Thread: Axioms

Can we build a whole epistemological system on one axiom? That is, do we have one axiom or many? Should we be pre or post-Cartesian foundationalists?

I contend that we should have many axioms upon which the epistemology rests.

The number of axioms which one uses ought to be the fewest needed ... if an "axiom" can be proved from other axioms, then it is not an axiom, it is a theorem. One of my complaints about the state of math being taught in our schools today is that more than the axioms of the system are stated as axioms. In the geometry book being used, they have 29 postulates. There are only five in euclidean geometry, and all the rest can be proven from those five.

So from a logical point of view, the viewer axioms the better.

So I suppose here that we must determine what axiomatic statements are merely axiomatic and cannot be proved or disproved.

Examples:

The senses are a sound source of knowledge.

Deductive logic is valid and describes the way things necessarily are.

That which is absurd in reality is absurd in the philosopher's chair.

etc.

Philosophy fails at the very point of beginnings, or axioms. The fear of the Lord is the axiom of knowledge.

Originally Posted by P. F. Pugh

So I suppose here that we must determine what axiomatic statements are merely axiomatic and cannot be proved or disproved.

Examples:

The senses are a sound source of knowledge.

Deductive logic is valid and describes the way things necessarily are.

That which is absurd in reality is absurd in the philosopher's chair.

etc.

I don't understand the third, but the first cannot support itself, and thus fails as an axiom, and the second depends upon more basic components, such as the law of contradiction.

Do you still have heartburn over the axiom of Scripture? It is quite easy to deduce from Scripture the reliability of the senses, and the validity of deductive logic.

-----Added 10/24/2009 at 03:05:36 EST-----

Originally Posted by Christusregnat

Philosophy fails at the very point of beginnings, or axioms. The fear of the Lord is the axiom of knowledge.

Augustine considered philosophy as a basic premise to be consistent with Christianity, for both seek after the blessed life.

Depending upon how you wish to define philosophy, I don't think it is inconsistent with your axiom, for true philosophy does seek knowledge where it may be found, does it not?

Originally Posted by JTB

Originally Posted by Christusregnat

Philosophy fails at the very point of beginnings, or axioms. The fear of the Lord is the axiom of knowledge.

Augustine considered philosophy as a basic premise to be consistent with Christianity, for both seek after the blessed life.

Depending upon how you wish to define philosophy, I don't think it is inconsistent with your axiom, for true philosophy does seek knowledge where it may be found, does it not?

Joshua,

Yes, since the Law of God is true wisdom, and therefore, the love or pursuit of the Law of God is the only true philosophy. I used the term philosophy in the generic sense of man seeking after wisdom independently of the Law of God.

Cheers,

Adam

Originally Posted by Christusregnat

Philosophy fails at the very point of beginnings, or axioms. The fear of the Lord is the axiom of knowledge.

What can you deduce from this? Is the "knowledge" meant here the same as we mean philosophically?

Originally Posted by JTB

I don't understand the third, but the first cannot support itself, and thus fails as an axiom, and the second depends upon more basic components, such as the law of contradiction.

The third axiom is illustrated thusly: if you were arguing in a court of law and you asked the court to discount a witness because sense perception is epistemologically unsound, you would be laughed out of court because such is absurd. If such an argument is absurd in the courtroom, or on the street, then it is absurd in philosophy.

This principle is one of methodology, by the way. Of course, if one reported a miracle in court one would be laughed at, but unreasonably so. This is with regard to methodology, not to fact.

The first axiom is necessary because you can't live without it. If it's necessary for life, then it can be taken as a necessary truth without further support. An axiom is, by its nature, unsupported, which is why one must have multiple axioms.

Do you still have heartburn over the axiom of Scripture? It is quite easy to deduce from Scripture the reliability of the senses, and the validity of deductive logic.

You can't deduce the validity of deductive logic from anything--that's circular. The laws of logic are axiomatic for intelligibility and coherence.

Epistemological deduction from Scripture is backwards--you are deducing what the Scriptures already assume (and you are still assuming that the deduction is valid--you can't prove validity with 100% warrant).

Backwards reasoning is valid, but it must be acknowledged to be a posteriori.

Originally Posted by P. F. Pugh

Originally Posted by Christusregnat

Philosophy fails at the very point of beginnings, or axioms. The fear of the Lord is the axiom of knowledge.

What can you deduce from this? Is the "knowledge" meant here the same as we mean philosophically?

That is one of the other problems with speaking according to what is falsely called philosophy: it does not mean the same thing by knowledge as Scripture does.

Originally Posted by Christusregnat

Originally Posted by P. F. Pugh

Originally Posted by Christusregnat

Philosophy fails at the very point of beginnings, or axioms. The fear of the Lord is the axiom of knowledge.

What can you deduce from this? Is the "knowledge" meant here the same as we mean philosophically?

That is one of the other problems with speaking according to what is falsely called philosophy: it does not mean the same thing by knowledge as Scripture does.

So please, define knowledge scripturally.

If we mean by knowledge, simply the comprehension and assent to facts and truths about the world around us, then yes we can have knowledge without the fear of the Lord. If we mean by knowledge understanding of the character of God and our relation to Him, then indeed, we must fear Him first as the beginning of knowledge.

I do not think that when Solomon speaks of knowledge here that he has in mind what we mean when we say "I know that the sun rises in the east and sets in the west." He has something more akin to what we would call "wisdom" in the sense of spiritual understanding.

I don't know what an "axiom" is; I'm a bit cloudy on it.

I suppose there are many methods of knowing, if this is what you mean; we know things by our senses, we know things by way of testimony of others, we know things by way of rational deduction, and so on.

An axiom is a proposition that cannot be proved or disproved but must be assumed by all parties in order for rational thought to take place. That is what an epistemological axiom is.

Another use of the term refers to the first principles of a discipline. Thus, the first law of thermodynamics is axiomatic in science.

Alright. We can accept some things as reliable simply because we have to: like the reliability of memory, reliability of our cognitive faculties, sense perception, that logical forms and inferences are valid, and so on. Maybe those can be our axioms.

Now your question is, can all these be reduced to a single axiom? Well, if they can, it surely will not be Christian scripture.

The reason being is that an axiom is, by definition as you supplied, something which cannot be proven or disproven. I don't know how to prove or disprove any of the above listed suggestions. But Christianity and the Scriptures can be disproven. So they cannot qualify as an axiom.

The Scriptures cannot be disproven because they are true. I think that they can be proven, but that's a whole different matter.

Originally Posted by P. F. Pugh

The Scriptures cannot be disproven because they are true. I think that they can be proven, but that's a whole different matter.

I didn't mean disproven in that sense.

It is hard to see how an argument form like modus ponens can be disproven. We have to use it., so in disproving it, we'd be using it. That doesn't prove that it is true to life, and that the inference from P ⊃ Q; P; ∴ Q always holds everywhere. But surely I can't help but to use it.

That, it seems to me, is what makes MP an axiom: the complete inability of proving it, yet the pragmatic necessity of it.

The same doesn't hold for Scripture.