bookmark_borderReply to Dr. Erasmus – Part 3: Clarification of My Reasoning


In Part 1 and Part 2 of this series, I have shown that Dr. Erasmus’ objection to my skeptical reasoning (a) attacks a STRAW MAN, and (b) is based on an INVALID INFERENCE.  In doing so, I also argued that Dr. Erasmus does not have a good understanding of probability calculations, especially concerning the use of Bayes’ Theorem.
In this post I will further defend my skeptical reasoning about the resurrection of Jesus found in the post that has been criticized by Dr. Erasmus. I will do so by presenting this skeptical reasoning in more detail, with more logical and mathematical rigor, and with greater clarity.


If we know for certain that statement (S) is TRUE, then the probability of (S) is ONE:

P(S)  =  1.0

If we know for certain that statement (S) is FALSE, then the probability of (S) is ZERO:

P(S)   =   0

If it is as likely as not that (S) is TRUE, then the probability of (S) is ONE-HALF:

P(S)   =   .5

The probability of each and every statement is greater than or equal to ZERO, and is less than or equal to ONE:

0  ≤  P(S)  ≤  1.0

Because a statement is either TRUE or it is not TRUE, the probability that a particular statement is TRUE when combined with the probability that it is not TRUE is equal to ONE:

P(S) + P(~S)  =  1.0

If two statements have the same truth value in any circumstance, then they are logically equivalent:

(S)  ≡  (Q)

If two statements are logically equivalent, then the probabilities of those statements are EQUAL:

IF (S)  ≡  (Q), THEN P(S)  =  P(Q)

If one statement logically implies another statement, then the probability of the second statement is greater than or equal to the probability of the first statement:

IF (S)  É  (Q), THEN  P(Q)  ≥  P(S)

The probability of one statement (S) GIVEN THAT another statement (Q) is the case is a conditional probability:


If the statement (Q) logically implies the statement (S), then the conditional probability of (S) GIVEN THAT (Q) is ONE:

IF (Q)  É  (S), THEN  P(S|Q)  =  1.0

If the statement (Q) logically implies that statement (S) is not the case, then the conditional probability of (S) GIVEN THAT (Q) is ZERO:

IF (Q)  É  (~S), THEN P(S|Q)  =  0

We can define the probability of a CONJUNCTION of two statements in terms of a CONDITIONAL PROBABILITY:

P(S & Q)  =  P(S|Q)  x  P(Q)

Note that the probability of (S & Q) is EQUAL TO the probability of (Q & S), in other words the order of the conjuncts makes no difference to the probability of the conjunction:

P(S & Q)  =  P(Q & S)

So we can infer another equation concerning the probability of a CONJUNCTION:

P(Q & S)  =  P(S|Q)  x  P(Q)

A basic principle of CONDITIONAL PROBABILITY is that the probability of one statement GIVEN THAT another statement is the case is EQUAL TO the probability that both statements are true DIVIDED BY the probability that the second statement is true:

P(S|Q)  =  P(S & Q) / P(Q)

Note that the probabilities on the right side of the above equation are UNCONDITIONAL PROBABILITIES, so this is a definition of CONDITIONAL PROBABILITY in terms of UNCONDITIONAL PROBABILITIES.   Because division by zero is undefined, the value of P(Q) must be greater than zero for this formula to work.
BAYES’ THEOREM can also be derived from the above basic principle of CONDITIONAL PROBABILITY:

P(S|Q)  =  [P(Q|S) x P(S)]  /  P(Q)

If the UNCONDITIONAL PROBABILITY of a statement EQUALS the probability of that statement GIVEN THAT another statement is the case, then those statements are INDEPENDENT of each other, in other words, the truth value of one statement has no impact on the probability of the other statement:

IF P(S)  =  P(S|Q), THEN (S) and (Q) are INDEPENDENT statements.

The probability of the CONJUNCTION of two INDEPENDENT statements EQUALS the product of the probabilities of those statements:

IF (S) and (Q) are INDEPENDENT statements, THEN P(S&Q)  =  P(S)  x  P(Q)


(GRJ) God raised Jesus from the dead.
(GPM) God has performed at least one miracle.
(JRD) Jesus rose from the dead.

What does the statement “God raised Jesus from the dead.” mean?  The meaning of a statement consists of the logical implications of that statement.  Here are some important logical implications of (GRJ):

  • (GRJ) implies (GPM)
  • (GRJ) implies (JRD)

Recall this basic principle of probability:

IF (S) implies (Q), THEN  P(Q)  ≥  P(S)

Based on this principle, we can draw some important inferences:

  • P(GPM)  ≥  P(GRJ)
  • P(JRD)   ≥  P(GRJ)

Furthermore, since (GRJ) logically implies both (GPM) and (JRD), it implies the conjunction of those two claims:

(GRJ)   É   [(GPM) & (JRD)]

This allows us to draw another inference using the above principle of probability:

P[(GPM) & (JRD)]   ≥  P(GRJ)

In English: The probability of it being the case both that God has performed at least one miracle and that Jesus rose from the dead is GREATER THAN OR EQUAL TO the probability that God raised Jesus from the dead.  So if we can determine the probability of it being the case that both (GPM) and (JRD) are true, that will establish an upper limit on the probability that (GRJ) is true.
We can use the general multiplication rule to draw this inference:

P[(GPM) & (JRD)]  =  P(GPM|JRD) x P(JRD)

And then we can use the substitution of equivalents to draw this inference:

P(GPM|JRD) x  P(JRD)   ≥   P(GRJ)

Let’s consider one element of this equation, the probability that Jesus rose from the dead:


The claim that Jesus rose from the dead can be analyzed into two basic components:

(DOC) Jesus died on the cross on the same day he was crucified.

(JAW) Jesus was alive and walking around in Jerusalem about 48 hours after he was crucified.

