Ed's first point is that there are different types of "law" that should be
modeled differently. His second one is that dispositions are different
than laws and also should be modeled. In many cases, a disposition is
easier to model than a "law". (01)
I agree with Ed here, but have a few comments. (02)
I was thinking of "natural laws" when i earlier mentioned that "laws" are
often contextual. Ed's response seems only to refer to governmental
laws. Most "natural laws" are approximations. F=ma; PV=rt;
A t = delta s; n m/s + p m/s = (n + p) m/s; ... all fall apart at
relativistic speeds. Chemical reaction equations are only valid for
a range of temperatures. (03)
Even social laws are often contextual even within the appropriate
jurisdiction and applicable time frame. Breaking & entering laws
stretch if someone breaks into a burning building to save a person
inside. Traffic laws bend for emergency vehicles or an individual
taking emergency action (such as rushing a critical person to a
medical facility). (04)
I agree with John, when he says
>> 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. (05)
Ed responds:
> I agree that you want categories and 'application rules'
> for contexts and circumstances. (06)
So it appears that we are all in agreement. (07)
Ed says that different types of "laws" should be distinguished.
I agree because they have different properties. John was
emphasizing some commonalities, but i would not be surprised
if he also found it useful to distinguish the subclasses. (08)
-- doug foxvog (09)
Ed later asks:
> 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? (010)
I'm sure that John would agree with me that an inference engine
should have an assortment of methods. There is no reason to
use Peano arithmetic or follow a long chain of proof steps if one
has an algorithmic method that is orders of magnitude faster. (011)
Someone who writes a program that includes ontological reasoning
already has a full programming language available. When designing
a program, they should use the appropriate tool for each part of the
job. (012)
-- doug foxvog (013)
On Tue, June 4, 2013 11:35, Barkmeyer, Edward J wrote:
> John,
>
> We seem to be miscommunicating. But there are a lot of interesting
> sidebars here.
>
>> 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.
>
> Yes, but you didn't mention nominalization of propositions in your earlier
> email.
>
>> 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. (014)
> 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''.
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> 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 even-handed 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.
>
>> 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.
>
> Yes. One can create a meta-ontology in which the mathematical
> inferencing rules are axioms of the ontology itself.
> So, if you want to reason about integers using Peano's axioms ...
> one can design a Turing machine ... (015)
Reasoning about assertions need not be reduced to such straw men. (016)
> 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. (017)
>> 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.
>
> 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.)
>
>> 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.
>
> 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.
>
> (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 first-order-plus reasoning, use it!)
>
>> From http://plato.stanford.edu/entries/laws-of-nature/
>> > 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.
>
> 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.
>
> 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.
>
>>
>> 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.
>
> 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.
>
>> I haven't checked all your citations, but these two certainly do not
>> make the
>> case that dispositions are more fundamental than laws.
>
> 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.
>
>> My primary argument is that laws are fundamental -- for the natural
>> sciences,
>> for the social sciences, and for everyday life.
>
> 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.
>
>> 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.
>
> 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'.
>
> -Ed
>
>>
>> John (018)
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