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BAYESIANISM AND RELIGION J. T. Allen
Arguments for the existence of God are generally
divided into two distinct kinds: logical arguments and empirical arguments. The latter type of arguments attempt
to prove that the proposition God exists
is a synthetic truth, whereas the former type attempt to
prove that the proposition God exists
is
an analytic truth. The ontological argument is representative
of a logical argument for God's existence,
due primarily to the work of St. Anselm,
and more contemporarily, Alvin Plantinga[1].
The majority of theologians, however, are
not convinced that logical arguments for
God's existence are persuasive for those
with a low or even high degree of belief
in God's existence. Empirical arguments,
such as the cosmological argument and the
design argument, are, on the other hand,
very much alive in theological discourse
and make up the majority of a natural theologian's
arsenal of arguments against atheism and
agnosticism. It will thus be enlightening
to see these empirical arguments in light
of the Bayesian A-S distinction[2]. It will
be shown that those arguments fail to establish
their conclusions as not just true or probable,
but synthetic, as well. Probability Preliminaries
Before we proceed to show why God's existence,
insofar as it is understood as the
conclusion
of either the design argument or the
cosmological
argument, is nonsciential (i.e., neither analytic nor synthetic),
it is important to see what its arguments
are intended to do, viz. to show that it is probably the case that God exists, H, conditional on some evidence E and putatively suitable auxiliary assumptions
or "background knowledge"
B. What this amounts to saying is that H has the greatest overall balance of prior
probability and likelihood of all the
alternatives
to H combined[3]. Pr(H|B) is H's prior probability (which entails the prior
probability of not-H), Pr(E|H&B) is H's likelihood, and Pr(H|E&B) is H's posterior probability, i.e., that statement
which says E&B makes H probable (or, more colloquially, H is probably true). To measure the overall
balance of a hypothesis' prior probability
and likelihood compared to all of its alternatives
combined, we use Bayes' theorem: (BT)
Pr(H|E&B) = Pr(H|B) Pr(E|H&B) / [Pr(H|B) Pr(E|H&B) + Pr(not-H|B) Pr(E|not-H&B)] Prior probabilities are required to include
all the relevant background information
to
the hypothesis in question and must be independently establish. The prior probabilities,
moreover, are a function of two factors:
simplicity and conservatism. There is, as Quine and Ullian[4] note,
"a nagging subjectivity"
in determining
whether one hypothesis is simpler than
another.
But, generally speaking, simplicity
refers
to "(roughly) a measure of the
number
of independent postulates that comprise
a
hypothesis"[5]. Suppose, for example,
that you hear a popping noise while
driving.
Considering two rival hypotheses, an
alien
implanted a devise in your ear that
makes
popping noises while you drive and
your car's
tire popped, the latter hypothesis
is clearly
simpler than the former. Conservatism
refers
to how well a hypothesis fits with
prior
well-established hypotheses. Considering,
again, the alien-hypothesis versus
the tire-hypothesis,
the latter will receive a greater prior
probability
in virtue of the fact that the alien-hypothesis
fits poorly with the already well-established
hypothesis about our place in the universe,
alone in a remote region of the Milky
Way
galaxy; if this be disputed, however,
it
is at least the case that there are
no prior
well-established hypotheses that contend
that alien visitation and, in particular, alien manipulation of human
eardrums, is probable in any case. Lastly, it is required that the background
information be independently established,
i.e., true independent of the hypotheses
in question. This provision is important,
for without it, one could simply invent auxiliary assumptions to prove any hypothesis
so desired. In order to determine,
for instance,
whether the relationship between pressure
and volume of gases we do not simply
invent
the auxiliary assumption that the measuring
devices are reliable. The reliability
of
measuring the geometrical dimensions
of the
container and the accuracy of the barometer
are independently attested to through
independent
test procedures from that of the experiment
testing Boyle's law. If this were not
so,
we could arbitrarily use something
like the
number of pulses per minute in one's
arteries
to measure pressure and the number
of pulses
per minute in another's arteries to
measure
volume. What is involved in likelihood
analysis
is telling how well the evidence in
