraphrased from page 53).[21] If the propositions still maintains its status of logical possibility, such proposition ought to be regarded metaphysically possible.[22] As Swinburne shows, God passes this criterion and hence ought to be regarded as metaphysically possible. But regardless of whether God passes this criterion, the criterion in itself disproves Ra’s principle, for it shows how possibility (logical and metaphysical) is assessed apart from his method.

 

CRITICISM 8:

Even if the criterion is wrong, God meets this criterion anyway, therefore invalidating Ra’s argument for God’s impossibility.

Ra’s criterion is wrong, therefore God’s impossibility is not demonstrated. But what if the criterion were right? Would Ra be justified in concluding God’s impossibility? I hold that he would still be wrong. Is there a way in which parallel phenomenon argues for God’s possibility? I think so. As I already said (see Criticism 5) this criterion has argumentative power in the realm of sufficiency (it can provide evidence for possibility) but not necessity (when the principle isn’t verified it does not deny possibility).

This is what philosopher R. Swinburne does in his previously mentioned book “The Coherence of Theism”. For example, in chapter 7 of his book, he argues for the modal status of possibility of a spirit (which he defines as a person without a body) through the analysis of precedent, verified and parallel cases within the realm of human beings. If an unembodied mind is possible in the context of humanity we have an argument for at least one attribute of God, the fact that an unembodied personal agent can possibly exist.

And so on, significant parallels can corroborate God’s possibility.

Another example of how the possibility of one of God’s attributes is corroborated by parallel phenomenon, is how the capability of the immaterial to exercise causality in the physical/material world is shown to be possible by proving substance dualism[23] and hence the actual state of affairs in which our human mind, an immaterial substance, works upon a material substance.[24] This is an indicator of how it can also be “possible” for God to exercise causality in the realm of the material yet being a spiritual being.

Omnipotence can be shown in several ways. One of them is done by verifying the parallel phenomenon in which ontological restriction is shown to limit potency. Consequently, the lack of restriction will bring about an increase in potency and hence power. This implies that a purely actual substance (I.e. what God can be argued to be), being also purely simple, is all powerful (note this is only one argument, presented superficially; there are lots of others which, unlike this one, do not require Thomistic philosophy).

I would also argue that the whole scholastic debate regarding the issue of analogy (whether with Thomistic or Ockhamistic lenses) among God and creatures, is filled with useful material and insights which provide numerous verifying parallel phenomena indicating the possibility of a Christian God.

It is beyond the scope of this already lengthy article to defend thoroughly the points made in Criticism 8. For more detail, I advise reading the books mentioned.

 

CRITICISM 9

Ra’s criterion is unsustained. At prima facie, given what stated in criticism 3, I’ll assume the possible truth of his criterion. Nonetheless, a possibly true statement can either be true or not be true in a certain possible world. Is Ra’s criterion true in this one?

I hold that if a proposition is not self-evident, that is, if it is not evidently logically necessary or if it is not intuitively true (like the Principle of Sufficient Reason) or if it doesn’t constitute a basic belief (like what A. Plantinga would argue God constitutes), the proposition ought to be warranted with something outside itself (i.e. evidence).

Does my claim pass its own test (does it result coherent when applied to itself)? Yes, my claim not being evidently true in itself has to be argued.

Clearly, internal coherence does not imply truth but simply possibility. Nonetheless, I think the truth value of this last principle can be argued.

Coming back to my point, Ra’s statement, not being self evidently true, remains unwarranted when presented by itself. His principle remains in the realm, at best, of being regarded as potentially true.

We can therefore say that, considering only Criticism 9, P(h/k) is 0.5 (which means that “the probability of the hypothesis given the background evidence is as likely true as likely false”). When justified belief occurs we have P (h/k) > 0.5 (Which means that “the probability of the hypothesis given the background evidence is more likely true than false”). But clearly this article has shown, throughout Criticism 1 to 9, that P (h/k +e) < 0.5 by far (Which means that “the probability of the hypothesis given the background evidence and the new evidence presented is more likely false than true”).

