Hoffmann's idea of
demonstrating truth of something is based on the notion of closing
off possibilities – when we can show that alternative accounts are
against some principle of reason, we can be sure that the remaining
account is the true one. In some cases, we cannot do this either for
a proposition or for its contradictory. In that case, we can just
conclude that both propositions are possible.
This possibility in
question is logical, and as one might have guessed, Hoffmann thinks
it is just one type of possibility. A more formal notion is verbal
possibility, which just means that the words used in a proposition
refer to some ideas. On the other hand, a more substantial notion is
metaphysical possibility, by which Hoffmann means lack of
contradictions, while even more substantial is physical possibility,
which means capacity to physically actualise content of some
proposition.
Getting back to
logical possibilities, they are lacking in the sense that they come
with no way to justify them. Indeed, this lack of justification makes
it natural for us to reject them and thus they can be called
internally improbable. As one can clearly see, if proposition and
its opposite are both considered just possible, both of them are
internally improbable. A more interesting notion of improbability is
relative improbability, which is improbability arising from
comparison of proposition with its contradictory. Probability is then
defined as a counterpart to relative improbability: if we consider
proposition to be more likely to affirm than its opposite, although
both are possible, the proposition is probable.
Just like
demonstration must be based according to Hoffmann to some principles,
so must argumentation through probabilities. The basic idea behind
argumentation of probabilities is that a proposition always implies
or involves a number of conditions that the world must satisfy. Some
of these conditions could be accepted without any ado, but others
require more justification. The more a proposition involves
conditions that require justification, the less probable it is.
One interesting
question is whether Hoffmann meant us to read these characterisations
of probability objectively or subjectively. The answer is that he
actually had both possibilities in mind. Probabilities might be just
subjective, if our incapacity to justify the seemingly improbable
propositions is just based on our lack of experience or on general
limitations of human cognition. If we can show that neither is the
case, we can conclude that the probabilities are objective.
It might appear that
Hoffmann's principle of probability is difficult to apply in concrete
cases. Yet, just like in case of demonstration, the highest principle
implies a number of more particular principles that are easier to
use. Thus, we know that the less possibilities an event has for
occurring, the less probable it is. This means, among other things,
that a single possibility is more probable than a combination of many
independent single possibilities and that a more indeterminate
possibility is more probable than a more determinate possibility.
Hoffmann is
satisfied with mere general rules, but notes that there are many
kinds of probability, each having their distinct rules. As one could
guess in case of Hoffmann, the probability could be about causal or
existential propositions. Causal probability can be physical, that
is, concern reasoning either from causes to effects or from effects
to causes. On the other hand, it may also be political probability,
which concerns reasoning from the means a person uses to the ends he
strives to attain, or moral-practical probability, which concerns
reasoning from given ends to means required for those ends.
Two kinds of
existential probability concern things past (historical probability
of what has happened) and things in future (whether something will happen in
these conditions). In addition, Hoffman points out a third class
relating to signs. These signs might be some concrete things, for
instance, when a diplomat tries to determine what a representative of
foreign nation means by his expression. Yet, in most cases the signs
are words. One is either trying to determine the meaning of words in
general, in critique, or then the meaning of words in a particular
text, in hermeneutics.
The importance of
emphasising these different types of probability lies in the distinct
presumptions made in each field. Presumption, Hoffman defines, is a
proposition taken as probable in some particular field of knowledge.
The presumptions are valuable, because due to their probability they
can be used as premisses in probable reasoning. Particularly, if some
proposition is in conflict with such a presumption, its contradictory
will be more probable. Hoffmann enumerates a number of possible forms
of presumptions: we might, for instance, think something is probable,
because its absence is rarity or because there is no cause to suggest
otherwise – or even that this presumption is accepted by reliable
authorities.
Hoffmann goes to
some lengths to describe how probabilities could be quantified. In
general he delineates two alternative possibilities, arithmetical and
geometrical. In arithmetical quantification of probability one
chooses some arbitrary unit of probability and compares other
probabilities to it, while in geometric quantification of probability
they are compared to the totality of completely certain proposition.
***
This is as far as I
will go with Hoffmann's Vernunftlehre,
although he still does have couple of interesting things to say about
the forms of method (analytical, synthetical and
analytic-synthetical) and their various subtypes (for instance,
mathematical synthetical method differs in Hoffmann's eyes very much
from other types of synthetical method, because it alone cannot be
used to justify existence assumptions). Instead, I am going to make a
comprehensive estimate of Hoffmann's life work.
Because
most of Hoffmann's shorter writings had been written against Leibniz,
Wolff and Wolffian school and even his masterpiece, Vernunftlehre,
contained many explicit and implicit criticisms of their positions,
it seems especially interesting to consider what are the actual
differences between Wolff's and Hoffmann's positions. Clearly, Wolff
and Hoffmann disagreed especially in metaphysical questions – e.g.
Hoffmann thought Leibnizian idea of pre-established harmony to be
ridiculous, while Wolff suggested it was the best possible hypothesis
about body-soul interaction. But what is especially interesting is
the question whether Hoffmann's
logical works are any different from Wolff's logic.
It
is easier to begin with similarities
and on basis of the common elements to find the specific differences characterising Wolff's and
Hoffmann's notion of logic.
First of all, it is clear
that both Wolff and Hoffmann understand logic not just as a
description of a formal structure of thinking, but as a methodology
of scientific research. But the two philosophers differ in their
beliefs concerning the unity of this methodology. Wolff strives to
give a unified methodology of sciences, and in cases where he admits
the existence of many methodologies (e.g. historical and
philosophical methods, or demonstration of truth and argumentation
for probability), he is keen to suggest that one of them is ideal.
Hoffmann, on the other hand, is more
aware of the differences between disciplines and their methodologies
– mathematical reasoning differs from physical and moral reasoning.
Wolff
is not a hard-headed rationalist trying to spin everything out of
empty definitions, which is often the caricature applied for him,
but instead, he used a more mixed methodology, in which empirically
discovered premisses play an important role. Hoffmann's methodology
is similar, when it comes to empirical matters, but his acceptance of
a variety of methodologies allows far more tools of securing
knowledge – all reasoning cannot be reduced to syllogisms, Hoffmann
insists.
Both
Wolff and Hoffmann also accepted that all human methodologies have
their proper limits and that especially divine affairs lie beyond the
ken of human understanding. Yet, the reasons for their acceptance
were somewhat different. For Wolff, it is more of a quantitative
question – human understanding just cannot regard all the infinite
facets of the actual world, let alone all the possible worlds or the
infinite mind of God. In Hoffmann's eyes, there are more essential
reasons, why human mind cannot understand some things – it
has to follow the agreement
of its ideas and shun from conflicts between ideas, but it might well
be that these are merely laws of human thinking, which might lead
even to contradictions if taken to extremes. This
brings us to the greatest difference.
What
is missing in Wolff's methodological works is a deep consideration of
the very capacity to know – he just assumes the psychological
make-up of human mind and proceeds to state what are the best ways to
gather knowledge for such a mind. It is characteristic that Wolff
relegates the question of truth to the applied part of logic. With
Hoffmann, on the other hand, this question takes the center stage. He
is quite aware that justifying our capacity to know the truth is
quite difficult and requires a completely different methodology from
other sciences – if we would dare, we could call him a
transcendental philosopher before Kant.
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