Causality and Causation
Chris Menzel asked what notion of causality I was using, and I realized
that it would be hard to explain within the 10K limit. So I started to
extract some relevant material from my KR book and added more material
to address the topics we were discussing. And it kept growing.
Right now, it's still an incomplete paper in HTML form. The abstract
and Section 1 are below, and the current state of the full paper is at
http://www.bestweb.net/~sowa/ontology/causal.htm
I'll send another note next week to address some of the topics that
have been discussed while I was trying to finish my little 10K+ paper.
John Sowa
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Causality and Causation
John F. Sowa
"Those who make causality one of the original uralt elements in
the universe or one of the fundamental categories of thought -- of
whom you will find that I am not one -- have one very awkward fact
to explain away. It is that men's conceptions of a cause are in
different stages of scientific culture entirely different and
inconsistent. The great principle of causation which, we are
told, it is absolutely impossible not to believe, has been one
proposition at one period in history and an entirely disparate
one at another is still a third one for the modern physicist. The
only thing about it which has stood... is the name of it."
Charles Sanders Peirce (1898), _Reasoning and the Logic of Things_
"The attempt to "analyze" causation seems to have reached an
impasse; the proposals on hand seem so widely divergent that one
wonders whether they are all analyses of one and the same concept."
Jaegwon Kim (1995), "Causation"
Abstract: In modern physics, the fundamental laws of nature are expressed
in continuous systems of partial differential equations. Yet the words and
concepts that people use in talking and reasoning about cause and effect
are expressed in discrete terms that have no direct relationship to the
theories of physics. As a result, there is a sharp break between the way
that physicists characterize the world and the way that people usually talk
about it. Yet all concepts and theories of causality, even those of modern
physics, are only approximations to the still incompletely known principles
of causation that govern the universe. For certain applications, the
theories proposed by philosophers, physicists, and engineers may be useful
approximations. Even "commonsense" theories that have never been formalized
can be adequate guides for people to carry on their daily lives. To
accommodate the full range of possible theories, whether formal or
informal, scientific or rule of thumb, this paper proposes a continuum of
law-governed processes, which bridge the gap between a totally random chaos
and a totally predictable determinism. Various theories of causality can
be interpreted according to the kinds of laws they assume and the tightness
of the constraints they impose.
Contents:
1. Thinking and Reasoning about Causality
2. Continuous Processes
3. Discrete Processes
4. Procedures and Processes
5. Frame Problem
6. Lattice of Theories
7. Efficient Cause, Final Cause, and Chance
References
1. THINKING AND REASONING ABOUT CAUSALITY
No consensus about causality has emerged during the century from Peirce's
remarks of 1898 to Kim's remarks of 1995. Yet people, animals, and even
plants benefit from causal predictions about the universe, independent of
any conscious thoughts they might have about causality. People plan their
daily trips to work, school, or shopping; squirrels bury nuts for the
winter; and plants turn their leaves upward and their roots downward. To
distinguish the way the universe really works from the way that anyone
thinks about it, this paper will reserve the term causation for the actual,
but incompletely understood physical principles and use the term causality
for the ideas that people use, either in their abstract theories or in
their daily lives.
In his lectures on cause and chance in physics, Max Born (1949) stated
three assumptions that dominated physics until the twentieth century:
* "Causality postulates that there are laws by which the occurrence of
an entity B of a certain class depends on the occurrence of an entity
A of another class, where the word entity means any physical object,
phenomenon, situation, or event. A is called the cause, B the effect."
* "Antecedence postulates that the cause must be prior to, or at least
simultaneous with, the effect."
* "Contiguity postulates that cause and effect must be in spatial
contact or connected by a chain of intermediate things in contact."
Relativity and quantum mechanics have forced physicists to abandon these
assumptions as exact statements of what happens at the most fundamental
levels, but they remain valid at the level of human experience. After
analyzing them in terms of modern physics, Born concluded "chance has
become the primary notion, mechanics an expression of its quantitative
laws, and the overwhelming evidence of causality with all its attributes
in the realm of ordinary experience is satisfactorily explained by the
statistical laws of large numbers."