If these two claims are both TRUE, then so is the claim that Jesus rose from the dead:

[(DOC) & (JAW)]   É   (JRD)

What Dr. Erasmus fails to notice, and fails to understand, is that the reverse is also the case:

 (JRD)    É   [(DOC) & (JAW)]

If the conjunction of (DOC) and (JAW) implies (JRD, and (JRD) implies the conjunction of (DOC) & (JAW), then we have a logical equivalence:

(JRD)   ≡   [(DOC) & (JAW)]

Recall the probability relationship between logically equivalent statements:

IF (S)  ≡  (Q), THEN P(S)  =  P(Q)

So, we can infer the following important probability relationship:

P(JRD)  =   P[(DOC) & (JAW)]

There are some plausible objections to my claim that (JRD) implies (DOC) and (JAW).  There appear to be various logically possible scenarios where we would be inclined to say that it is TRUE that Jesus rose from the dead, even if (DOC) was FALSE.  There also appear to be various logically possible scenarios where we would be inclined to say that it is TRUE that Jesus rose from the dead, even if (JAW) was FALSE.
Here are a few such counterexamples:
Alternative Location:  Jesus was crucified in Rome and he died on the cross on the same day he was crucified, and he was entombed in Rome and was alive and walking around in Rome about 48 hours after he was crucified.
Alternative Death:  Jesus was NOT crucified, but he was killed by being be-headed.  He then was entombed, and he was alive and walking around in Jerusalem about 48 hours later.
Long Crucifixion: Jesus died on the cross, but only after hanging on the cross for a week.  He then was entombed, and he was alive and walking around in Jerusalem about 48 hours later.
Long Entombment: Jesus died on the cross on the same day he was crucified, but after his body was placed in a tomb, he stayed dead for a week and then came back to life and walked around in Jerusalem.
Non-walking Jesus:  Jesus died on the cross on the same day he was crucified, and he was alive in Jerusalem about 48 hours later, but he never walked again, but was instead carried around everywhere by his disciples.
In all of these scenarios we are inclined to say that it is TRUE that Jesus rose from the dead, but that either (DOC) or (JAW) is FALSE.  However, there are a couple of considerations that mitigate the force of these counterexamples.
If Jesus was NOT crucified, but was actually be-headed, then the Gospel accounts of the death of Jesus are works of fiction that have little connection to reality and actual history.  Similarly, if Jesus was crucified, but the crucifixion took place in Rome rather than in Jerusalem, then the Gospel accounts of Jesus’ death are works of fiction that have little connection to reality and history.  In other words, in the case of most such counterexamples we imagine scenarios that are completely contrary to what the Gospel accounts of Jesus’ death and burial and resurrection state, and so if such a scenario was TRUE, then that would largely or completely destroy the credibility of the Gospel accounts of Jesus’ death, and burial, and resurrection.  But if the credibility of the Gospel accounts is largely or completely destroyed, then there is NO HOPE of establishing the resurrection of Jesus.
So, although I admit that we can imagine scenarios in which it appears that (JRD) is TRUE but (DOC) or (JAW) was FALSE, such scenarios would at the same time destroy the credibility of the Gospel accounts of Jesus’ death, burial, and resurrection, thus destroying the possibility of showing that it is PROBABLE that Jesus rose from the dead.  Such counterexamples, therefore, can be ignored, because they are NOT compatible with the aim of building a strong case for the PROBABILITY of the resurrection of Jesus.  Therefore, it is reasonable to treat (JRD) as being logically equivalent to the conjunction of (DOC) and (JAW), even though there are some logically possible scenarios in which (JRD) appears to be TRUE while (DOC) or (JAW) are FALSE.
A second mitigating consideration concerning these counterexamples is that what Christians mean by “Jesus rose from the dead” is something MORE than just the literal meaning of the words in this sentence.  We need to take into account the CONTEXT in which this statement is typically asserted.  In making this claim, most Christian believers have in mind the Gospel stories about the death, burial, and resurrection of Jesus.  In asserting that “Jesus rose from the dead” they have in mind various historical claims and details about how these events allegedly unfolded.  They are, in effect, asserting that the Gospel accounts of the death, burial, and resurrection of Jesus are basically correct, that those accounts are true for the most part.  I take it that the truth of their claim depends to a large degree on the truth of various key historical claims and details provided in the Gospel accounts.
Now, it would obviously be UNFAIR and UNREASONABLE to insist that the claim “Jesus rose from the dead” was FALSE unless EVERY last detail in all four canonical Gospel passion narratives was TRUE.  It is only reasonable to allow for some of the details in those accounts to be FALSE and yet to still admit that “Jesus rose from the dead” if enough of the key historical claims and details were TRUE.
If the Gospel accounts of the crucifixion of Jesus are true for the most part, and if the burial stories are true for the most part, and if the resurrection stories are true for the most part, then that could be enough to make it the case that the claim “Jesus rose from the dead” is TRUE, even if some of the details were incorrect or FALSE.  Therefore, the meaning of the claim “Jesus rose from the dead” when this claim is asserted by Christian believers is tied up with historical claims and details found in the Gospel accounts of Jesus’ death, burial, and resurrection.  The meaning of this claim, what it implies, is more than just the literal meaning of the sentence “Jesus rose from the dead”.  The additional details implied in this claim rule out many or most of the counterexamples to the logical equivalence of (JRD) with the conjunction of (DOC) and (JAW).
To Be Continued…

bookmark_borderResponse to Dr. Jacobus Erasmus on the Soul

It is always pleasing—especially these days—to see a critique that does not descend into invective. Dr. Jacobus Erasmus does me the favor of offering such a critique of my earlier blog post on the soul:
He gives his reply at:
Here I would like to offer a response.
In my OP, I gave three arguments against the existence of souls. First, though, I gave two reasons for why I consider the burden of proof to be on the defender of substance dualism, the claim that there exist substantial spiritual entities that constitute persons and which perform all mental functions. My first reason was this:

We know that certain configurations of matter—those configurations we refer to as “human beings,” for instance—are capable of performing mental functions. They think, feel, perceive, imagine, desire, will, believe, and so forth. If, then, certain configurations of matter can perform mental functions and possess mental properties, the parsimonious, spontaneous, and natural assumption would be that matter, when organized in suitable ways, can perform mental functions and possess mental properties.
It seems perverse to make the opposite assumption, namely that material beings cannot think, and that therefore their mental functions and properties must be due to the operation of something non-physical, a soul perhaps. To make this last assumption would seem to be a bizarre instance of an a priori prejudice. The proper starting point therefore appears to be that material beings are capable of doing whatever we observe them doing, not with the gratuitous and a priori assumption that they cannot.

