|
|
by: Eric Engle
I. Practical Reasoning via induction: Reasoning from "Is" to "Ought"
III. Circular patterns of inference
a. Repetition
b. Recursive Algorithms
a. Tautology
b. Self definition
c. Rationalisation
d. Reductio or indirect proof
The objective of this brief paper is to expose the basic heuristics
of legal reasoning. These heuristics are exposed both to show how legal
science is based on logic and also to further efforts to represent law
computationally. This paper does not attempt to prove that Hume´s
law is only a counsel of practical reasoning but is intended to show, among
other heuristics, the fundamentals of practical reasoning.
I. Practical Reasoning via induction: Reasoning from "Is" to "Ought"
David Hume argues, supposedly, that one not ought to reason from factual
“is” statements to normative “ought” statements. Many contemporary theorists
overstate Hume – ignoring or dismissing outright the paradox that Hume
himself presents an ought statement. Hume only offered a practical piece
of advice, that thinkers must explicitly demonstrate their chain of inference
from "is" to "ought" or risk incomprehension and rejection for failing
to carry their burden of proof. Hume’s counsel is certainly correct, given
the controversy concerning normative inference. Thus in adressing the question
of the relationship between "is" and "ought" we must first determine exactly
what is meant by the term "ought". "Ought" statements are first irreal;
they concern factual conditions which do not exist. Second, the "ought"
statement
indicates the desire of one person. So if we are to understand what is
meant by "ought" statements, we must also understand what is desirable.
In other words, the
questions of value (axiology) are inherently linked to (normative) questions
of what "ought" to be.
The relativist line of reasoning argues that in fact
values are personal preferences having no objective existence. For this
perspective, values do not exist outside of personal
On the other hand, an "objectivist" proposes that
values have an objective existence. That is, it would be possible to say
that something is good or bad and to verify that statement according to
objective facts, such as statistics.
Our position is that there are in fact objective standards
of what is desirable (the good) and what is undesirable (the bad).Quite
simply, it is desirable for humans, both individually and as a species,
to survive and reproduce. Further many other 'goods' can be expressed in
terms of their tendancy to increase individual or species survival. It
is founded on an essentially teleological argument. The finality of the
human species is survival and well being. This finality is served by certain
acts, and disserved by others. However our position that certain acts are
desirable and others undesirable appears self evident. Our position could
also be presented as a postulate. Either as a teleological argument or
as a mere postulate it seems practical. For in fact any society which does
not assure its own survival within one generation and its regeneration
via reproduction would become extinct.
Our position, while correct (extinction being the
lot of any other arrangement) is however faced with a dilemma. Individual
and species survival are normally mutually reinforcing. After all, the
species is composed of individuals. The dilemma which arrives however is
that individual and species survival are not always mutually reinforcing.
Further determination of moral priorities in choice of evil problems cannot
be determined without a knowledge of the specific facts of the case in
question. Thus while our position seems self evident it does not permit
easy resolution of difficult problems.
Ought statements are in fact possible because what is desirable ('good')
is not purely subjective - though any adequate definition of 'the good'
is necessarily complex. If ought statements are possible, can we then determine
'ought' from 'is'?
Remember in our definition we simply say that 'ought'
is a description of a desired factual condition. In fact whether 'ought'
conditions can be objective or are always subjective is irrelevant in determining
whether we can infer from a description of what is to a description of
what one ought to do to obtain a certain desired state of affairs. Once
we admit that person X desires outcome A under condition Y and that steps
1, 2 and 3 will create outcome A if condition Y is true, it is logical
for person X to infer that he should undertake steps 1 to 3. And thus we
have in fact reasoned inferentially from 'is' (condition Y) to 'ought'
(steps 1 to 3, necessary to create outcome A). Of course if steps I, II
and III led to that outcome the person would have another prudential choice
to make. But in any case his or her choice would be a form of practical
reasoning.
Thus, for an example of the inferential pattern of
practical reasoning:
[i believe] All killing is wrong
Capital punishment is killing
therefor [I believe] capital punishment should be
outlawed
The brackets indicate how the argument is transformed
if on adopts a relativist moral theory.
