Presuppositionalism and Metaphysics

Larry Hamelin

Formal Systems

Formal 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.

A dualistic 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.

For 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.

A formal 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.

Consistency 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 be formal.

Ontology and Epistemology

Of 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 "reality"?

When 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 system.

All 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?

Can we 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.

Then we 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.

Can we 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.

Empirical Objectivism

What we 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 perceive it.

We have 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.

What we 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.

We have 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.

Since 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

There 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.

So how 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.

There is no basis for choosing a metaphysical system other than personal opinion. We have to accept metaphysical relativism.

Do you 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.

Do 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.

Epistemological Christianity

There 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.

Empirical 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.

Christian Presuppositionalism

Christian 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.

Christian 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 systems.

The 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 others.

Another 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.

Deconstruction

One can pretend to demolish a metaphysical system by using deconstruction.

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.

To "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.

Epistemological Closure

Biblical 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.

Fundamentalism 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.

Empirical 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 objective reality.

One 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 supplanted.

However, 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.

However 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

As noted 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.

Empirical 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 undeniable.

The 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.

Imposition 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 coerce others.

However 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

One can 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.

Indeed, 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.

Indeed, 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.

Of 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 than science.