Erasmus responds that this argument is viciously circular:

Parsons first assumes non-dualism in order to argue that one should first assume non-dualism, and this is viciously circular (I use the term ‘non-dualism’ as an umbrella term to refer to all views that claim that the soul does not exist, such as physicalism, materialism, and property dualism). When Parsons claims that it is the brain that can ‘think, feel, perceive, … and possess mental properties’, he is simply describing non-dualism. Dualism, on the other hand, states that it is the soul (or the immaterial mind or self), and not the brain, that feels, perceives, has mental properties, etc. Thus, Parsons first assumes non-dualism, and then he concludes on the basis of this assumption that one should first assume non-dualism…

But the argument is not circular at all. It makes no assumption whatsoever about souls, brains, or dualism. It simply makes the (I think) utterly uncontroversial and everyday assertion that we know that human beings think, feel, perceive, imagine, etc. In our own cases, that we are capable of doing these things is obvious to our first-person consciousness. With respect to others, we often see and hear them engaging in rational discourse and argument and displaying emotional reactions. Saying that we know that human beings think, feel, etc. is certainly no more controversial than saying that we know that chimps, cats, or dogs have a mental life. If I see my cat displaying anger, fear, or affection, then I conclude that cats are capable of feeling emotion. I further observe that, like cats, humans are physical beings, and I make no assumptions at all about anything more than physical that a human might be.
Therefore, from
(a) Human beings think.
(b) Human beings are physical beings.
I conclude that the parsimonious, natural, and spontaneous assumption should be:
Some physical beings are capable of thinking.
I see this reasoning as no more controversial or circular than:
(a) Cats have feelings.
(b) Cats are physical beings.
And so:
Some physical beings have feelings.
Further, it would be a piece of perverse a priori prejudice to recognize that some physical objects think, feel, etc. but to assume that they cannot qua physical, think, feel, etc. and instead to assume that such capacities must be due to hidden spiritual entities. In general, if F’s are known to G, then the assumption should be that F’s are capable of G-ing not that F’s are incapable of G-ing—which capacity must be attributed to something unobserved.
Where is the circularity? Actually, Erasmus puts in “brain” where I have said “human beings” and this creates an appearance of circularity, as though I were presuming a physicalist thesis when I am not.
If, then, it is utterly uncontroversial that some physical beings think and feel, then, as I say, it seems to be a peculiar a priori prejudice to begin the discussion on the assumption that such beings cannot think or feel, but only are capable of doing so by the operation of something nonphysical. Therefore it seems eminently fair to ask that those who think that, despite appearances, physical beings cannot think should bear the burden of proof.
A further reason I give for putting the burden of proof on the dualist is this:

… surely, by now, the heuristic assumptions of neuroscience have gained some degree of authority. As I mentioned earlier, a regulative assumption of all the sciences that study mind and brain is that the brain is sufficient for all mental activity. Perhaps, as David Chalmers famously argued, we may never solve the “hard problem,” that is, to understand exactly why some physical events should cause mental events. Still, Chalmers takes for granted that physical events cause mental events, so he accepts the regulative assumption. When a program of inquiry has produced hard, reproducible, and important results, as has neuroscience, then this would warrant prima facie acceptance of the heuristic principles that have guided such research.

To which Erasmus replies:

To make such a bold claim as ‘neuroscience presupposes (A)’, one must provide some evidence for the claim. Parsons does not do this. He does not reference any neuroscientist that explicitly states that (A) is the heuristic principle of neuroscience. Nor does he reference any study that supports his argument above. Nor does Parsons interact with the recent scholarly work that shows that Parsons has got it completely wrong. For example, in their recent paper titled ‘Neuroscience: Dualism in Disguise’, Riccardo Manzotti and Paolo Moderato (2014) persuasively argue ‘that most of current neuroscientists, contrary to often-heralded physicalist credo, embrace dualism … [and, furthermore] that the implicit assumptions adopted by most neuroscientists invariably lead to some sort of dualistic framework’ (Manzotti and Moderato, 2014:81). Contra Parsons, most neuroscientists assume dualism and, thus, according to Parsons’ argument, the burden of proof should fall, not on the dualist, but on the non-dualist.

My assertions about the regulative or heuristic assertions of neuroscience follow Owen Flanagan’s conclusions in The Problem of the Soul. After quoting a passage from a compendium of brain science to the effect that all the artifacts of human culture are accomplished by the brain, Flanagan concludes:

Modern mind science regulates its inquiry by the assumption that mind is the brain in the sense that perceiving, thinking, deliberating, choosing, and feeling are brain processes…That the mind is the brain is thus a regulative assumption that guides contemporary mind science. (Flanagan, 2002, pp. 77-78.)

Flanagan is a philosopher but also a professor of neurobiology, so he should speak with some authority.
Neuroscientist David Eagleman has this to say in the preface to his primer of neuroscience, The Brain (2015, p. 1):

The strange computational machinery in our skulls is the perceptual machinery by which we navigate world, the stuff from which decisions arise, the materials from which imagination is forged. Our dreams and our waking lives emerge from its billions of zapping cells.

Francis Crick offers what he calls “the Astonishing Hypothesis”:

The Astonishing Hypothesis is that “You,” your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behavior of a vast assembly of nerve cells and their associated molecules.” (Crick, 1994, p. 3).

William H. Calvin, a theoretical neurophysiologist, in his book with the telling title How Brains Think, locates our unique human aptitude for linguistic creativity in the brain:

Yet we are all constructing brand-new utterances hundreds of times every day, recombining words and gestures to get across a novel message. Whenever you set out to speak a sentence you have never spoken before…you do all your trial and error in your brain, in the last second before speaking aloud. (1996, p. 2).

