systems are about sentences. A
sentence is a string, a collection of symbols. "God exists" is a
sentence; it consists of symbols. We have simple syntactic and grammatical rules
that determine which sentences are well-formed
statements; these rules are trivial, and we can (for the purposes of
this article) ignore non-well-formed sentences.
system divides statements into two categories, value and invalid. A formal
system is a dualistic system that defines a set of axioms,
statements that are valid a priori,
and a set of inference rules for
deriving new valid statements from
existing valid statements. A statement is valid
within that formal system if it is an axiom or it can be derived from the axioms
according to the inference rules. By definition, the negation of a valid
statement is an invalid statement.
Valid statements that are not axioms are also called theorems.
instance, Peano’s Arithmetic is a formal system: It contains a set of
axiomatically valid statements (including a statement describing mathematical
induction), and uses the inference rules of propositional calculus to create new
statements. Thus we can say that 2+2=4 (actually SS0+SS0=SSSS0) is a theorem, a
valid statement, according to Peano’s Arithmetic.
system is consistent if and only if
no invalid statement can be derived from the axioms using the inference rules.
In other words, consistency means that no statement is both valid and invalid
according the definitions above. A formal system is complete
if every well-formed statement can be proven either valid or invalid.
is very important. A formal system that uses a variant of propositional calculus
is either entirely consistent or it is explosive: all
statements are both valid and invalid! There are some formal systems that are paraconsistent;
their inference rules keep a single inconsistency from getting out of hand;
unlike propositional calculus, you cannot infer the validity of every statement
from a single inconsistency. A dualistic system without a set of inference rules
is automatically paraconsistent.
Meaning is an expression of isomorphism
between a formal system and some other system. A statement in a formal system is
true if it corresponds to a valid statement in another system.
A formal system itself is sound if
all its valid statements correspond to valid statements in another system. Note
that the system against which we are checking the formal system need not itself
Ontology and Epistemology
course, it’s unsatisfying to simply match one formal system to another. What we
want to do is map a formal system to "reality". But we have a
bootstrap problem: How do we determine what is a valid statement of
discussion reality, we want to make a distinction. We want to talk about what
reality really is, and what we know about reality. We have the intuitive sense
that there is a significant distinction between what really is and what we know,
so we divide our philosophy and create ontology,
what is, and epistemology, that
which we know about, and a way to relate the two. We call the collection of
ontology, epistemology and the method to relate them a metaphysical
philosophy happens via a subset of language that operates as a formal system. As
philosophers, we want to create true sentences about reality and true sentences
about knowledge. We can create plausible axioms, and we can create rules of
inference that seem reliable, but how do we create meaning?
simply construct a formal system of ontology, claim all the valid statements are
true by definition and leave it at that? We simply assume that meaning is
inherent in the formal system itself. Such is the claim of Platonism and other
forms of rationalism. This metaphysical system has some problems though. The
first is sterility. If we say that "reality" is the inference rules
themselves, our philosophy seems sterile. We can construct complicated
statements in propositional calculus with lots of p’s and q’s e.g.
"(p->q)^(r->~q)->(q->p)^(q->~r)", and call them valid
or invalid, but it’s hard to understand those strings by
themselves as statements about reality. We need some axioms to work
with — we need to map the p’s and q’s to something more satisfying.
run into the other horn of the dilemma: we can add axioms to make a formal
system, but we can make formal systems that contradict each other, but are
internally self-consistent! I can create a formal system where the string
"2+2=4" is true, and another where "2+2=4" is false.
Obviously, the axioms differ, but that still leaves the question of which axioms
we should assume first place.
just take what we believe that we know and use that for an axiom set? In essence
we assume we know something, and reason from there. This tactic is difficult
because we really have no basis for assuming axiomatic knowledge other than our
perceptions, but our perceptions make poor axioms since they are complex.
Statements about perceptions always include three terms: this brain in this set
of circumstances will have this perceptual experience. It is difficult to use
propositional calculus or other inference rules on complex statements; it is
easier to infer complex theorems from simple axioms rather than the opposite.
can do, though, is create an empirical epistemology: We define repeatable
statements of perception as valid statements. We reverse the true and valid
qualifiers defined above: a statement is true if it maps to an actual
perception; all true statements are axiomatically valid. But, as noted above,
perceptions make poor axioms for a formal system, so we will abandon inference
rules and make our epistemology merely dualistic. This restriction has intuitive
appeal: we cannot infer the existence of a perception, we have to actually
a definition of knowledge. But to gain it, we’ve had to throw out inference
rules entirely; every perception has to be taken on its own terms and we can
never think about relationships between perceptions, since those relationships
have to be deduced using the inference rules we have thrown away.
then do is create an ontological formal system and give it meaning by relating
it to our epistemological system. Thus an ontological statement is valid if it
follows from the axioms and inference rules, and it is true if it maps directly
to an epistemological axiom as determined by perception. We can then say that
our ontological axioms represent reality, at least to some degree.
constructed for ourselves a fairly simple metaphysical system: Empirical
Objectivism. Our epistemology is empirical and perceptual, and our ontology
postulates the existence of an objective reality that causes these perceptions.