question
is expected to occur given the hypothesis
in question (and the auxiliary assumptions,
of course). That is, when analyzing
likelihoods,
we want to know which hypothesis the
evidence
favors more. This idea is captured by the Law of
Likelihood[6]: (LL)
Pr(E|H1&B) > Pr(E|H2&B) just in case E favors H1 more than H2. Favor can be equally expressed in the two following
ways: E is more expected given H1 than it is given H2; or E is more surprising given H2 than it is given H1. If we wish to say which hypothesis is
more probable, i.e., which hypothesis we should have the
highest degree of belief for, the prior
probability
of H, the likelihood H and all of H's alternatives combined must be evaluated;
i.e., we must establish the overall
balance
of H's prior probability and likelihood compared
to all of H's alternatives. The Design Argument
The design argument begins with the evidential
proposition: (1) E1: the vertebrate eye exhibits features F1, ... , Fn, where 'F1, ... , Fn' include the features delicacy and teleology. Most simply, a teleological system is one
that is purposeful, i.e. goal-directed. The vertebrate eye
is a teleological system inasmuch as
its
underlying function is to serve the
purpose
of allowing an organism to see. The
vertebrate
eye, moreover, is delicate in that
if parts
of it are removed, such as the iris,
the
eye fails to serve its purpose of enabling
sight. The second premise is also an
evidential
proposition, this time involving a
machine,
viz. a watch: (2) E2: a watch exhibit features F1, ... , Fn. The third premise expresses the following
likelihood relation between two rival
hypotheses,
the watch was created by an intelligent
designer
and the watch was created by a mindless
chance
process: (3) Pr(E2|the watch was created by an intelligent
designer) > Pr(E2|the watch was created by a mindless chance
process), i.e., a watch having features F1, ... , Fn is more likely to occur given an intelligent
designer created it than a mindless
chance
process having created it. The next
premise
expresses the following likelihood
relation
between two rival hypotheses, the vertebrate
eye was created by an intelligent designer
and the vertebrate eye was created
by a mindless
chance process: (4) Pr(E1|the vertebrate eye was created by an intelligent
designer) > Pr(E1|the vertebrate eye was created by a mindless
chance process), i.e., the vertebrate eye having features
F1, ... , Fn is more likely to occur given an intelligent
designer created it than a mindless
chance
process having created it. Before we
proceed
to the rest of Paley's argument, something
needs to be said about what is meant
by "mindless
chance process". In Paley's age,
chance
processes were generally seen as what
are
now termed uniform chance processes, where each possible outcome is equally
probable. It is easy to see that not
every
chance process is uniform. Suppose
I construct
a coin such that it is biased on heads.
It
is still a chance process when I flip
the
coin; however, the two possible outcomes
(heads or tails) will not be equal--heads
will have a higher chance of coming
up than
tails will. Mindless, moreover, refers
to
an event coming about by no intervention
of intelligence or intensions (of an
intelligent
entity) in the chance process. If a
roulette
wheel is rigged by the dealer to land
on
one and only one color, we'd say that
the
spin of the wheel is not a mindless chance process. Paley, rightfully
so, supposes (7) is justified on the
basis
that a mindless chance process' resulting
in the existence of a delicate and
teleological
machine such as a watch is highly unlikely compared to the hypothesis that
an intelligent entity designed it.
From this,
Paley concludes: (5) Pr(the vertebrate eye was created by an intelligent
designer|E1) > 0.5, i.e., the design-hypothesis for the vertebrate
eye has the greatest overall balance
of prior
probability and likelihood compared
to all
of its competitors.
There are a number of glaring problems with
this argument. The first, which is
common
amongst arguments for the revivification
of Jesus[7][8], is that a vital step
in the
argument is entirely glossed over,
viz. an analysis of the hypothesis' prior probability.
Assuming, however, that a prior probability
analysis of the hypothesis is given,
there
is an essential problem with its likelihood
which inherently prevents a greater
overall
balance of the hypothesis' prior probability
and likelihood compared to all of its
alternatives.
Notice that steps (3) and (4) of the
argument
make no mention of auxiliary assumptions,
B. In order for the hypothesis to receive
an adequate likelihood analysis, however,
auxiliary assumptions are essential.
