Vollenhoven,
part 2 (disk 8)
Vollenhoven
and Dooyeweerd began the development of WdW with the analysis of the particular
modes of reality. Dooyeweerd set
his attention to the legal and the moral.
This had been the major focus in Jurisprudence as well as Philosophy and
Theology. Dooyeweerd had called
this the Cape Horn of Jurisprudence.
Vollenhoven approached matters from the point of view of the problems
dealt with in his dissertation. He
dealt with two problems 1) The relationship between mathematics and logic and
2) The relationship of mathematics to natural science especially to physics.
Vollenhoven
sought in his dissertation that certain lines of thought in the theory of
mathematics are a direct result of positions are taken in respect to
metaphysics. He talked about
Empiricism, Formalism, and Intuitionism.
He viewed the Empirical and Formalistic as monistic and Intuitionism as
dualistic. Monism starts with the
1 to explain the many. Dualism
starts with the many to explain the 1.
Vollenhoven takes the position that the theistic standpoint that is able
to develop a consistent dualistic viewpoint. The reason is that it does not have to deny the peculiarly
of mathematical knowledge. Here
you get the sphere sovereignty idea creeping in. How are we going to understand the diversity of the cosmos
in relation to its unity? Our
Christian viewpoint does not have to deny the peculiarly of mathematical
knowledge by making it subject to logic or natural science. Thus, we attempt to show that theism
accounts for multiplicity in the cosmos.
We note the refusal to base mathematics in logic is in both Vollenhoven
and Dooyeweerd and this denial was crucial for the development of the law
spheres. It is opposed to the
attempt of Bertrand Russell and Alfred North Whitehead in Principia
Mathematica, to
understand the foundation of mathematics in logical terms.
According
to Dooyeweerd, all of these aspects are going to be empirical in a broad sense
of the term, because they are going to fall in our experience and modes of our
experiencing.
With
respect to Vollenhoven’s idea that Christianity offers a most consistent
dualism, did he distinguish sufficiently between the creator creature
distinction and a philosophical dualism within the confines to the cosmos?
Vollenhoven
concluded that monism in the guise of materialism or psycho-monism was not able
to provide mathematics a solid basis in a system. Dualism saw distinctiveness of the psyche, it had to be
distinguished from the physical and both make contribution to the knowledge
situation. In contrast monism
discovers an all-inclusive principle in the empirical.
Vollenhoven
included that intuitionism had brought to light a truth that even though those
not of the household of faith they can come up with truth. Vollenhoven said that thought play a
part with respect to that which is not thought. In mathematics that which is non-mental is never absent from
thinking. WdW later in the
development of the idea of the concept; a theoretical concepts involves the
logical and non-logical (synthesis).
Vollenhoven
maintain that if intuitionism had come up with insight and if he agreed monism
either sacrifices the mental to the non-mental or the non-mental to the mental
(reductionism).
In
Vollenhoven’s stance there is a departure from the idea of the objective
logos. Vigorous departure from the
idea that what is amendable to thought, logical forms embedded in reality by
the divine Logos.
Furthermore,
intuitionism has room for the normative.
It can recognize the peculiarity of mathematical principles. It does not fall into the problems
connected with actual infinity as logicism does. If you absolutism the logical and if you do not see in its
distinction from the mathematical you can fall into problems with actual
infinity.
Vollenhoven
insisted that there is no reduction of space to number and he resists subordinating
mathematics to logic. Logic may
not be reduced to number. Axioms
are not purely mathematical.
Axioms presuppose the norm of the logical.
Norms are
not simply methodological, but are divinely ordained. Vollenhoven in his dissertation opposes Neo-Kantianism,
which gave undo place to methodological procedure. Neo-Kantianism the object of your thought is developed in
the process of thought itself.
Vollenhoven distinguishes the logical object from other objects, there
is a logical subject-object relationship which has its own identity. Generally speaking in the
subject-object relationship you have the subject (observer) over against the
object (observed), the thinker over against the object of thought in which
there are these objective logical forms.
The
subject-object relation exists in each aspect of reality (subject to the law
that holds for that aspect).
Vollenhoven begins here; the logical object is distinguished from all
other objects. When you have a
logical object, you don’t have reality as a whole but just a part that must be
seen within the whole. All norms
are divine in origin and that divine authority is the ground of the norms of
thought. Norms are not purely
methodological. The norms are
divine in origin because of the subject-object relationship.
You have a
logical subject-object relationship, you have other subject-object relationship
and they then are on the subject side and subject to divine law. The object then can occur in relations
other than that of the Gegenstand relation. Vollenhoven (and
Dooyeweerd) hold that there is a subject-object relation outside the Gegenstand relation. They make a distinction between the subject-object relation
in all of our activity and the Gegenstand relation where we abstract a side of it.
Examples
given:
A
chalkboard eraser – it is for something and used by me (Knudsen).
A table –
it is constructed for something
A bird’s
nest – has meaning in the life of the bird.
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