John, (01)
We seem to be miscommunicating. But there are a lot of interesting sidebars
here. (02)
> Quine, for example, restricts his logic to FOL. His axioms state
>propositions,
> but he does not allow variables to refer to propositions.
> That option is important for many purposes, especially for reasoning about
> human organizations and social interactions. (03)
Yes, but you didn't mention nominalization of propositions in your earlier
email. (04)
> The police don't use Bayesian inference when they give you a ticket for a
> traffic violation. In any case, the issue of where you put propositions in an
> ontology is independent of what you do with them. (05)
Because John described 'vehicles in motion do not cross the center line'
(social law) and 'things at rest remain at rest until acted on by an outside
force' (natural law) as variants of a common idea, I took him to mean that one
might write both as axioms in an ontology. I observed simply that the first
statement should not be simply 'taken to be true', but rather 'taken to be true
with some probability', which gives rise to "Bayesian reasoning''. (06)
John's mention of nominalization (reasoning about propositions) offers an
alternative approach. There is still a big difference between:
No vehicle crosses the centerline.
And
It is unlawful that a vehicle crosses the centerline. (07)
The first statement above is an axiomatic capture of the law as a 'fact', an
axiom. It is taken to be true. The second statement above is an axiomatic
capture of the law as a '(deontic) rule'. The idea 'that a vehicle crosses the
centerline' is a (nominalized) proposition, which is itself an argument to the
predicate 'is unlawful' (aka 'is prohibited'). The nominalized proposition
itself is not taken to be either true or false. (08)
In the first case, if a vehicle actually crosses the centerline and you capture
that fact, as the police officer does, then your knowledge base is
inconsistent, and you may be able to conclude that the vehicle is moving faster
than light and the police officer is a grapefruit. In the second case, if a
vehicle actually crosses the centerline, you have two facts in your KB, but
they are consistent, and you can conclude that there has been a violation of
the law, and that the police officer should write a ticket. (09)
The important difference is this: If I encode the 'laws of physics' in my
ontology, I will doubtless encode them as axioms of the first kind 
statements that certain things do or do not happen in nature. And I will
accept the possibility that if someone records an observation that conflicts
with such an axiom, the KB IS inconsistent, and either the observation or the
theory is FALSE and is ERRONEOUSLY 'taken to be true'. If I encode the 'laws
of the land' in my ontology, however, I will be well advised to encode them as
axioms of the second kind  statements that certain propositions describe
situations that are violations of the law, but may nonetheless be observed and
recorded in the KB. (010)
The point I was making is that there is a big difference between axiomatizing
the 'laws of nature' and axiomatizing the social contracts that are the 'laws
of the land'. John's evenhanded treatment of these things obscures an
important difference in the nature of the logical formulations,, and, as John
observes (re: Quine's FOL), an important difference in the required
expressiveness of the logic language. (011)
> And for that matter, any version of logic, CL or not, can be used to state the
> propositions used for induction, abduction, deduction by any method of
> reasoning, including Bayesian, heuristics, etc. (012)
Yes. One can create a metaontology in which the mathematical inferencing
rules are axioms of the ontology itself. So, if you want to reason about
integers using Peano's axioms and an inference engine instead of arithmetic,
don't let us stop you. OTOH, one can recognize the gain in encoding and using
other mathematical theories directly to achieve the predictions that those
theories were designed to deliver. The fact that one can design a Turing
machine to solve aerodynamic equations does not make it a good practice, and
the fact that one can encode induction and abduction axioms does not make that
a profitable approach to statistical reasoning. (013)
If you don't think 'disposition' is the best choice of ontological model for
reasoning about the state of the real world, you should not suggest that
encoding mathematical methods in formal logic is an appropriate means for
reasoning about the state of the real world, either. (014)
> DF
> > Ed, i guess that you see the danger as being people using rules
> > outside of their scope of applicability (i.e., the context in which
> > they are valid). This suggests that the context for any set of rules
> > should be specified, and that anyone intending to use such rules
> > should verify that they are within a context in which the rules are
> > defined to be valid.
>
> Yes. And that is why it's important to make laws a *category* in the
> ontology. If you do that, you can do metalevel reasoning about them and
> examine the various contexts and circumstances. (015)
That is true, but it is one step beyond what we are suggesting. For a given
application, I can encode the laws as "laws" (deontic rules) rather than
statements of fact. I only really have to deal with the context of a law when
the laws in question change over time or jurisdiction, and the variants in time
or jurisdiction are relevant to the application. The 'circumstance' of a law
may well be captured in the law itself, by means of an implication. But I will
agree that the circumstantial applications for many laws go well beyond what
one would want to capture as an antecedent. If you are that deep into the
formalization of the written law, I agree that you want categories and
'application rules' for contexts and circumstances. (Having recently served on
a jury, I found it quite remarkable that the prosecution had to demonstrate 7
or 8 distinct elements to show that the actual act violated the law.) (016)
> DF
> > I would not equate the axiomatic model with the ontology. An ontology
> > can model a game theoretic model.