 

God bless,

For the greater glory of Christ,

Amedeo Da Pra

 

[1] I excluded the “or” clauses (which might have been mentioned in his speech) between the three conditions (precedent, parallel, and verified) because he obviously intended the “or” as inclusive and not exclusive. Their presence would be misleading towards a non-expert. It is clear to everyone how something not only has to be precedent in order to argue for possibility, but also parallel and verified. What argumentative power would a precedent phenomenon which is not verified or parallel have? And so on, these conditions are inherently meant to function together. Also, by “phenomena” Ra probably meant “phenomenon” I will therefore use the term “phenomena” only when I directly quote is statement.

[2] I.e. what concerns possibility, necessity, and impossibility.

[3] To be precise, Swinburne makes a distinction between logical and metaphysical impossibility. The former consists in an internal contradiction which allows to assess it’s modal status a priori; the latter consists in something that can exist (if an entity) or be true ( if a proposition) only if “some different logical impossible proposition [or entity] was true”; hence its evaluation proceeds from a posteriori considerations.

[4] which would be the “antecedent” in a “hypothetical”, that is the “p” in the relation “if p then q”

[5] which means that, when affirmed, makes true/actual the consequent (by modus ponens), therefore making true the argument.

[6] To restate this in more precise terms, in a formal hypothetical proposition (if p then q) the modal status would represent the antecedent (the “p”), while the definitional entailment would be the consequent (the “q”). Given the rules of classical and modern logic, the denial of the consequent represents a defeater for the antecedent (such logical relationship is called “Modus Tollens”). Therefore “not q” (written ¬q) brings about” not p (written ¬p).

[7] For more information on this specific issue see https://en.wikipedia.org/wiki/Possible_world (link from which I borrowed some definitions). See also https://en.wikipedia.org/wiki/Modal_logic#The_ontology_of_possibility and https://plato.stanford.edu/entries/logic-modal/#WhaModLog

[8] See the clause “until you can show” from Ra’s criterion.

[9] At this point, a question arises:” Why would the parallel phenomenon, given that reality exists, come about together besides the fact that they would have to come about together if they had to exist?”. Clearly, most (to be conservative) of existing things result to be contingent and therefore do not “have to exist”. So why do phenomena happen to come into existence with their parallel? Is it a brute fact? If so, this brute fact counts as a defeater against Ra’s principle given the fact that there are theories (al ontologies that do not include Ra’s principle) which do not entail such inexplicable facts. A theory, in fact, which makes reality explicable ought to be preferred to the theory which entails the inexplicable.

[10] Ra’s literal answer was: “God is not even possible”. I assume that answer means that God’s existence is impossible even if, on a literal point of view, the “not even possible” clause could mean “necessary”.

[11] For more information and a detailed defense on this specific statement read my article https://apologeticaecreazione.wordpress.com/2017/08/22/largomento-cosmologico-di-leibniz-e-la-difesa-del-principio-di-ragion-sufficiente/ and the book “The Principle of Sufficient Reason: A Reassessment” by A. Pruss in which he provides a similar and more detailed argumentation.

[12] The counterintuitivity is assessed by the lack of an apparent answer to the question: “why should it not be applied to itself?”. Such counterintuitivity is reinforced by the background evidence of the scope of a principle which is always comprehensive and generic in nature with respect to what is addresses. To conclude, the burden of proof lays, when the principle is assumed or shown to be true, on he who asserts where the principle does not apply and not where it does.

[13] Definition of defeater: “a defeater is a belief B1 that is held to be incompatible with another belief B2, hence arguments or evidence supporting B1 can be used to refute B2” (taken from Wikipedia article “Defeater”)

[14] The clause he inserts inverts the sound hypothetical: “if we have a parallel, then we have possibility” with the unsound hypothetical “if we have possibility, then we have a parallel”. The “consequent” (the clause after the “if”) in a hypothetical represents the necessary conditions for the fulfillment of the “antecedent” (the clause before the “if”). The fulfillment of the antecedent, on the other hand, represents the sufficient condition for the truth of the hypothetical and implies necessarily the consequent. Having said this, it is clear how holding to the sound version of the principle asserts its sufficiency, while holding to the unsound one asserts its necessity (which has proven to be false throughout this article).