What
sorts of auxiliary assumptions are
made in
regard to (3), Pr(E2_|the watch was created by an intelligent
designer)? That is, what background
information
is required and independently established
which, together with the hypothesis
that
an intelligent designer created the
watch,
make the presence of the watch likely
to
occur? Firstly, it would involve the
abilities of the type of intelligent designer in question.
We know, before the evidence of a particular
presence of a watch is brought to bear
on
the matter, that there exist humans
that
have the ingenuity to construct elaborate
devices for a variety of purposes;
some,
moreover, have easy access to the sufficient
(and limited) amount of resources (glass,
metal, etc.) that would make up something
like a watch. In addition to independently
established premises regarding the
putative
designers' abilities, we also know
that some
(if not most or all) have a desire
for telling
time to a high degree of precision.
Such
devices enable higher proficiency in
coordinating
events (be it of production or education)
where the society outgrows a family
or small
village. Thus, given a designer created
the
watch and such a creation fits well
with
the goals and abilities of the putative designer, we'd expect the
existence of a watch, much more than
we would
against the hypothesis that the watch
was
the result of a mindless (uniform)
chance
process. The fourth premise, therefore,
is
more correctly formulated as follows: (4') Pr(E2|the watch was created by an intelligent
designer & B) > Pr(E2|the watch was created by a mindless chance
process & B). What, now, when we turn to (5)? Does it have
an analogous formulation? Indeed, it
does: (5') Pr(E1|the vertebrate eye was created by an intelligent
designer & B) > Pr(E1|the vertebrate eye was created by a mindless
chance process & B), where B includes, most importantly, the goals and
abilities of the putative designer
of the
vertebrate eye. The question we must
ask,
as was settled in the case of (7'),
is whether
the auxiliary assumptions are independently
established. The answer is no: ...[W]hether intelligent design has a higher
likelihood than chance depends on what we
are entitled to assume about the goals and
abilities that the designer of the eye would
have had if such a being had existed...Paley
assumes that if an intelligent designer created
the human eye, the designer would have wanted
to give us eyes with features [F1, ..., Fn] and would have had the [goal and] ability
to do so...What is required...is an independent reason for believing assumptions about goals and
abilities.[9] The problem is that such independent reasons
for the goals and abilities for the
putative
designer are nonexistent. Michael Behe,
a
contemporary proponent of the design
argument,
concedes this point, unaware, of course,
of its probabilistic consequences: [T]he argument from imperfection overlooks
the possibility that the designer might have
multiple motives, with engineering excellence
oftentimes relegated to a secondary role...The
reasons that a designer or would not do anything
are virtually impossible to know unless the
designer tells you specifically what those
reasons are.[10] Specifically, what Behe misses is that it
is impossible to have a defined (let alone, high) posterior
probability of design without a defined
likelihood.
But for those reasons noted above,
safely
assuming there is no independent and
well-established
attestation that a designer has given
us
his motives, the likelihood of the
design-hypothesis
is undefined—it cannot be used as a premise in Paley's argument
that the design hypothesis is probable,
i.e.,
that it has the greatest overall balance
of prior probability and likelihood
compared
to all its competitors; thus, the design
argument collapses altogether.
Applying these results to the Bayesian A-S
distinction, it is clear that the sentence
'An intelligent designer created an
organism,
viz. the vertebrate eye' (let alone the sentence
'God created an organism, viz. the vertebrate eye') is nonsciential, i.e.,
neither analytic nor synthetic: (6) There is no time t such that Pr(the vertebrate eye was created by an intelligent
designer|B) = 1 or 0. and (7) There is a time t such that it's not the case that 1 >
Pr(the vertebrate eye was created by an intelligent
designer|B) > 0. (6) holds because the hypothesis that the
vertebrate eye was created by an intelligent
designer is not a syntactical truth
or falsity,
and (7) holds since, in order to excrete
a value for Pr(the vertebrate eye was created by an intelligent
designer|B), the likelihood of the hypothesis must
be well-defined, which it is not in
virtue
of the fact that B does include independently established propositions
about the putative designer's goals
and abilities.
