Offering a response to Chris Bolt Part 2

This post is a follow up to this one.

Conventional notions of truth and falsity in our natural language and in our everyday discourse are what I consider to be a useful fiction. It is not that these every day notions are just flat our wrong, but they are the products of our natural language, which is a messy and vague affair. I adhere to a correspondence theory of truth or to put it more finely, a proposition is true if and only if the proposition’s satisfaction conditions have the relevant truth maker(s).

I’ve been persuaded by Alfred Tarski  that the best way to pursue and understand truth when it comes to object languages and logic, is that truth is a hierarchical affair. Propositions must have their satisfaction conditions met from another source not itself. The paradox Chris Bolt and I have been discussing is a paradox rooted in epistemology and metaphysics. We have been looking at a proposition that simultaneously meets and does not meet the satisfaction conditions, the truth doesn’t seem discernable prima facie, but let us take a closer look and see if we can’t make sense of the issue.

 

Let us say that the following the following takes place in language lⁿ. In this case lⁿ is an object language and a meta-language;  l^n-1 is an object language from lⁿ and lⁿ⁺¹ is the meta language for lⁿ.  Each language lⁿ contains every wff from l^n-1 and has a predict that belongs to every true wff* and only true wffs of l^n-1, let us call this Tⁿ. Tⁿ cannot apply to any wff of lⁿ unless that wff also belongs to l^n-1.  Let us assume the following T-schema:

(A1) s is true iff p

Understand (A1) as s being a designator (understand this as just being a name) of a wff and p is the wff itself. An instance of this would be something like this:

(P1) the sun is a star

Using s as the designator (P1) and p as the wff:

(A1a) "the sun is a star" is true if and only if the sun is a star 

Simple enough, but let's generate the paradox Chris and I are discussing:

(P2)   P2 is false

Using (A1) we get:

(A1b)    "P2 is false" is true if and only if P2 is false.

While it looks like the semantic paradox, it actually isn’t. Let me put a few things in brackets to show why:

(A1b) "P2 is false" [lⁿ] is true [Tⁿ⁺¹] if and only if P2 is false [lⁿ]

The liar paradox cannot be stated in this hierarchy, because any language it is written in will not have the proper truth predicate. Problem solved.  But what of Chris?

What tools does the Presuppositional/Covenantal have at their disposal? After all, philosophy, logic, and (dare I say) Truth as well, are all subservient to theology proper in the Presuppositional/Covenantal system. Consider what Van Til wrote:

If then every fact that confronts me is revelational of the personal and voluntary activity of the self-contained God, it follows that when I try to think God’s thoughts after him, that is to say, when by means of the gift of logical manipulation which this Creator has given me, I try to make a “system” of my own, my system will…at every point be analogical of the system of God…On the other hand, since he human mind is created by God and is therefore in itself naturally revelational of God, the mind may be sure that its systems is true and corresponds on a finite scale to the system of God. That is what we mean by saying that it is analogical to God’s system. It is dependent upon God’s system, and by being dependent upon God’s system it is of necessity a true system…(Taken from Van Til’s Introduction to Systematic Theology, page 181)

In what way does Chris’ simulacrum of God’s divine system answer this paradox? In what way are we thinking God’s thoughts after him when think of this scriptural passage that was at the top of my original post?

“One of the Cretans, a prophet of their own, said, "Cretans are always liars, evil beasts, lazy gluttons." This testimony is true.” (Titus 1: 12-13a)

Now I can respect that Paul was making a rhetorical point in citing Epimenides, he was as Greek as they come. To most Christians (and to most apologists) this isn’t much of an issue, but it is for the Presuppositional/Covenantal apologist. Here we have a proposition embedded in scripture that is both thought of by unregenerate and regenerate minds, both Jew and Gentile, that simultaneously affirms and denies its own truth value.

This proposition exists. It is a contradiction. How does it stand in relation to the Triune God? How is this proposition grounded in Almighty God? How does Chris account for it? Notice that is what was lacking in Chris’ response to me, he assured me that:

For the sake of context, Pat should probably know two other things going into his argument. First, more sophisticated presuppositional apologists, including Greg Bahnsen, recognize that classical logic is not the only game in town. There are many logics. Second, not all presuppositionalists affirm the so-called “impossibility of the contrary” as a part of their apologetic. Some third generation Van Tilians in particular have advocated “attenuated Van Tilianism” instead. These two points do not constitute an earth-shattering reply to Pat, but they are worth considering.

But no reply as to how this paradox is resolved within Presuppositional/Covenantal framework. The standard Presuppositional/Covenantal reply I’ve gotten use to is just to shift the conversation and focus in on some facet of what I said, looking for some hidden nugget to call a contradiction and avoiding the issue at hand (looking at you Sye), but Chris isn’t that type and I hope that at least these issues prod him into some useful reading and thinking.

 

 

* For now, understand well formed formulas as propositions and their negations.