>
> I agree with Doug. The axioms of any ontology can be used for many
> different purposes. The inferences for reasoning about hypothetical events
> in game theory could use the same axioms and the same theorem prover as
> they would for reasoning about an actual event. (017)
Absolutely. But the game theoretic model depends on placing a cost/value on
each 'terminal' event. Now, one can indeed use axioms to do that. Are you
also going to axiomatize the development of the minimax and the maximin and
encode the distribution algorithm for finding candidate partial strategies? Or
are you in fact going to use a software program that is internally encoded to
do all of that correctly and efficiently? One uses formal logic to prove the
validity and effectiveness of a mathematical method. Thereafter, one can use
the method itself. I do not want to suggest to any knowledge engineer that
s/he use the proof of a method and a reasoning engine as the means of employing
the mathematical method. (018)
(And if I thought that was a good way to think about the problem, I might also
suggest that s/he start with 'disposition', which is at least a less indirect
abstraction. That is to say: What message are you trying to convey? I thought
the email was about the suitability of philosophical abstractions for dealing
with real world ontologies. I don't see encoding mathematical abstractions as
any better. If the application calls for a better mathematical method than
firstorderplus reasoning, use it!) (019)
> From http://plato.stanford.edu/entries/lawsofnature/
> > For example, it seems that, for there to be any interesting
> > counterfactual truths, there must be at least one law of nature. Would
> > an ordinary match in ordinary conditions light if struck? It seems it
> > would, but only because we presume nature to be regular in certain
> > ways. We think this counterfactual is true because we believe there
> > are laws. Were there no laws, it would not be the case that, if the
> > match were struck, it would light. As a result, it would also not be
> > the case that the match was disposed to ignite, nor the case that striking
> the match would cause it to light.
>
> This is the basic point that I was trying to make: the existence of a
>disposition
> depends on the existence of some law. (020)
Make that 'some "law"'. It seems to me that in this case, at least, the
notions 'law' and 'disposition' are just different views of the same
phenomenon. Whether you think that sulfur and saltpeter has a 'disposition' to
ignite at 88 C or that there is a 'law' that it ignites at 88 C seems to be
more a matter of taste than fundamental distinction. The Greeks called the
observed regularities in the behavior of things in nature 'dispositions'; in
the 12th century, we came to call them the 'natural law', without having any
clearer idea what was actually going on. We now refer to the carefully
formulated theories of natural behavior as 'the laws of physics', etc., but the
distinction is that we have a carefully formulated theory, rather than a
presumption of behavior based on induction. And all of that said, I don't
think our models tell us what the ignition point of a substance will be.
AFAIK, that is still determined by experiment/observation. So the only
theoretical "law" involved here is the idea of an ignition point, and the
relationships between friction, heat, and temperature that are involved in
striking the match. That is, we have used our theory to replace the crude
'disposition' idea  if you scratch a match on a rough surface, it is disposed
to ignite  to the refined disposition idea  if you create enough heat via
friction or other means to raise the temperature of a match tip to 88 C, the
chemical composition of the match tip has a disposition to ignite. (021)
But that only says this is a bad example. Engineers used induction to build
medieval cathedrals. Friedrich Eiffel used theory, not induction, to build the
Tower. The laws of mechanics are not 'dispositions' of stone and steel. And
in that regard, I agree completely with John's position. (022)
>
> But the author, John W. Carroll, goes on to discuss many thorny philosophical
> issues about *recognizing* and *stating* laws.
> I certainly agree. He also says that the notion of disposition is often a
>shorter
> and simpler way to express the point without requiring a complete analysis
> of all the laws and their interactions.
> I also agree with that point. (023)
Exactly. I would have said only that 'disposition' is a way of explaining
things we (think we) know by observation, i.e., when you haven't done, or don't
need to explain, the complete analysis. (024)
> I haven't checked all your citations, but these two certainly do not make the
> case that dispositions are more fundamental than laws. (025)
Well, disposition is based on observation. Observation is the starting point
for scientific theory, and in that sense, it is more fundamental. In science,
there are many areas in which we still depend entirely on observation, because
we have not yet advanced the theory far enough to explain the phenomena. The
match, and the earlier example of crystallography, are demonstrations of the
reality that science only MOVES the 'disposition' threshold. (026)
> My primary argument is that laws are fundamental  for the natural sciences,
> for the social sciences, and for everyday life. (027)
My primary argument is that those are very different kinds of "laws".
Accepting a 'natural science law' means you regard its predictions as 'true'.
Accepting a 'social law' means that your regard its predictions as 'probable'.
Accepting a 'legislated law' means you regard its predictions as 'obligatory'.
But in neither case do we regard those predictions as 'true'. From an
ontological point of view, that is a major difference. (028)
> Dispositions can be a useful heuristic (a convenient shorthand) for properties
> such as fragility, which are difficult to specify in terms of the more
> fundamental laws. (029)
Or for any property the domain expert lacks the scientific knowledge (whether
it exists or not) to explain as anything more than 'based on observation'. (030)
Ed (031)
>
> John
>
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