by JLS
-- for the GC
-- I OWE to discussion with R. B. Jones the importance of recognising the 'bete noire' of "Extensionalism" qua attack to 'abstract entities', as Grice puts it in "Reply to Richards". But what sense can we make of the concrete versus abstract?
Thus writes Quine in Methods of Logic, p. 160:
"Besides the classification of terms into singular and general, there is a
cross clasification into concrete and abstract. Concrete terms are those
which purport to refer to individuals, physical objects, events; abstract
terms are those which purport to refer to abstract objects, e.g., to
numbers, classes, attributes. Thus some singular terms, e.g., 'Socrates',
'Cerberus', 'earth', 'the author of Waverly', are concrete, while other
singular terms, e.g., '7', '3+4', 'piety', are abstract."
From the OED:
1530 Palsgr. 50
All such substantives
especially if they be such as the
logicians call abstract.
Then we have from T. Mcarthur, Oxford Companion to Language
http://www.xrefer.com/entry.jsp?xrefid=440804
'abstract'. 15th. century. From Latin "abstractus", drawn away (Antonym:
concrete 14th century. from Latin "concretus", grown together). A term
contrasting "concrete" in traditional philosophy and grammar, "concrete"
referring to the material and specific, and "abstract" to the ideal and
general. Abstraction as a mental process starts with many particular things
or events and moves to a single generality within or behind them, such as
the concept time abstracted from such changes as day and night, the
seasons, and ageing. Although the use of language depends on abstract thought and everyone therefore engages in it, such thought is widely regarded as difficult, the
domain of intellectuals and scholars.
"In grammar, an "abstract noun" refers to any 1-5 below."
1. action
2. concept
3. event
4. quality, or
5. state (love, conversation)
-- "On the other hand, a concrete noun refers to a touchable, observable person or thing (child, tree)."
This semantic classification cuts across the syntactic division of nouns as
1. countable
2. uncountable noun.
Although abstract nouns tend to be uncountable ("courage", "happiness",
"news", "tennis", "training"), many are countable ("an hour", "a joke", "a
quantity"). Others can be both, often with shifts of meaning from general to particular ("great kindness"/"many kindnesses"; "not much industry"/"a major
industry"; "some success"/"a remarkable success").
http://www.englishclub.net/grammar/glossary/index.shtml
A "concrete noun" is something you can see or touch like a person or car. An "abstract noun" is something that you cannot see or touch like a decision or happiness."
Something that Grice and Strawson considered profusely when lecturing on categories in Oxford. And it was very good that Grice kept the notes now deposited at Bancroft and of which Chapman has made some rather good use of.
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Russell talked about "logical fictions" and I think of abstract objects in that way, which is consistent with Carnap's pragmatic ontology (and Grice's).
ReplyDeleteWe know things about abstract objects because we invented them, they are what we define them to be (though we had better decide on something coherent).
For the sake of ensuring consistency, its good to build them out of sets.
But we mustn't forget the hybrids, sets of rocks.
However, I'm tempted to say that, at least for scientific purposes, its best to remember them just long enough to set them aside.
When we talk about science providing mathematical models, that might as well be abstract models.
Do it all in set theory.
RBJ
That's very good. It somehow goes over my head why 'sets of rocks' is a hybrid.
ReplyDeleteI like the application of 'abstract' to 'model' that you use.
I suppose the extensionalist use of set-theoretical notions (like the sign for 'belonging' to a set -- as per Grice footnote in the last page but three in WoW:vi) is a good sign in Grice. And it may lead to diverge on what we mean when we say
"an item"
belongs in "a set"
---- as a different idiom for the same thing: 'the item HAS feature f".
----
When it comes to rocks, I suppose the idea of hybridity comes from the plural of 'set'. I.e. Speranza has this 'set of rocks' and Jones has this other 'set' of rocks. So we have 'sets of rocks'.
In the end, we just have items (rocks) which have features (or belong in this or that set).
Or not.
I go with your over the importance of set-theory. A beautiful thing to behold. There was a time when a child was forced to learn mathematics by ways other than 'set-theory'. Cruel, no?