We could also look at the question from a materialist
perspective. A purely materialist perspective would lead to the argument
that all ought statements are in fact derived from what is. For the materialist,
mentation is a simple chemical reaction. Thus mind does not exist apart
from brain. And in this sense all phenomena, including moral theory are
merely material. However since this argument requires one to assume materialism,
and since our demonstration of the operation of practical reasoning seems
adequate even if "good" and 'evil' were fictions, the materialist position
seems actually less certain - though it is a valid position, if one presupposes
that all phenomena are in fact material.
The question as to whether a form of practical reasoning
exists shows how persons think to solve problems. However in considering
how we think - in thinking about thinking - we descover that our thought
process, while apparently intuitive and wholistic in its elaboration, is
verified and demonstrated in a linear fashion. Thus our intuitive hypotheses
are either refuted or maintained through rather rigid structured and finally
empirical methods.
In
terms of modeling intelligence, intuitive creativity appears to grow out
of illogical patterns, such as rhyme, free association, and the linking
apparently unrelated phenomena. Reproducing creativity and intution in
machines will be for this reason probably the final step in artificial
intelligence - barring a breakthrough at the level of microprocessors which
would permit non-hierarchical permutations of data stored in a hierarchical
fashion. In other words, just as todays computers have math co-processors,
tomorrows may have pseudo-random permutational coprocessors. This of course
does not rule out revolutionary changes in microprocessor technology such
as nano-technology or biological or analogical computers - all of which
are possible.
One
of the reasons for considering methods of reasoning from real to irreal
conditions is that it forces a reconsideration of mental algorithms. As
we increase our awareness of these algorithms we can discover a multiplicity
of methods for problem solving. Our task as logicians would then be to
trace these different algorithms and attempt to develop a heuristic for
determining which algorithm to apply under which circumstance.
The
elaboration of heuristical algorithms is of course also the foundation
for the creation of systems of artificial intelligence. If a.i. is to develop
from highly specialised expert systems into more complex generalist systems
then it might do so through linking of a variety of different expert systems
with some form of general 'choice' heuristical algorithm to determine which
expert system to apply.
So
what exactly happens in reasoning from a real to an irreal condition? First,
a desired conclusion is formulated (let us ignore for the moment how).
Then a question is posed: what steps would lead to this conclusion? This
question may yield several different responses, or none at all. After potential
'solutions' are elaborated, they are then tested. So if we have four possible
'solutions', but 1 is impossible and 4 is untrue we must then determine
which of the two remaining solutions - both are possible - is best suited
to achieve our desired outcome. We might refine this technique to say that
we test each potential solutions possibility and truth, before admitting
it into the list of available solutions. In either case an algorithm to
choose among or between different possibilities could involve a system
of weighted averaging; it could also be elaborated to consider
other exogenous goals.
It
should also be noted that this technique is morally empty. It could be
used for the elaboration of any goal, whether good or evil. Tools are neutral.
It is possible, using existing technology, to model intelligence in this
fashion.
It
is entirely possible to write a computer program to effectuate this task
provided we can represent the desired outcome, and potential steps to achieve
it, in mathematical terms. For example, a binary variable "achieved" with
two states, true and false.
It
is our position that considering supposedly flawed methods of reasoning
can be heursitically fruitful for machine models of intelligence. Thus
we are going to examine the methods of reasoning traditionaly presumed
invalid in order to determine what is their invalidity and whether they
might help us to model intelligence with machines.
III.
Circular patterns of inference
Attacks upon a line of reasoning are often based upon the accusation
that that line of thought is in fact a circle.
I
have quite carefully chosen to consider 'logic' in linear terms, and errors
in logic in elliptical terms, for that is the dominant pattern of western
rationalism since Aristotle. The male/vertical/line/argues to build a hierarchical
structure. If the capstone of that structure is in fact also the foundation,
the structure collapses from lack of internal hierarchisation. Now
the problem with this circular reasoning is that logic must, if we continue
the analogy, be based upon some foundation. That foundation is of course
the necessary presuppositions - the postulates - of the hierarchical edifice
described or constructed. In other words, the potential of infinite regress
is inherent in circular argument. We can always ask 'why this presupposition'.
If we are honest we either admit the presupposition is indemonstrable (my
position) or refer to another argument; yet this second argument will also
have... a necessary presupposition. The inquiry into first causes, if pursued
relentlessly, is interminable. What happens after we reach the horizon?