Paul Churchland, another philosopher who has spent his career engaged with neuroscience, confidently claims that we now have exciting results:

…[W]e are now in a position to explain how our vivid sensory experience arises in the sensory cortex of our brains: how the smell of baking bread, the sound of an oboe, the taste of a peach, and the color of a sunrise are all embodied in a vast chorus of neural activity. (1996, p. 3).

These quotes should be sufficient to indicate that I was not making an idiosyncratic or groundless claim about the assumptions of neuroscience about the efficacy and sufficiency of the brain for the mental. Given more time and space, I am sure I could adduce quite a few more such quotes. At a more basic level, William Lyons’ excellent history of the philosophy and sciences of the mind, Matters of the Mind, makes very clear the decisive break with Cartesianism that occurred with the rise of behaviorism in the early twentieth century. As he shows, though behaviorism was rejected, the commitment to a third-person, scientific, and objective understanding of the mind was permanent and there has been no move, either in science or philosophy, to return to substance dualism.
As for the piece by Manzotti and Moderato, it does not deny what I assert, namely that neuroscientists explicitly invoke assumptions about the mental arising from the physical. Their argument is that neuroscientists implicitly accept a dualism that they explicitly reject. In other words, their argument is that neuroscientists are not aware of the actual implications of their own stated assumptions. Yet if neuroscientists are united in explicitly affirming physicalism, the burden of proof has to be on those who say that they are wrong, i.e. that they fail to recognize the implications of their own assumptions. This burden Manzotti and Moderato attempt to shoulder in their article, and this is the burden that I assert must be borne by those who oppose the explicit assumptions of brain science. In other words, Manzotti and Moderato accept the burden of proof and do not try to evade it as Erasmus does. Whether they are successful in their argument or not is not my place to say here. I would like to see the responses of practicing neuroscientists.
My first argument has to do with the interaction problem. Erasmus begins by offering an argument that I never make or endorse and attacks that straw man. I will pass over these passages in silence.
Erasmus’s statement of the interaction problem is quite inadequate:

Parsons’ first move against dualism is to appeal to the interaction problem, which states that it is difficult to see how a non-physical, immaterial entity, such as a soul, can causally interact with a physical entity, such as a brain.

But the problem is not merely that it is “difficult” to see how souls affect brains. This seriously understates the problem. The problem, is that in substance dualism “mind” and “matter” are defined in mutually exclusive terms. Mind has no physical properties; it is not composed of atoms or any other physical entities; it is not bound by the laws of physics or describable in terms of physical theory; it cannot be detected by any physical means; it is perhaps not even locatable in space. Its putative interactions with matter therefore must be of a wholly different sort than the interactions of physical things. For instance, interactions between fundamental physical particles are mediated by gauge bosons. Is that how it works with souls and matter? If not, how? We have very well developed physical theories about, say, the interaction of electrons and photons (quantum electrodynamics). With putative soul/body interactions there is a lot of speculation and hand-waving, but nothing definite—certainly nothing to compare to the detailed, coherent, rigorous, testable theories of fundamental physics. It is with justification that Flanagan says that dualists believe in psychokinesis.
The standard reply of substance dualists seems to be to concede that we do not know how souls and bodies interact but to assert the tu quoque that we do not know how bodies interact with bodies. Well, then, is it a tie? Are physical theories and soul theories equal in that neither can really explain interaction? Are we each just stuck with saying “shit happens” and that is all we can do? Here is what I said in the OP:

Even if we reach a brutally factual rock bottom in physical theory, where we just have to postulate fundamental entities and forces that turn out not to be further explicable, such brute facts lie at the end of a very long chain of deeply satisfactory explanations. Hume somewhere asserts that we will probably never understand why bread nourishes. Ah, but we do. We have for quite some time understood in very considerable detail how mitochondria break down complex carbohydrates and, via the chemical pathway known as the Krebs cycle, provide energy at the cellular level. Indeed, molecular biology is full of extremely detailed explanations of physiological processes that tell us why they happen just as they do. At a more basic level, nuclear physics can explain in detail why nuclear weapons bang so prodigiously. In innumerable cases, we do not say just that shit happens, but precisely why it happens.

But contrast the “explanations” offered by soul-theory:

With soul-theory, the incomprehensibility is right up front and on top. Your inquiry immediately hits a wall. “How do I think?” “Your soul does it.” “How does it do it?” “Let me explain: Shut up!” Sorry, but I am not just being flippant here. It matters where you put your brute facts. Mystery-mongers take you right to the occult, “explaining” in terms of astrological influences, or hexes, or psi, or chakras, or qi, or whatever. Honestly, the postulation of souls just seems to be another appeal to the occult. Neuroscience thinks we can go deeper without any such paranormal postulates, and we can.

Erasmus replies:

Parsons is essentially stating (without defending) the following argument:
(B1) A brute fact that lies at the end of a very long chain of deeply satisfactory explanations is acceptable.
(B2) If soul-body interaction is a brute fact, it does not lie at the end of a very long chain of deeply satisfactory explanations.
(B3) Therefore, it is unacceptable to claim that soul-body interaction is a brute fact.
As noted above, Parsons simply states these premises without defending them. But why, exactly, should it matter where a brute fact is situated in a chain of explanations? And why, if soul-body interaction is a brute fact, would it not be situated at the end of a long chain of satisfactory explanations? Surely such interaction would take place at a very fundamental (perhaps even quantum) level of physical reality, with the chain of explanations running up to a higher level, such as the brain itself. And why think that soul-body interaction must be a brute fact? Parsons does not interact with the dualistic arguments that try explain soul-body interaction (e.g., some argue that both the soul and brain have the property of being (or being able to be) conscious, and soul-body interaction occurs, not as a brute fact, but in virtue of the transference of consciousness from the soul to the brain).