The design-hypothesis may, however,
sometime
in the future become defensible on
the grounds
that we actually obtain independently
attested
observed data relevant to the putative
designer's
goals and abilities. Nevertheless,
I wouldn't
hold my breath. The kalam Cosmological Argument Amongst the variety of cosmological arguments,
the most recent and perhaps most persuasive
is that of the kalam Cosmological Argument (KCA). Though it has
clear historical traces, the argument
did
not breathe life in the twentieth century
until William Lane Craig's The Kalam Cosmological Argument[11]. The core layout of the argument consists
of three steps, making up a (putatively)
deductively valid argument: (8)
Whatever begins to exist has a cause. (9)
The universe began to exist. (10)
(Thus) the universe has a cause. From (10), Craig goes onto to argue that
[12]:
(11)
God's act of creation is the best candidate
for the cause of the universe.
(12)
(Thus) God exists. The primary focus of my criticism will be
premises (8) and (9) and will support
my
general conclusion that (10) is neither
synthetic
nor analytic.
There is a preliminary concern, when criticizing
the KCA that rendering it as a probabilistic
argument, or, at any rate, involving
probabilistic
premises, seriously misconstrues the
argument,
particularly when the argument is rejected
for its failure as such an argument.
Nonetheless,
the KCA is, at heart, a probabilistic argument. The methodology of classical apologetics
was first to present arguments for
theism,
which aimed to show that God's existence
is at least more probable than not,
and then
to present Christian evidences, probabilistically
construed, for God's revelation in
Christ.
This the method I have adopted in my
own
work. By means of the kalam cosmological argument, I have endeavored
to show that a Personal Creator of
the universe
exists[13]. The KCA "strikes" Craig as a "good
argument" on the basis that its "premises
are both true and more plausible than [their]
contradictor[ies]"[14] I don't know
what it means to say a premise is both true and more plausible than its contradictory,
unless one is being misleadingly redundant;
to add to a statement that it is "true"
when it is probable is to do no more
than
give the statement a "rhetorical
pat
on the back"[15]. Even so, it
is strange
that there is not a single construal
of the
KCA in its properly probabilistic setting.
Craig's writings are filled with vague
references
to the inductive justification of its
premises,
but nothing that gives a hint that
this evaluation
is actually cogent. The consequences
of putting
the KCA in its proper probabilistic
setting
have been long neglected.
Given Craig's motive for showing his conclusion
to be more probable than its negation,
we
can interpret the conclusion more precisely
thus: (10') Pr*(the universe has a cause|background information)
> Pr*(the universe does not have a cause|background information).[16] Since "the universe does not have a
cause" is the denial of "the
universe
has a cause," the conclusion may
be
written more precisely:
(10'') Pr*(the universe has a cause|background information)
> 0.5. In order for this assessment to be rationally
justified, i.e., if our rational degree
of
belief in the conclusion is to exceed
0.5,
three other values must be evaluated,
viz.
(13) Pr(the universe has a cause|whatever begins
to exist has a cause), (14) Pr(the universe began to exist|the universe
has a cause and whatever begins to
exist
has a cause), and (15) Pr(the universe began to exist|the universe
does not have a cause and whatever begins to exist
has a cause). We will now proceed to see whether these
values provide the requisite support
for
the KCA. The Prior Probability of the Universe Having
a Cause Given the following key: H: The universe has a cause E: The universe began to exist B: Whatever begins to exist has a cause what is the value of Pr(H|B)? Before this question is fully answered,
however, it is important to realize
what
it is not, for it determines the general epistemological
nature of its answer. Since B does not entail H, it is clear that H is not a syntactical truth (or falsity);
that is to say, H, if known, does not constitute a priori knowledge. Moreover, though less clear than
its lack of a priority, H is, if true at all, synthetic since H does not follow from any (behavioral) synonymy
relation between 'begins to exist'
and 'has
a cause'; there simply is no synonymy relation to be had. This is not
to say, however, that 'begins to exist'
and
'has a cause' are not extensionally equivalent (i.e., that they are not true
of the same objects), but to further
say
that they are alike in meaning is to
ignore
the fact that we can imagine an object
having
the property 'begins to exist' whilst
clearly
lacking the property 'has a cause'
(which
does not prove that the terms fail
extensional
equivalency—it shows, rather, that
they are
intensionally distinct, i.e., different in meaning). The
former point, that H, if known, does not constitute a priori knowledge restricts Pr(H|B) such that it is less than 1 and greater
than 0; furthermore, the latter point,
that
H is synthetic, restricts Pr*(H|B) such that it is less than 1 and greater
than 0. Hence, the goal for the KCA
is to
show that the Pr(H|E&B) > 0.5 (or Pr*(H|B) > 0.5).