This essay obviously sweeps a huge amount of subtlety under the rug, but we’re
just looking for a broad overview.
western experimental science rests on the metaphysics of Empirical Objectivism,
we can refer to a person who holds these metaphysical views as a scientist.
Comparing Metaphysical Systems
are many other metaphysical systems that differ greatly from Empirical
Objectivism. They are all formal systems of some kind: They include axioms and
inference rules of one sort or another. They are all dualistic: They try to
divide statements into valid and invalid. They all try to capture meaning: They
want to say their valid statements are true statements of reality.
can we compare them? In essence, we want to privilege
a metaphysical system and claim that its statements about reality are
"better" than an alternative. However, to talk about
metaphysical systems, we have to construct a new metaphysical system to do so.
In essence, we have to privilege a metaphysical system to determine which
metaphysical system to privilege! We have an unsolvable bootstrap problem.
no basis for choosing a metaphysical system other than personal opinion. We have
to accept metaphysical relativism.
have faith in the Judeo-Christian Bible? Then you accept the Judeo-Christian
Bible as a collection of valid epistemological statements about reality. You
pretty much have to assert the existence of God and many of His properties as
ontological axioms. No one can argue with you, No one can impose a different
metaphysical system on you.
have faith in your perceptions? Then you have to accept your perception as valid
epistemological statements about reality. You pretty much have to assert the
existence of an objective reality that gives rise to your perception as an
ontological axiom. No one can argue with you, No one can impose a different
metaphysical system on you.
are two forms of Christian metaphysical systems. One uses the same sort of
ontological and epistemological structure as Empirical Objectivism – The
Judeo-Christian Bible forms the definitional epistemological system and its
adherents construct an ontological system that maps to their epistemological
system. Since the bible contains statements apparently in contradiction to each
other, this method allows biblical epistemology to remain at least
paraconsistent; additional ontological axioms can be added to resolve these
apparent contradictions. Different sets of ontological axioms define different
Christian sects. It is even possible to merge biblical and empirical
epistemologies, and construct an ontology that maps to both.
Objectivism and these sorts of Christian metaphysical systems use epistemological
primacy. True knowledge comes from an epistemological definition of
knowledge. Ontological statements are always conditional; although the theorems
map to valid epistemological statements, it is always possible to construct a
superior ontological formal system – the new system might derive more theorems
that correspond to actual knowledge or have simpler axioms or inference rules.
Presuppositionalism, however, like Rationalism and Scholasticism, uses ontological
primacy. The ontological formal system is defined to be correct, and
its theorems are defined to be knowledge. The advantage is that your derived
knowledge is absolutely true.
Presuppositionalism attempts to compare its ontological axioms, its presuppositions,
to those of an alternative metaphysical system; we will use Empirical
Objectivism as defined above. We don’t need too much subtle detail –
Presuppositionalism compares only broad features of alternative metaphysical
Transcendental Argument for God forms the first comparison method of
Presuppositionalism. Ontological formal systems include inference rules, usually
some variant of propositional calculus. But why should we use propositional
calculus instead of surrealism or pure chance? The Presuppositionalist proclaims
he has a reason: That God mandated
a particular logic. But the TAG just moves the hiding place for the axioms and
logic. Both the theist and the non-theist are making assumptions for the purpose
of constructing an ontological formal system. The theist just moves the
underlying assumption back a step, from the inherent validity of logic to the
inherent validity of God. This form of ontological proof of God has been around
for a long time and has been extensively refuted by Michael Martin, among
technique is to take criteria by which an alternative metaphysical system
evaluates itself, and then show that the metaphysical system itself does not
meet its own criteria. This method was used to destroy Logical Positivism as a
consistent metaphysical system, by hoisting itself on its own petard by
elevating the verification postulate from an epistemological definition to a
metaphysical criterion, which it itself could not satisfy. Since then,
philosophers are more careful. They don’t directly include in their
metaphysical system self-invalidating criteria.
pretend to demolish a metaphysical system by using deconstruction.
is actually a fallacious technique: It misuses the ideas of logic that it claims
are supporting its analysis, but the inherent fallacy is subtle and often hard
to see. It rests on the tiniest shade of equivocation fallacy between
alternative metaphysical systems.
"deconstruct" a metaphysical system in comparison to an alternative
system, you must first identify a criterion that exists in both systems, but has
subtly different meanings in the two. Introduce the criterion as defined by the
original system, then evaluate a different piece of the original system by that
criterion as defined by your own system
and show the contradiction. Once you have "proven" a contradiction,
then the rest of the original metaphysical system falls apart. You then step in
with your own metaphysics, yell QED, and skip off the Caymans while your
bewildered victims are still trying to figure out the books.
Fundamentalism is a metaphysical system that considers only the statements of
the Judeo-Christian Bible to be epistemologically true – they are primary
knowledge, revealed by God. All knowledge comes from this reference, there is no
other source of primary knowledge.
is thus epistemologically closed.
The Bible is, by definition, a complete epistemological foundation — it is
finite and unchanging; all the facts are in. If it’s in the Bible, it is a fact;
if it’s not in the Bible it’s not a fact.