Does it matter where, in an explanatory chain, we put a brute fact? Of course it does. Three centuries ago if you asked how bread nourishes the body the answer would be shrug. It just does. Nobody really knows how or why. Today we can give a very detailed answer to that question right down to the molecular level, and below. Suppose our current explanations still reach an explanatory “rock bottom,” maybe with the fundamental properties of fundamental particles. Who knows more about how bread nourishes, us or the people in the 18th century?
Erasmus also suggests that maybe soul/body interaction takes place at a very fundamental level, perhaps the quantum level, and so a long chain of satisfactory explanations would also lead up to brute soul facts as with brute physical facts. So, this suggestion is that explanations will be satisfactory as long as they are physical, but they become brute the moment they appeal to souls. In other words, the instant that soul theory starts to do any work it becomes incomprehensible. This seems to concede my point, namely that we have many excellent physical explanations of how matter interacts with matter, but as soon as we invoke souls, understanding ends. Further, with physical theory, if and when we reach something inexplicable, it is contingently and perhaps temporarily inexplicable, and the development of theory might explain the currently inexplicable. With soul-theory, no conceivable development would make it into anything other than the blank it is. Its incomprehensibility is in principle; it is occult by nature.
Erasmus says that I fail to engage with those dualists who have offered explanations of how souls and bodies might interact. I have seen a number of these “explanations.” At best, they amount to scenarios, and there is no responsibility to engage with every scenario that pops up. Give me a theory, a real theory, one that makes robustly testable, rigorous, and specific claims—and not hand-waving, speculation, or pseudoscience—and I will engage it.
My second argument against souls is that soul-theory thinks of the self as a simple, abiding, spiritual entity that constitutes our personal identity. This is the theory of the self as a Cartesian Ego. I opposed to this theory a version of what is normally called the “Bundle” theory of the self, which is traced back to Hume, but which also has roots in Buddhism. On this theory, personal identity is not constituted by a spiritual essence or entity, but is a nexus of heterogeneous experiences and traits.
Erasmus says that in this section I equivocate between two different senses of self, meaning “self”:

Parsons…is here using the term ‘self’ to mean ‘non-spatial substance that has mental properties’. Parsons then goes on to use the term ‘self’ to refer to a set of connected mental properties and personal characteristics that change over time.

Not so. Throughout I am using self in the entirely neutral sense of my personal identity—that—whatever it is—that makes me me at any given time and over time. Further, I am considering two different theories of personal identity—the Cartesian Ego theory and the Bundle theory, and giving my reasons in support of the latter. No equivocation.
My third objection to souls begins with the simple and undeniable observation, backed by enormous empirical research, that non-human animals have minds, that is, they are capable of quite sophisticated acts of cognition and intelligence and display many of the emotions that we do. Soul-theory holds that we think, feel, etc. with our souls. So, do animals have souls? If we say “no,” then we admit that the brain is sufficient for the mental life of non-human animals. At what level of cognition or consciousness, then, are brains no longer sufficient and why? How do we give a principled, non-arbitrary answer here? If brains can do that much, then why not more?
If, on the other hand, we say that some non-human animals do have souls, then the same problem arises again. Just as Darwin did with the eye, we can point to a continuum of cognitive aptitudes and levels of sentience. As I say:

Animals show a broad range of mental functions from none at all to quite sophisticated competencies. At what point do we say that here, just here is where souls are needed and brains are not enough? With which animals do we say that their mental functions are so sophisticated that they must have souls? Bonobos? Monkeys? Cats? Snakes? Frogs? Oysters? Again, any answer would seem to be arbitrary.

Again, where do we drive the golden spike to show where brains cease to be sufficient and souls are needed? So, whether or not we say that animals need souls, soul-theory looks arbitrary and groundless.
Erasmus’ bravely bites the bullet and says that animals have souls—not just chimps and dogs and cats, but all animals. Insects and oysters have souls. There is no place to drive the golden spike. It is souls all the way down. OK. Consider the sea slug, Aplysia california. The sea slug is a big snail with a few large neurons making it easy to study. Despite its paucity of neurons, the sea slug can learn. It can be conditioned by giving it a painless electrical stimulus at the same time as a painful stimulus. Soon it reacts the same way, by withdrawing its gills and siphon, just when exposed to the painless electrical stimulation. The training causes the release of proteins that cause synapses to open between the slug’s neurons, permitting easier transfer of electrical charges between neurons. The more synapses that open, the longer the conditioning lasts. So, is learning in sea slugs not sufficiently explained in terms of neurons and synapse? Do we have to invoke sea slug souls? To me, this has the air of a reductio ad absurdum.
I conclude that, though Erasmus admirably refrains from invective in criticizing my post, his critique fails comprehensively.
Calvin, William H. How Brains Think: Evolving Intelligence Then and Now. (New York: HarperCollins, 1996).
Churchland, Paul M. The Engine of Reason, the Seat of the Soul: A Philosophical Journey into the Brain. (Cambridge: MIT Press, 1996).
Crick, Francis. The Astonishing Hypothesis: The Scientific Search for the Soul. (New York: Simon & Schuster, 1994).
Eagleman, David. The Brain. (New York: Pantheon Books, 2015)
Flanagan, Owen. The Problem of the Soul: Two Visions of Mind and how to Reconcile Them. New York: Basic Books, 2002).
Lyons, William. Matters of the Mind. (New York: Routledge, 2001).

bookmark_borderReply to Dr. Erasmus – Part 2: Straw Man and Invalid Inference

In this post I will reply to an objection that was raised by Dr. Jacobus Erasmus against my reasoning in one of my skeptical posts about the resurrection of Jesus.