In physics, the best available approximations to the ultimate principles of
causation are expressed as laws. In a discussion of causality, Peirce gave
the following definition of law:
What is a law, then? It is a formula to which real events truly
conform. By "conform," I mean that, taking the formula as a
general principle, if experience shows that the formula applies
to a given event, then the result will be confirmed by
experience. (1904, p. 314)
This definition is a realist view of the laws of nature, which is widely
accepted by practicing scientists and engineers. Aronson, Harre, and Way
(1994) presented a more recent, but essentially compatible view:
Laws are invariant relations between properties. We have argued
that judgments of verisimilitude are based on similarity
comparisons between the type of object referred to by a scientist
and the actual type of the corresponding object in nature. The
relative verisimilitude of laws can be thought of in the same
way, namely as the degree to which the relationships between
properties depicted in relevant theories resemble the actual
relationships between properties in nature. (p. 142)
In continuing their discussion, they remarked that the empirical
methodology of science is not a rejection of "commonsense" practice,
but a refinement of it:
It is the method of manipulation. It is so commonplace that we
are hardly aware of its ubiquitous role in our lives and
practice. Every time we turn on the shower and stand beneath it
we are, in effect, using the unobservable gravitaional field to
manipulate the water. The way that Stern and Gerlach manipulated
magnetic fields to manipulate atomic nuclei in their famous
apparatus is metaphysically much the same as our everyday
strategy of standing under the shower. (p. 200)
As Peirce would say, experience provides a pragmatic confirmation of the
law of gravitation and its applicability to the event of taking a shower.
The "impasse" that Kim observed in the divergent proposals about causation
results from a fundamental divergence between practicing scientists and
many, if not most twentieth-century philosophers. For scientists, the
discovery of the laws of nature is the ultimate goal of their research;
but for philosophers of a nominalistic bent, the very concept of law is
an embarrassment. To unify the divergent views, both in science and in
philosophy, this paper takes the notion of a law-governed process as
fundamental. But to accommodate chance, either the fundamental uncertainty
of quantum mechanics or the epistemological uncertainty that results from
experimental error and limited observations, it does not assume that a
law-governed process must be completely deterministic. Instead, there is a
continuous range of possibilities between a totally random process and a
totally deterministic process:
* Random. Total chaos is random. Nothing is predictable, and the state
of the universe at one instant has no relationship to its state at any
other instant, before or after.
* Law governed. Some things are predictable, and some things aren't. The
law of gravitation imposes sufficient constraints on the flow of water
that a person who takes a shower can predict where to stand, but
cannot predict the exact trajectory of every drop.
* Deterministic. As the constraints are tightened, a law-governed
process may approach pure determinism as a limit. Newton once claimed
that the celestial bodies followed a more deterministic course than
any clock that human beings could contrive. Yet today, atomic clocks,
which are still not perfect, are routinely used to detect and
accommodate minor fluctuations in the earth's orbit. A truly
deterministic process is as unobservable as a perpetual motion
machine.
Section 2 of this paper relates continuous processes of these three kinds
to the laws of physics. In Section 3, discrete processes are defined as
directed acyclic graphs, which can approximate the continuous processes as
a limit. Section 4 introduces procedures as specifications for classes of
discrete processes, and shows how they can be expressed in the formalisms
of Petri nets and linear logic. Section 5 shows how Petri nets or linear
logic can be used to reason about discrete law-governed processes. To
relate theories to one another and to the ultimate laws of nature, Section
6 introduces the lattice of all possible theories and the techniques for
navigating it. In conclusion, Section 7 shows how various theories of
causality can be interpreted in terms of the lattice.
For the full text, see http://www.bestweb.net/~sowa/ontology/causal.htm
As of 16 June 2000, Sections 1, 4, and 5 are more or less complete.
All of the sections will continue to be revised as time goes on.