[15]  I emphasize temporal progression because the principle stated by Ra implies such progressional confirmation of events which completely rules out circular mutual causality, given the fact that the principle demands linear causality. Even if the two parallel phenomenon were to be brought about together, this single pairing of phenomena, according to the principle, would have to have a parallel phenomena itself in order to be verified and be regarded as possible. So, no matter how you start, and how you try to insert mutually dependent causality, you cannot avoid an infinite regress.

[16] If the ontological interpretation were to be taken, which would entail that the subject renders the phenomenon possible by his sentient verification, we would incur in the explicit contradiction among the two entailments of the principle itself: on one side phenomena ought to be concurrent (see Criticism 4 point c), on the other, as just mentioned, the sentient action of the subject, which recognizes the parallel phenomenon, happens within a temporal sequence which excludes the contemporaneous/concomitant presence of the two parallel phenomenon. This paradox counts as a further defeater against Ra’s principle.

[17] The ontological impossibility can be further defended though arguments against an actual infinite and the impossibility of reaching infinity by passing through each singular member of the infinite set (see W.L. Craig’s argument for the Kalam Argument here https://www.reasonablefaith.org/writings/popular-writings/existence-nature-of-god/the-kalam-cosmological-argument/). If the interpretation of the criterion is ontological in the sense described in Criticism 4 a), the fact that our power to recognize possibility is limited, given our limited lifespan, counts as a further defeater against this infinite regress. If the interpretation of the argument is epistemological, nonetheless the finitude of our life, makes for us impossible to assess the possibility of a proposition through a parallel proposition whose possibility is assessed (given the infinite amount of time that it would require us to reach such a proposition, granted such proposition can even be reached). As you can see, this argument would go against an infinite regress regardless of whether Craig’s second philosophical argument against an actual infinite is sound or not (which states that an actual infinite cannot be reached by passing through each singular member of the infinite set because, even if it were possible conceptually, our limited lifespan would make it impossible).

[18] https://www.youtube.com/watch?v=w4AHFBft2L8

[19] The reasons that have to be provided have to go besides the principle itself because using the principle against it’s contrasting evidence (the fact that unique things and ultimately comprehensive entities seemingly have a possible existence) is a circular reasoning in which the principle under fire is assumed to be true or not regarded to be weakened by the objection.

[20] See “The Coherence of Theism) by Swinburne page 12 which quotes the following works: “Does Conceivability Entail Possibility?” in T.S. Gendler and J. Hawthorne, Conceivability and Possibility, Oxford University Press, 2002) and “Is Conceivability a Guide to Possibility” by S. Yablo in Philosophy and Phenomenological Research, 53 (1993), 1-14.

[21] An informative designator is a rigid designator (that is, a term that “refers to the same object, however the object may change in respect of its non-essential properties”) which people know its meaning, that is, know “the criteria determining under what conditions it applies to a thing” and know “what those conditions are”. The sentences in brackets are quoted from the book (respectively page 48 and 50).

[22] For the person who doesn’t recognize the inherent plausibility of this principle, I advise reading the whole third chapter of Swinburne’s book.

[23] As done by J.P. Moreland in his books https://www.amazon.com/Consciousness-Existence-God-Theistic-Argument/dp/0415989531, https://www.amazon.com/Recalcitrant-Imago-Dei-Persons-Naturalism/dp/0334042151/ref=pd_lpo_sbs_14_t_2?_encoding=UTF8&psc=1&refRID=TM5ZRDFKW9JE9FPQBTZK,  and in his more popular work https://www.amazon.com/Soul-How-Know-Real-Matters/dp/0802411002/ref=pd_lpo_sbs_14_t_1?_encoding=UTF8&psc=1&refRID=TM5ZRDFKW9JE9FPQBTZK

[24] Just for clarification, this basic description of mind-body interaction, given its general wording, does not entail any specific Dualistic theory such as the Cartesian one or the Thomist one.

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