The most basic problem with the objection raised by Dr. Erasmus is that he commits the all-too-common STRAW MAN fallacy.
He does NOT understand my reasoning, and as a result he mischaracterizes my reasoning, and then he criticizes the inaccurate and distorted representation of my reasoning instead of criticizing my ACTUAL reasoning.  I am being charitable in assuming that Dr. Erasmus did not intentionally mischaracterize and distort my reasoning.  However, this charitable assumption leads me to the conclusion that Dr. Erasmus has a poor understanding of probability.  He mischaracterized my reasoning because he does NOT have a good understanding of probability.
In the previous post where I began my reply to Dr. Erasmus, I have already pointed out the fundamental mistake that Dr. Erasmus made:  there is no hint that he noticed that I was making use of CONDITIONAL PROBABILITY in my calculations.  But for anyone who has a basic understanding of probability, it would have been obvious that I was making use of CONDITIONAL PROBABILITY.  So, because Dr. Erasmus lacks a good understanding of probability, he failed to notice the obvious and important fact that I was making use of CONDITIONAL PROBABILITY.  This resulted in his mischaracterizing my reasoning, and attacking a STRAW MAN, instead of pointing out a problem in my ACTUAL reasoning.
I could go into more detail in supporting my charge that Dr. Erasmus has committed a STRAW MAN fallacy against my skeptical post on the resurrection of Jesus, but I don’t see the point.  He clearly misunderstood my reasoning, so his objection does NOT address my actual reasoning.
If Dr. Erasmus wants to make a more serious effort to understand my reasoning, then I would be happy to discuss any new objections that he might offer, but his first attempt at an objection completely misses the mark, and is unworthy of any more analysis and discussion by me.


Not only does Dr. Erasmus take aim at a STRAW MAN by mischaracterizing my reasoning about the resurrection, he also FAILS to support his objection about that STRAW MAN.  He attacks reasoning that is NOT mine, and his attack of that other reasoning is based on an INVALID INFERENCE, and thus it FAILS.  His critique is doubly wrong.  He aimed at the wrong target and he also missed the target!
In his attempted counterexample, Dr. Erasmus needs to establish two main things about his example, in order for his example to make the objection that he wants to make:

  • The probabilities of (C1) and (C2) and (C3) are low.
  • The probability of (H2) is high.

Dr. Erasmus FAILS to establish either one of these key points.  I will skip over the problem with the first point, and focus on his FAILURE to establish the second point.  Actually,  I have already described the problem with the second point in my previous post where I began my reply.  So, I will be very brief here.
Dr. Erasmus uses Bayes’ Theorem to infer that the UNCONDITIONAL probability of (H2) is 0.9.   I agree that a probability of 0.9 is indeed “high”.  The problem is that the instance of Bayes’ Theorem that he uses only yields a CONDITIONAL PROBABILITY of (H2), not an UNCONDITIONAL probability.  The condition in this case is that (C1) and (C2) and (C3) are all true.
In other words, the probability of (H2) would be 0.9 IF we knew for certain that (C1) and (C2) and (C3) were all true.  But if we knew for certain that (C1) and (C2) and (C3) were all true, then it cannot also be the case that the probability of each of those three claims is low.
In any case, Dr. Erasmus does NOT understand Bayes’ Theorem well enough to grasp the obvious fact that it is an INVALID INFERENCE to conclude that the UNCONDITIONAL probability of (H2) is 0.9 based on a calculation using his instance of Bayes’ Theorem.  His formula implies only that the probability of (H2) would be 0.9 IF we knew for certain that (C1) and (C2) and (C3) were all true.
Dr. Erasmus does NOT have a good understanding of probability.  As a result, he distorts my reasoning about the resurrection and attacks a STRAW MAN instead of pointing to a problem in my ACTUAL reasoning, and his attempt to attack that STRAW MAN itself FAILS because it is based on an INVALID INFERENCE, an inference that he would not have made if he had a better understanding of Bayes’ Theorem.

UPDATE  on  1/7/19

I took another look at Dr. Erasmus’ instance of Bayes’ Theorem (“the odds form of Bayes’ Theorem”) and discovered that instead of CALCULATING the probability of the hypothesis H2, he simply ASSIGNED a probability to H2!!  So, it is clear that Dr. Erasmus does NOT understand Bayes’ Theorem, and he is very confused about what he was doing with the theorem.
When Dr. Erasmus introduces his instance of Bayes’ Theorem, he makes this statement:

We may now use Bayes’ Theorem to calculate the probability of H2.

His aim, of course, is to use Bayes’ Theorem to SHOW that the probability of H2 is high, even when the probabilities of (C1), (C2), and (C3) are low.  But in his example he simply fills in the probability for H2 on the right-hand side of the equation; he does NOT calculate that probability at all!  Furthermore, he is assigns H2 the probability of .6, which is NOT what most people would consider to be a high probability!  So, he shoots himself in both feet.
On the left-hand side of the equation is a single fraction with a CONDITIONAL probability in the numerator and a CONDITIONAL probability in the denominator:

P(H2 | C1 & C2 & C3) / P(~H2| C1 & C2 & C3)  

This ratio of CONDITIONAL probabilities is apparently what Dr. Erasmus is attempting to calculate, because the values that he provides or assigns as inputs are four fractions that appear to each be ratios of probabilities, which is exactly what we find on the right-hand side of his instance of Bayes’ Theorem:

[P(H2) / P(~H2)]  x  [P(C1|H2) / P(C1|~H2)]  x  [P(C2|H2) / P(C2|~H2)]  x  [P(C3|H2) / P(C3|~H2)]

Here are the values that Dr. Erasmus assigns to the probabilities on the right-hand side of the equation:

(0.6 / 0.4)  x  (0.7 / 0.5)  x  (0.8 / 0.5)  x (0.9 / 0.3)

Reading those assigned values back into the right-hand side of the equation, we see that he has assigned the following values to these probabilities:

P(H2)  =  0.6

P(~H2)  =  0.4

P(C1|H2)  =  0.7

P(C1|~H2)  =  0.5

P(C2|H2)  =  0.8

P(C2|~H2)  =  0.5

P(C3|H2)  =  0.9

P(C3|~H2)  =  0.3

When he assigned the value of 0.6 to P(H2), he was assigning a moderate probability to H2, the hypothesis that he was supposed to be using Bayes’ Theorem to SHOW that H2 has a high probability, even when (C1), (C2), and (C3) have low or moderate probabilities.
Instead of SHOWING that H2 has a high probability,  Dr. Erasmus was SHOWING that he does NOT understand probability calculations, especially probability calculations that make use of Bayes’ Theorem.