What background information is relevant to
the assessment of the probability of
'the
universe has a cause'? In the first
place,
it could be argued that such a proposition
is simpler than its negation. For most (if not all)
physical objects are ascribed the property
'has a cause'; and since the universe
is
itself a physical object, comprised
of a
vast network of spatiotemporally related
physical objects (galaxies, nebulae,
dark
matter, etc.), it is simpler to suppose
that
all physical objects are predicated by 'has
a cause' (i.e. they are caused by something)
rather than to suppose that one physical
object is an exception, which requires
an
additional premise regarding its existence.
In terms of conservatism, either hypothesis,
H or not-H, seems plausible. Yes, supposing the universe
does not have a cause seems unfit with
respect
to the fact that causal principles
are used
in almost all areas of everyday discourse
and science. On the other hand, we
are still
left with the unusual problem of predicating
'has a cause' to an object that is,
on Craig's
account, unaccounted for unless we
opt for
a particular 'cause', viz. God, which utterly unlike anything else
in the universe, such as physical objects.
Because of the simplicity of H, however, it is apt to give the following
assessment:
Pr(H|B) > 0.5. Perhaps these remarks over the prior probability
of H, viz. the evaluation of H's conservatism (I think it is reasonable to hold that H is at least simpler than not-H), can be modified and even completely rejected
for a view either more supportive of
H or not-H. In any case, we will see that the real
trouble of the KCA is, like the design
argument,
a problem of likelihoods. The Likelihood of the Universe Having a Cause
In regards to H's and not-H's likelihoods, what are we dealing with?
Specifically, what is at hand is the
expectancy
of E, the universe began to exist, given H, the universe has a cause and B, whatever begins to exist has a cause; and,
for not-H, the universe does not have a cause, it
is the expectancy of E given not-H and B. That is to say, we need to evaluate two
separate likelihoods, viz. Pr_(E|H&B) and Pr(E|not-H&B).
Clearly, in the case of H, H&B does not entail E, i.e. it is a logical error to suppose the
following argument is deductively valid:
The universe has a cause. (H)
Whatever begins to exist has a cause. (B)
Therefore, the universe began to exist. (E) Though invalid, it is nonetheless possible
that H&B confer a large probability on E, i.e., E may still be an expected outcome given H&B even if H&B does not logically imply E. Indeed, it seems generally plausible to
suppose that when something possesses
a cause,
then it also begins to exist.
The final step in evaluating Pr(E|H&B) is to make sure B is independently established. Can we be
confident in the proposition that if
something
began to exist, then it has a cause?
Before
I give a negative answer to this question,
it is worthwhile to see what types
of defenses
have been used by Craig in support
of B's independent justification.
In various places, Craig defends B as a "metaphysically necessary truth"[17];
an "ontologically necessary truth"[18];
"intuitively obvious"[19][20];
and “one which is constantly confirmed
in
our experience”[21]. Given these comments
alone, Craig blatantly obfuscates the
A-S
distinction[22]. To say B is a "metaphysically necessary truth"
or an "ontologically necessary
truth"
and "intuitively obvious"
suggests
that the (new) prior probability of
B is equal to 1 or 0; that is to say, B is analytic. On the other hand, to say B is "constantly confirmed in our experience"
suggests that the (new) prior probability
of B is unequal to 1 or 0 (though it suggests, also,
that the probability of B is high). A proposition cannot be both analytic
and synthetic, for if a proposition is analytic, it cannot receive
confirmation; and if a proposition
can receive
confirmation, then it is unable to
receive
a probability of either 1 or 0 through
a
series of confirmation instances[23]. Craig is, therefore, unclear about
how B should be understood epistemologically.
