[FRIAM] abduction and casuistry

[Steven A Smith]

Maybe, but I'm literally on my way to visit Glen in Portland.  
Actually... to visit daughter and grandson and much more but hoping to
see him on the trip!   I'll take a closer look in the next few days and
see if there is anything I can add.

- Steve

On 8/22/19 7:25 PM, Nick Thompson wrote:
> Hi, Glen, 
>
> This is one of those moments when Steve Smith may be able to rescue my ability to participate further in this conversation by making a translation.   Steve?  Can you help here?  
>
> By the way, I am still puzzled by how one makes inferences or explanations without categories and/or principles?  Can you give me an example from everyday life?  
>
> So, the way into my basement requires passing through a low doorway.  Every year, in the first week we come here, I go down there and ram my head on the top of the door.   Ok, so the next time I go down, as soon as I enter the passageway leading to the door, I feel uneasy ...."This is like the time I bumped my head" ... and, unless I am demented by haste, I duck my head.  Simple as this example is, still it involves (on my account, anyway), the application of a principle to a category.  
>
> Which suggests to me that when you seem to talk about rule-less thinking (unruly thinking?), you actually talking about choosing among different sorts of rules and categories, how we decide amongst them, when we decide to give up on one and employ another. 
>
>  Perhaps this is a way of asking the same question:  As you understand "deontological" thought, how is it different from plain-old logical thought?  
>
> Nick  
>
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Biology
> Clark University
> http://home.earthlink.net/~nickthompson/naturaldesigns/
>
> -----Original Message-----
> From: Friam [mailto:friam-bounces at redfish.com] On Behalf Of u?l? ?
> Sent: Thursday, August 22, 2019 1:49 PM
> To: friam at redfish.com
> Subject: Re: [FRIAM] abduction and casuistry
>
> Maybe to give context to my hand-wavey colloquial nonsense below, I *really* like Gabbay and Woods' [†] formulation of an "abductive schema":
>
>> Let Δ=(A_1,…,A_n) be a *database* of some kind. It could be a theory or an inventory of beliefs, for example. Let ⊢ be a *yielding relation*, or, in the widest possible sense, a consequence relation. Let Τ be a given wff (well-formulated formula) representing, e.g., a fact, a true proposition, known state of affairs, etc. And let A_(n+j), j=1,…,k be wffs. Then <Δ,⊢,Τ,A_(n+j)> is an abductive resolution if and only if the following conditions hold.
>>
>> 1. Δ⋃{A_(n+j)} ⊢ Τ
>> 2. Δ⋃{A_(n+j)} is a consistent set
>> 3. Δ ⊬ Τ
>> 4. {A_(n+j)} ⊬ Τ
>>
>> The generality of this schema allows for variable interpretations of ⊢. In standard AI approaches to abduction there is a tendency to treat ⊢ as a classical deductive consequence. But, as we have seen, this is unrealistically restrictive.
> (Emphasis is theirs, at least in the draft copy I have.) They go on to assert:
>
>> ⊢ can be treated as a relation which gives with respect to Τ *whatever* property the investigator (the abducer) is interested in Τ's having, and which is not delivered by Δ alone or by {A_(n+j)} alone.
> In my colloquial description, Δ is the collection of old dots there at the start of the process and Τ is the new dot. It's open whether or not the set of wffs (A) are also dots or part of the connections drawn between them, depending on how you feel about *dot composition* (e.g. subsets of dots that are all very close together, so we just draw them as one big dot or somesuch) and scale/resolution. Rule (2) is *clearly* a rule for how the dots can be connected. In general, consistency is also an ambiguous concept.
>
> As always, I'm probably wrong about whatever it is Gabbay and Woods are saying. Any errors are mine. But maybe their words above can give some context for how I feel about "reasoning from particulars".
>
> [†] https://www.powells.com/book/-9780444517913
>
>
>
> On 8/22/19 8:26 AM, glen∈ℂ wrote:
>> First, did you miss Dave's contribution?  It was more on-topic than mine!
>>
>> On Rigor: Yes, there's quite a bit of what you say I can agree with. But only if I modify *my* understanding of "rigor". I think rigor is any methodical, systematic behavior to which one adheres to strictly. It is the fidelity, the strict adherence that defines "rigor", not the underlying structure of the method or system. And in that sense, one can be rigorously anti-method. Rigorously pro-method means adhering to that method and never making exceptions. Rigorously anti-method means *never* following a method and paying (infinite) attention to all exceptions, i.e. treating everything as a single instance particular, an exception. I grant that "methodical anti-method" is a paradox... but only that, not a contradiction.
>>
>> On monism vs. monotheism: The simple answer is "no". I'm not confusing the two. By reducing every-stuff to one-stuff, *and* talking about types of inference like ab-, in-, and de-duction, you are being (at least in my view) axiomatic, with a formal system based on 1 ur-element. Everything else in the formal system has to be derived from that ur-element via rules. To boot, your attempt to classify casuistry and abduction (same or different is irrelevant, it's the classification effort that matters) argues for some sort of formalization of them. A/The formalization of abduction is an active research topic. My use of the word "deontological" was intended to refer to this rule-based, axiomatic way of thinking. I'm sorry if that lead to a red herring off into moral philosophy land.
>>
>> On inferring from particulars: While it's true that induction builds a predicate around a particular, it is a "closed" set. (Scare quotes because "closed" can mean so much.) Abduction doesn't build predicates and any explanation it does build is "open" in some sense. So, I would agree with you that one can't really *argue* from a particular using abduction. I tend to think of it more like brain storming, in a kindasorta Popperian, open way. Any proto-hypothesis can be brought to bear on the abductive target. And the best we can do is play around with the abductive target to see if it might kindasorta *fit* into that open set of proto-hypotheses. Once you land on a set of proto-hypotheses that's small enough to be feasibly formulated into testable hypotheses, then you reason by induction over those hypotheses.
>>
>> In some ways, this would be very like what I, in my ignorance, think casuistry is. I'd argue that an experimentalist's focus on putting data taking in 1st priority and hypothesis formulation in 2nd priority falls in the same camp. So, I agree that casuistry looks a lot like abduction. But I don't think that that criminologist was doing either of them.
>>
>> On ontology vs. rules *and* reasoning from particulars: The proto-hypotheses I mention above do not have to take the form of "rules to apply" to the abductive target. Think of the game "connect the dots", where the dots are particulars and they are/can be interpolated and/or extrapolated by an infinite number of lines between them. On the one hand, more dots can make it more difficult to find a pattern that includes the *new* dot, but perhaps only when you're already pre-biased with a set of lines that connect the old dots. On the other hand, if you're rule-free when you look at the old set of dots *and* rule-free when you look at them with the new dot included, you're open to any set of connecting lines.
>>
>> Of course, in science, we do have an ur-rule ... that *all* the dots must be connected. So, that constrains the set of lines that connect the dots. And the more dots, the fewer ways there are to connect them. But practicality demands that we doubt at least some dots. So, we're allowed to throw out the weakest dots if that allows us to form more interesting connective patterns.
>>
>> So, in this scenario, the proto-hypotheses are really just collections of old dots in which the new dot must sit.  We're not reasoning from *one* particular to testable hypotheses. We're reasoning from the addition of that particular to collections of other particulars.
> --
> ☣ uǝlƃ
>
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