More horizon... At
the same time as western rationalism has sought to demonstrate, to prove,
the positions of some line of reasoning, it also ellides about another
position. Now if we can, to borrow from Claude Levi-Strauss, describe a
line of reasoning as implying male/vertical/hierarchy, we might also associate
(in the non rational imagination) circular argumentation with spheres/female/darkness/night.
In other words rational-linear verification in fact work in tandem with
irrational-circular-intuitive creativity. Whether
such free associations have any collective purpose or objective existence
is actually irrelevant. These types of analogical links even when non rational
allow us to improve our own self understanding by giving organising principles.
Further they allow us to “think outside of the box” and can thus help us
to 'shift' our mental state revealing new solutions to old problems. Irrationalism
and intuitionism are possible keys to developing self-teaching inference
engines or other problem solving forms of machine intelligence. Upon
an examination of circular patterns of inference we discover that in fact
there are several different forms of circularity. Some of these forms of
reasoning are quite correctly dismissed as illogical and leading to untrue
conclusions. Other forms of circularity are however perfectly valid. Some
of these valid forms of circularity are accepted as valid, while others
are incorrectly rejected as invalid. These final forms of circularity -
arguments traditionally rejected as invalid but which may in fact be valid,
are especially of interest to our analysis. These
two forms of errors are both invald - which may explain why some imprecision
in terminology. It is best to simply say 'the argument assumes the position
it tries to proove' in order to avoid any ambiguity as to ones critique
or to say that the argument must consider the validity of its presumption.
The first critique invalidates the truth of the argument in question. The
second merely asks us to reconsider the argument and thus is not a refutation
- particularly if the position critiqued was presented as a postulate.
1.
Circular inferential patterns which are perceived as invalid and which
are invalid
This
category of erroneous reasoning is the easiest in that it is habitual.
We say nothing new here.
a. Question Begging (Petitio
de Principe)
If
we assume the point to be proven as a foundation for an argument to prove
the point presumed then our reasoning must be characterized as erroneous.
This type of error - assuming the argument to be proven - is often called
question begging, or in latin petitio de principe. It is better
to use the latter term because sometimes question begging is used to describe
the situation in which a person ignores a flaw or error in their own position.
Sometimes a philosopher does not adress the validity of a postulated position,
and is then accused of question begging.
2.
Circular inferential patterns which are perceived as valid and which are
valid
a. Repetition
This form of circularity is rather straightforward. If I present an
argument, and merely repeat myself, there is nothing inherently circular.
For example at Time 1 (T1) I argue 1+2 thus 3. At time 2 I repeat this
same argument. While there is a repetition, it is certainly not in itself
invalid.
b. Recursive Algorithms
if yes then end
if no try B
If we have a 1 digit code between 0 and 9 generated
randomly a simple for...next loop of ten iterations will determine the
code value.
A recursive algorithm in contrast requires a function
call to another procedure. For example, if I am to determine the number
of words which may be formed using the letters a, b, and c then a recursive
method would determine:
1. the number of letters (n)
2. the combinations possible for letters (n-1)
until such point as it had exhausted all letters.
Recursive functions are complex in that they call
themselves. However they are perfectly valid.
For example recall the famous experiment wherein captive monkeys are given a ladder or a stick and bannanas are suspended from a cieling. The desired outcome is to eat the banannas, and the possible solution is to use the ladder as a tool to obtain the fruit. If problem solving is a part of intelligence then monkeys appear intelligent - for they do indeed use the tool given them to obtain the goal desired.
Our conclusion then is that good and bad can be objectively defined in terms of their tendancy to further individual and species survival; that this objectivist conclusion is in fact irrelevant to the determination of how one can legitimately infer from a statement of what is to the materialisation of a currently irreal condition. And that this raises other tangential questions of intelligence and logic which merit exploration for their potential contribution to the field of artificial intelligence. We note that the term 'circular reasoning' is not at all monolithic. There are several different forms of circularity. Some appear invalid and are invalid. Others appear valid and are valid - simple repetition, but also recursive algorithms. The truly problematic category of circularity in patterns of inference is the form of reasoning which is generally construed as faulty but which in fact is valid. Tautology, mutual definition, and rationalisation are all potentially fraught with the risk of ill reason. However these forms of argumentation can be used, with certain caveats, in structurally valid hierarchical argumentation, despite the recursions that they imply. These forms of reasoning, particularly rationalisation, will be central in the evolution of artificial intelligence from expert systems to generalist systems as machine intelligence 'learns' how to solve complexe problems.