We simply cannot both look for experiences to support this proposition
and understand it as a type of necessary truth (if this implies that it is either
analytic or a priori or even a vague reference to "possible-world"
necessity). Morevoer, inventing a stronger
sense of necessity, as Nowacki[24]
recommends,
to justify such a mix-match of epistemological
properties of B unduly strains the needed distinction we
require to explicate the differences
of logical
and empirical truths; to obfuscate
this at
the expense of saving the KCA is, thus,
painfully
ad hoc and seems only appropriate for serious consideration
if the Bayesian A-S distinction falls
through.
Craig is, furthermore, so bold as to say
that "scarcely anyone could sincerely
believe it [B] to be false"[25]. It is interesting
that, in the following paragraph in
Reasonable Faith, he cites Quentin Smith as saying "the
most reasonable belief is that we came
from
nothing, by nothing, and for nothing".
Insincere? I find it outstandingly
difficult
to have a high rational degree of belief
in such an accusation. But I digress.
Though I have already argued that B is not analytic, let us examine if it is
synthetic, i.e., if it is, as Craig
claims,
"constantly confirmed in our everyday
experience". Actually, let us
grant
that this is the case--that the evidence,
E1, consisting of the claim that 100% of the
physical objects (observed, either
by gas-chamber
clouds or by the naked eye), excluding
the
universe (the physical object in question),
have causes, is veridical. I contend
that
this is all the evidence in favor of B. But notice that all the physical objects
independently justified as having causes and, thus, having a start
to their existence, are objects within a spatiotemporal framework. All these objects
make up a set, so-called the universe, which is the overall spatiotemporal framework in which
all those objects we know to have causes
exist. Since it requires an additional
premise
to argue that a set of objects has
the same
property shared by each and every one
of
its members, on pain of committing
the fallacy
of composition, E1 independently establishes B but at the cost of limiting the range of
values of the bound variable in B such that E is no longer deductively entailed by H&B. To make this point explicit, suppose we
insert the symbol "^" after
the
quantification idiom in B to denote an ontology limited to the objects
within a spatiotemporal framework, and pose the
argument as follows:
The universe has a cause.
Something^ begins to exist when and only
when it has a cause.
Therefore, the universe began to exist. Not only is this argument invalid, there
is no indication that if a spatiotemporal
framework itself has a cause that it must begin to exist.
I am not proposing that the spatiotemporal
framework, the universe, is not like its members in that we can rationally
expect it to have causes without a
temporal
moment in which it began; however,
to suppose
otherwise requires independent establishment.
An additional premise, with independent
justification,
is required to say that the set has
the property
confirmed of its members, viz. if it has a cause then it begins to exist.
Otherwise, the likelihood is undefined,
and
the posterior probability of H is, as well; and hence, H is neither analytic nor synthetic. It is,
as H fared in the context of the design argument,
nonsciential, amongst a category of sentences entirely
irrelevant to the theory of knowledge. Notes [1] Alvin Plantinga, God, Freedom, and Evil (1974; repr., Grand Rapids, MI: William
B. Eerdmans Publishing Co., 1977). [2] In a paper, forthcoming, I explicate
the A-S distinction (i.e., the analytic-synthetic
distinction) probabilistically. The
general
formulation is that, for any hypothesis
H: H is analytic if and only if there is a time
t such that the prior probability of H at t is either 1 or 0. H is synthetic if and only if for all times
t the prior probability of H is less than 1 and greater than 0. The merit of the forgoing analysis of the
design argument and the cosmological
argument
depend on the worth of the above A-S
distinction;
thus, the arguments presented will
not be
sound unless the Bayesian A-S distinction
is critically examined. Nonetheless,
the
conclusions in the paper still stand