Objectivism is epistemologically open.
We may always get new perceptions that may radically change our conception of
ontology. Additionally, the very existence of an objective reality seems to be
inferred from the apparent consistency of perception. But this is not really
true — new perceptions don’t change objective reality itself; they merely
reveal subtleties or errors in the ontological formal system that represents
equivocation confuses certainty with epistemological closure. Since the
fundamentalist has epistemological closure (he has, by definition, all
the facts), he can call his metaphysical system "certain"; no new
knowledge will subvert his ontology. Since the scientist may always receive new
perceptions, he doesn’t know that his ontology will not be completely
Presuppositionalism ignores the connection between his own epistemology (the JC
Bible) and his ontology is just as tenuous. His ontology also must be inferred
from epistemology. The ontological fact of God’s existence certainly can be inferred
from the valid biblical statement "God said, X", but his inference is
no more "direct" than the scientist’s inference that atoms exist from
the valid empirical perception of an experiment.
closure is only a valid criteria according to Fundamentalism; to make this
evaluation work, the fundamentalist has to privilege fundamentalism as an
evaluative metaphysics; it’s then trivial and obvious that according to
Fundamentalism’s criteria, fundamentalism is superior to Empirical
Objectivism. It’s equally unsurprising and trivial that Fundamentalism fails
badly in the reverse scenario.
Epistemological vs. Ontological Primacy
above, Christian Presuppositionalism uses ontological primacy. This method has
the advantage of defining all knowledge as absolutely correct. If the axioms and
inference rules are never directly testable no one can ever make a substantive
refutation of the specific claims of this metaphysical system. But ontological
primacy, used for a millennium by Catholic scholastic philosophers, has a severe
limitation: It doesn’t make any progress in describing the physical world. One
can’t postulate the existence of the Triune God and conclude that you’ll eat
better if you rotate your crops. Another problem is that the supposed absolutely
true axioms of the JC Bible contradict each other – you need additional axioms
of interpretation to maintain consistency.
Objectivism uses epistemological primacy. This method abandons the idea of
gaining knowledge with deductive certainty. However, the scientist can predict
new experiences. If he can create a theorem from a set of axioms that maps to an
actual perceptual experience, then he might hope that other theorems will also
map to perceptual experiences. The predictive power of Empirical Objectivism is
presuppositionalist equivocates the term deductive certainty an internal
contradiction of Empirical Objectivism. Empirical Objectivism defines knowledge
only in terms of statements about perception. Ontological deductions are not
knowledge in the strict sense of the word; it’s better to use the term
"understanding" for valid and true ontological statements. Deductive
epistemological certainty has no meaning in Empirical Objectivism unless you
confuse empirical knowledge with ontological understanding. This confusion is
understandable since ontological deduction is
knowledge according to Presuppositionalism.
is another equivocal criterion. It is an ontological conclusion of
Presuppositionalism that it is ethically wrong to for anyone to hold a contrary
metaphysical system. Thus the Fundamentalist must coerce others to adhere to his
metaphysical system; otherwise he himself is an accessory to an ethical wrong.
Of course, one must be "certain" of one’s conclusions before one can
the scientist is under no such internal imperative to impose or coerce Empirical
Objectivism on others. He simply makes his specific conclusions available to
others. If someone wants the pragmatic value of Empirical Objectivism, he may
then adopt it. And the pragmatic value of Empirical Objectivism is undeniable —
all of modern technology relies on it.
Reversing the Fundamentalist Attack
show, however that the fundamentalist explicitly
makes use of Empirical Objectivism, whereas the scientist never explicitly makes
use of Christian Fundamentalism. All of the tasks of daily living make use of
the presuppositions of Empirical Objectivism. When one is looking for one’s car
keys, even the fundamentalist will try to deduce non-theistic ontological
theories and test them by empirical observation — He will think, "where
did I last see them," and go check there.
the intelligent fundamentalist (especially one communicating with a product of
technology such as a computer) will claim that Empirical Objectivism is just a
special case of Biblical Fundamentalism. However that "special case"
seems to cover every aspect of ordinary life. The fundamentalist must go to
areas of inquiry unavailable to perception to find a domain where Christian
Fundamentalism differs from Empirical Objectivism: Life after death, the
creation of the Universe as a whole, and the existence of ethical facts.
to reconcile the plain meaning of Biblical text with the plain meaning of actual
perceptions, the fundamentalist must either construct a complicated, rococo
ontology, create "interpretations" 180 degrees from the apparent plain
meaning of biblical verses and/or perceptual facts, or deny the evidence of his
own senses. Although the objective reality of Empirical Objectivism is certainly
non-trivial, one has, at least, the plain meaning of perceptions as a shared
epistemology to maintain consistency.
course fundamentalists are not stupid. They’re not going to create a
metaphysical system with obvious internal contradictions. But the fact that even
the fundamentalist relies on Empirical Objectivism for his daily life gives a
patina of ridiculousness to his claim that faith is somehow better
‘ 2001 Larry Hamelin. All rights reserved.