UPDATE  on  1/8/19

Given the above probability values that Dr. Erasmus assigned to the elements of the right-hand side of his instance of Bayes’ Theorem, we can calculate the probabilities of of (C1), (C2), and (C3).  When we do so, it turns out that NONE of them have a LOW probability, which means that his counterexample FAILS.
We know that the probability of (C1) is EQUAL to the SUM of the probability of (C1|H2) times the probability of (H2) and the probability of (C1|~H2) times the probability of (~H):

P(C1) = [P(C1|H2)  x P(H2)] + [P(C1|~H2)  x P(~H2)]

We can use the probabilities assigned by Dr. Erasmus to calculate the probability of (C1):

P(C1) = (0.7 x 0.6) + (0.5 x 0.4)
P(C1) = 0.42 + 0.20
P(C1) = 0.62

We can similarly infer the probabilty of (C2) using a similar formula to that used above:

P(C2) = [P(C2|H2)  x P(H2)] + [P(C2|~H2)  x P(~H2)]

We can use the probabilities assigned by Dr. Erasmus to calculate the probability of (C2):

P(C2) = (0.8 x 0.6) + (0.5 x 0.4)
P(C2) = 0.48 + 0.20
P(C2) = 0.68

We can also infer the probability of (C3) using a similar formula to that used above:

P(C3) = [P(C3|H2)  x P(H2)] + [P(C3|~H2)  x P(~H2)]

We can use the probabilities assigned by Dr. Erasmus to calculate the probability of (C3):

P(C3) = (0.9 x 0.6) + (0.3 x 0.4)
P(C3) = 0.54 + 0.12
P(C3) = 0.66

Based on the probabilities that Dr. Erasmus assigns to elements on the right-hand side of his instance of Bayes’ Theorem, the probabilities of (C1), (C2) and (C3) would be as follows:

P(C1) = 0.62
P(C2) = 0.68
P(C3) = 0.66

NONE of these probabilities is a LOW probability. A low probability would have to be less than .5, but all three of these probabilities are significantly greater than .5.
So, Dr. Erasmus FAILED to assign probabilities in such a way that (C1), (C2), and (C3) have low probabilities, and thus his counterexample FAILS. The point of his counterexample was to SHOW that the probability of the hypothesis H2 could be high even if the probabilities of (C1), (C2), and (C3) were low. But his assigned probability values FAIL to provide an example where the probabilities of (C1), (C2), and (C3) are all low. In his example NONE of these statements has a low probability.

bookmark_borderReply to Dr. Erasmus – Part 1: Untrained in Probabilistic Logic?


Dr. Jacobus Erasmus has raised an objection to one of my posts on the resurrection.
Before presenting his objection he takes a swipe at my credibility:
…Bowen’s argument is an example of what happens when a blogger who is untrained in probabilistic logic tries their hand at probability.
…Bowen does not seem to be aware of Bayes’ Theorem; it appears that he has come up with his own idea of how probabilities should be calculated.
I’m not sure what Dr. Erasmus knows about my education, because he provides NO FACTS or evidence about my education.  It is not correct to say that I am “untrained in probabilistic logic”.  I took multiple courses in logic and critical thinking as an undergraduate student of philosophy, and I took multiple courses in logic and was a teaching assistant for multiple courses in logic and critical thinking as a graduate student of philosophy.  I learned some basic probabilistic logic in these courses both as an undergraduate student and as a graduate student.
I did not learn about Bayes’ Theorem in the logic and critical thinking classes that I took nor in the logic and critical thinking courses that I helped teach.  So, that is a potential weakness in my educational background.  However, I have been studying Richard Swinburne’s book The Existence of God  for many years, and that has required that I develop a basic understanding of Bayes’ Theorem.  Most of what I have learned about Bayes’ Theorem comes from Swinburne, who is an expert on this subject.  Although I have not had any courses that included Bayes’ Theorem, I have learned about this theorem from a qualified expert.


Since Dr. Erasmus questions my credibility in terms of my educational background,  I will return the favor.  His educational background is in Information Technology (an undergraduate degree) and Philosophy (a PhD).  So far as I know, courses in Probability are NOT required for either Information Technology nor for Philosophy degrees.  So, it is not clear to me that Dr. Erasmus has had ANY classes in Probability.  I suspect that he has had some classes in logic, but logic classes don’t necessarily cover Probability calculation.  Maybe Dr. Erasmus took a Probability class or two in order to fulfill a math or logic requirement.  I don’t know.  But his degrees don’t imply that he has ANY background in probability calculation.
There are a few obvious problems with Dr. Erasmus’ short post that indicate to me that he does NOT understand probability well.
First, he provides NO EXPLANATIONS in his post.  He neither EXPLAINS my alleged error, nor EXPLAINS his own example of a probability calculation.  If he really understood probability, then I would expect him to clearly EXPLAIN both points, so the absence of any such explanations suggests to me that he doesn’t really understand what he is talking about.
Second, he contradicts himself in the counterexample that he provides.  On the one hand, he assigns an estimated probability of 0.6 to the claim that The butler is a murderer.  But then he immediately turns around and calculates a probability of 0.9 that  the butler murdered Jones.   Those two probabilities CANNOT BOTH BE CORRECT.  A third grader could see that!  But not Dr. Erasmus.
If the probability that the butler murdered Jones was truly 0.9, then the probability that The butler is a murderer must be AT LEAST 0.9; it can’t be less than 0.9.  There is some chance that the butler murdered somebody else besides Jones, so the probability that The butler is a murderer must be 0.9 plus the probability that the butler murdered someone else besides Jones.   Dr. Erasmus contradicts himself in the space of just a few paragraphs while presenting his counterexample to my reasoning.  I am not impressed by such sloppy thinking.
Third,  one of the pieces of evidence in Dr. Erasmus’ counterexample makes his example inappropriate:
The butler was the only other person in the house when Jones died.
This bit of evidence all by itself makes it highly probable that the butler murdered Jones.  The counterexample involves the murder of Jones by means of someone hitting him in the head with a brick.  If the butler was “the only other person in the house when Jones died”, then it would be nearly impossible for anyone other than the butler to have committed the murder of Jones.  This one bit of evidence makes the other evidence largely irrelevant. Given this one bit of evidence, it is already determined that it is highly probable that the butler murdered Jones.   But Dr. Erasmus fails to see this obvious point.
Furthermore, this makes the supposed counterexample a poor one, since the probability calculation concerning the resurrection of Jesus does NOT include such a bit of evidence that all by itself could settle the issue, at least not in support of the hypothesis.  Many of the claims that I consider are necessary conditions of the hypothesis “God raised Jesus from the dead”.  The falsehood of a necessary condition would thus immediately establish with certainty the falsehood of the hypothesis.  But none of the claims I consider would all by itself show the hypothesis to be true or highly probable.
Fourth,  Dr. Erasmus complains about my supposed ignorance concerning Bayes’ Theorem, but he inaccurately describes my reasoning by leaving out the fact that I make use of CONDITIONAL PROBABILITIES, which are crucial to Bayes’ Theorem.  So, Dr. Erasmus mischaracterizes my reasoning in a way that divorces my reasoning from the logic of Bayes’ Theorem.  It is very clear that I am making use of CONDITIONAL PROBABILITIES when I talk about multiplication of probabilities in the case of assessing the hypothesis that “God raised Jesus from the dead”:

The main claim that God raised Jesus from the dead, (GRJ), assumes or implies various other related Christian beliefs:
(GE) God exists.
(GPM) God has performed miracles.
(JEP) Jesus was a Jewish man who existed in Palestine in the first century.
(JWC) Jesus was crucified in Jerusalem in about 30 CE.
(DOC) Jesus died on the cross on the same day he was crucified.
(JAW) Jesus was alive and walking around in Jerusalem about 48 hours after he was crucified.
(JRD) Jesus rose from the dead.
The multiplication of probability applies to the claim that Jesus rose from the dead, (JRD). Suppose that the probability of (JEP) was .8, and that the probability of (JWC) was .8 given that (JEP) is true (and 0 if (JEP) is false), and suppose that the probability of (DOC) was .8 given that (JWC) is true (and 0 if (JWC) is false), and suppose that the probability of (JAW) was .6 given that (DOC) is true, then the probability of (JRD) would be approximately:
.8 x .8 x .8 x .6 = .3072
or about three chances in ten.  Thus, (JRD) could be improbable, even if the various individual claims related to it were ALL either probable or very probable.
[an excerpt from my post that Dr. Erasmus is criticizing]
If Dr. Erasmus is familiar with probability calculations, then he would know that the expression
…the probability of (JWC) was .8 given that (JEP) is true…
is a reference to CONDITIONAL PROBABILITY.  But there is no hint in Dr. Erasmus’ post that he is aware that I was making use of CONDITIONAL PROBABILITIES.
So, either he FAILED to notice this obvious and important element of my reasoning, and thus shows himself to be ignorant about probability calculations, or else he DID notice this obvious and important element of my reasoning, but he dishonestly suppressed this fact in order to make me appear to be ignorant about probability calculations.  Bayes’ Theorem is derived from a basic principle of CONDITIONAL PROBABILITY.
Fifth, Dr. Erasmus appears to infer an UNCONDITIONAL PROBABILITY, when the instance of Bayes’ Theorem that he spells out clearly only establishes a CONDITIONAL PROBABILITY:
In this case, the odds in favour of H2 is about 10:1 (ten to one), which converts to a probability of 0.9 (or 90%) for H2.
He appears to infer that the unconditional probability of H2 is 0.9, but that is NOT what his instance of  Bayes’ Theorem shows.  The left side of his instance of the equation contains CONDITIONAL PROBABILITIES:
P(H2 | C1 & C2 & C3) / P(~H2 | C1 & C2 & C3)
So, what Dr. Erasmus is calculating is the relative probability of H2 vs. not-H2, given that C1 and C2 and C3 are true. 
This tells us NOTHING about the probability of H2 if we don’t know whether C1, C2, or C3 are true!  What he has shown is merely that H2 is highly probable IF we knew for certain that C1, C2, and C3 were true.  This example is irrelevant to the case of the resurrection of Jesus, where we are not dealing with facts that are known to be true, but are instead dealing with claims that only have some degree of probability.
It might be the case that Dr. Erasmus has more “training” or education than I do about Bayes’ Theorem, but his degrees don’t show that to be the case,  and the various problems with his post (that I have pointed out above) suggest to me that he does NOT have a good understanding of probability.
To Be Continued…

bookmark_borderLinks: Two Metaethical Arguments for Atheism from John J Park

Park, John. “The Moral Epistemological Argument for Atheism.” European Journal for Philosophy of Religion 7, no. 1 (n.d.): 121. doi:10.24204/EJPR.V7I1.133.

Abstract: Numerous supposed immoral mandates and commands by God found in religious texts are introduced and discussed. Such passages are used to construct a logical contradiction contention that is called the moral epistemological argument. It is shown how there is a contradiction in that God is omnibenevolent, God can instruct human beings, and God at times provideus with unethical orders and laws. Given the existence of the contradiction, it is argued that an omnibenevolent God does not exist. Finally, this contention is defended from several objections.

Park, John Jung. “The Problem of Error: The Moral Psychology Argument for Atheism.” Erkenntnis, n.d. doi:10.1007/S10670-017-9900-8.

Abstract: The problem of error is an old argument for atheism that can be found in Medieval and Early Modern Philosophy. Although it is not widely discussed in the contemporary literature in the Philosophy of Religion, I resurrect it and give it a modern spin. By relying on empirical studies in moral psychology that demonstrate that moral judgments from human beings are generally susceptible to certain psychological biases, such as framing and order effects, I claim that if God is responsible for making human beings such that we have these biases, this means that God is not a perfect being. The findings in empirical moral psychology create a problem for the existence of God, traditionally conceived.