to be
supported by cogent arguments, given
a revamped
A-S distinction designed to overcome
its
difficulties in the philosophy of language
(Vide Quine, “Two Dogmas of Empiricism”). [3] Robert Greg Cavin and Carlos A. Colombetti,
The Doubting Thomas Guide to Logic and Religion (Casper, WY: RandomNPC LLC, 2008), 52. [4] W.V. Quine and J.S. Ullian, The Web of Belief, 2nd ed. (1970; repr., Np.: McGraw-Hill, 1978), 69. [5] Robert Greg Cavin and Carlos A. Colombetti,
The Doubting Thomas Guide to Logic and Religion (Casper, WY: RandomNPC LLC, 2008), 53. [6] Elliott Sober, Evidence and Evolution: The Logic Behind the Science (Cambridge: Cambridge University Press,
2008), 32. [7] Robert Greg Cavin and Carlos A. Colombetti,
The Doubting Thomas Guide to Logic and Religion (Casper, WY: RandomNPC LLC, 2008), 56-75. [8] Robert Greg Cavin, "Is There Sufficient
Historical Evidence to Establish the
Resurrection
of Jesus?" Faith and Philosophy: The Journal of the
Society of Christian Philosophers 3 (1995): 361-79. [9] Elliott Sober, Evidence and Evolution: The Logic Behind
the Science (Cambridge: Cambridge University Press,
2008), 143-44. [10] Michael Behe, Darwin's Black Box: A Biochemical Challenge
to Evolution (New York: Free Press, 2006). [11] William Lane Craig, The Kalam Cosmological Argument (London: Macmillan & Co., 1979). [12] Though the advancement from (8) to (10)
is deductively valid, the advancement
from
(10) to (12) is not. [13] William Lane Craig, "Classical
Apologetics," in Five Views on Apologetics, by K. J. Clark et al., ed. S. N. Gundry
(Grand Rapids, MI: Zondervan, 2000),
25-55. [14] op cit. [15] Richard Rorty and Pascal Engel, What's the Use of Truth?, ed. Patrick Savidan, trans. William McCuaig
(New York, NY: Columbia University
Press,
2007), 8. [16] "Pr*(p|background)" is understood as the "new"
or updated probability of p, in light of three "old" probability
values, viz. p's prior probability (before evidence is
considered), p's likelihood and not-p's likelihood. To signify updated probabilities
that explicitly take all those factors
into
account, I will use an asterisk "*" after the probability function "Pr". For the values being used for the updated
probability, I will simply leave out
the
asterisk. [17] William Lane Craig, "Classical
Apologetics," in Five Views on Apologetics, by K. J. Clark et al., ed. S. N. Gundry
(Grand Rapids, MI: Zondervan, 2000),
50. [18] Ibid., "The Existence of God and the Beginning
of the Universe." Truth: A Journal of Modern Thought 3 (1991): 85-96. http://www.leaderu.com/truth/3truth11.html (accessed January 5, 2009). [19] Ibid., The Kalam Cosmological Argument (London: MacMillan & Co., 1979). [20] Ibid., "The Kalam Cosmological Argument and
the Anthropic Principle," in Philosophy: The Quest for Truth, ed. Louis Pojman, 6th ed. (Oxford University
Press, 2006), 54-71. [21] Ibid., "The Existence of God and the Beginning
of the Universe." Truth: A Journal of Modern Thought 3 (1991): 85-96. http://www.leaderu.com/truth/3truth11.html (accessed January 5, 2009). [22] I am indebted to Professor Martin Young
for this remark. My exact explication
of
it, however, in terms of a Bayesian
A-S distinction,
is unique to my own views on the matter. [23] The only exception to this rule, regarding
what may loosely be called 'semantical'
truths
(i.e. truths established by synonymy
relations),
has already been ruled out as applying
to
B. [24] Mark R. Nowacki, The Kalam Cosmological Argument for God (Amherst, NY: Prometheus Books, 2007). [25] William Lane Craig, "The Kalam
Cosmological Argument and the Anthropic
Principle,"
in Philosophy: The Quest for Truth, ed. Louis Pojman, 6th ed. (Oxford University
Press, 2006), 54-71. References Behe, Michael. Darwin's Black Box: A Biochemical Challenge
to Evolution. New York: Free Press, 2006. Cavin, Robert Greg. "Is There Sufficient
Historical Evidence to Establish the
Resurrection
of Jesus?" Faith and Philosophy: The Journal of the
Society of Christian Philosophers 3 (1995): 361-79. Cavin, Robert Greg, and Carlos A. Colombetti.
The Doubting Thomas Guide to Logic and Religion. Casper, WY: RandomNPC LLC, 2008. Craig, William Lane. The Kalam Cosmological Argument. London: MacMillan & Co., 1979. |
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