Jon A and Edwina T,
I strongly agree with both you that processes are more fundamental than objects. In fundamental physics, everything is a process. In semiotic, all perceptions, actions, and communications are processes. The concept of stable things is at best a rough approximation about slowly changing processes.
Even the words we use are based on verbal roots: 'objectum' in Latin is something thrown against, and 'Gegenstand' in German is something standing against. For the top of an ontology, the word 'Entity' is better than 'Thing' because it does not make any commitments about the nature of what exists.
There is much more to say about this topic. Following is an article I wrote on a closely related topic: "Signs, processes, and language games", http://jfsowa.com/pubs/signproc.pdf .
John
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> ET:
I particularly like your (JA's) comment that "signhood is a role
> in a triadic relation, a role that a thing bears or plays
> in a given context of relationships" it is not an
absolute,
> non-relative property of a thing-in-itself, one
that it
> possesses independently of all relationships to other things†.
>
> ET: I myself emphasize that this
context of the role is made up
> of relationships (plural) -- which gives the triad its capacity
> for complexity.
Therefore, as we see in Robert Marty's lattice,
> a thing is
never a thing-in-itself but is an action, a process,
>
composed of complex relations.
JA
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Jon A,
It's important to distinguish the intension and the extension of a function or relation. The *intension* is its definition by a rule or set of axioms. The *extension* is the set of instances in some domain or universe of discourse:
JA> We can now define a “relation” L as a subset of a cartesian product.
That is a purely extensional definition. If we're talking about a database, for example, the extension may be constantly changing, but the intension may be the same for all the variations in extension
For the distinction between extensions and intensions, see the discussion by Alonzo Church: http://jfsowa.com/logic/alonzo.htm .
John
Terry, I completely agree with what you wrote (copy below).
But I emphasized database relations because they are the most commonly used examples of relations that are defined by extension.
However, the meaning of the data is specified by the rules or axioms that state the intensions. Those specifications are what we have been calling ontology.
John
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The intension / extension distinction is also crucial in the epistemology of science, insofar as the aim, goal, objective, etc. of genuinely rational scientific inquiry is to identify and express causal laws. For those laws aren’t merely descriptive of what actually has or is occurring in a context of precipitating conditions (as observed), but also – in a cosmically nomic sense – prescriptive of what would happen (under those conditions) if those conditions were met – whether they actually are ever fulfilled or not.
Reference class membership criteria are intensional, for instance, while the actual membership inclusion under those criteria is extensional. That intensionality of scientific language is essential for expressing the subjunctive and counterfactual nature of causation, especially for purposes not only of description (which only requires the use of extensional language), but for explanation, prediction, and corroboration as aspects of truly rational scientific methodology in general.
These considerations are fairly well-covered in philosophy of science, of course, and one source I recommend is Jim Fetzer’s 1981 Scientific Knowledge. I’m sure Susan Haack has also done important work on this, though I’m at a loss for the moment as to which of her works is best to cite here. I’ll look into it and report back ….
Helmut,
The distinction between intesion and extension is important for every version of logic since antiquity. The oldest example is "rational animal" vs. "featherless biped" -- those are two terms with different intensions, but the same extension. Diogenes the Cynic plucked a chicken and threw it into Plato's Academy while shouting "Here is Plato's man."
Alonzo Church, who wrote that excerpt I cited, had been the editor of the Journal of Symbolic Logic for many years.
It's just as important for the latest work in computer science for both theory and applications.
John
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Helmut,
In every version of language and logic -- ancient or modern, informal or formal -- the intensional definition is fundamental. It corresponds to the definition you'll find in a typical dictionary of any natural language or in any formal specification in science, engineering, business, or the arts.
The extensional definition is determined by using the intensional definition to check for instances. If you have the intensional definition, you have all the information necessary to do anything you wish. But if you only have the set of instances (extension), you have insufficient information to determine the intended meaning.
For example, if you find a set of people, you have no idea what intensional criteria were used to select them: Human beings? Featherless bipeds? Visitors from Los Angeles? Visitors from Australia? Students on a spring break? Musicians taking a lunch break between rehearsals?
JohnAzamat,
People observe the intension/extension distinction without learning the name for the distinction.
AA>It implies that operational meanings or definitions could be more significant than an intension/extension or representation/reference or connotation/denotation dichotomy.
Languages developed thousands (millions?) of years before writing, and writing was used for a few thousand years before anybody started to write definitions in any kind of language or logic.
For that matter, every infant learns language from use, not from definitions. But whatever meaning is learned may begin as extensional (particular names for individual persons or things) but children very quickly generalize them to kinds of individuals. The intensional meanings are generalizations learned from patterns of usage.
Summary: Intensional meanings are essential for generality. People use the intensional meanings in the same way that they speak prose without knowing the word for what they do.
John