Abstraction 101

Philosophy Forums Philosophy
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Abstraction is the process of limiting or reducing information, and while all abstraction is essentially the same process, it may be useful to delineate a couple of different types of abstraction.

We see (or somehow observe) some empirical event or phenomenon. We see a cat, for instance. The question is not, and never was, “How do we know it’s a cat?” The question is, “Why - for what purpose - do we call it a cat?”

Purpose is the operative concept here. “How do we know it’s a cat?” has caused much confusion, evidently. The question is fundamentally not about knowledge but about purpose. Asking the wrong question is ostensibly what led Plato astray and what leads people astray to this day.

We have a purpose when we abstract. The reason we abstract is to place an object or idea in a group - in a category. In a class. For a particular purpose. Taxonomy has a particular purpose.

It should already be obvious why an error in or about abstraction will lead to errors in logic and in philosophy in general, but probably it’s not obvious at all to many.

We abstract, perform abstractions for particular purposes, and in doing so retain only the information that suits that purpose. That purpose, in general, is to conceptually place the objects or ideas from which we create the abstraction in a particular group or class.

So “cat”, as a label for a class of objects, is useful to us. If we see an ad on Craigslist titled “cats for free”, we have enough of an idea about the contents of that ad to know if it’s worth our time to click on the ad and read it. This by no means limits the number or types of classes that these cats may belong to. Later, one of the cats may belong to the class “my pets” or “Dave’s pets”, for instance, and still belong to the class “cats”. And these class labels would be employed as they are useful, if at all. But the part to understand here is that there is nothing intrinsic to these cats that dictates what classes they belong to.

So the label “cat” is the device by which we group together individuals, by ignoring some of the information we have about them and including only that information that suits our present purpose, to form a conceptual group that we have some purpose in forming. In the end, that is all that abstraction is. But this means that an abstraction (here meaning the product of the process of abstraction) is conceptual only - it is not taken to be real - even if the object itself is. It’s the product of a purely mental process, and a product of language. Without a label, there is no class, no group and no abstraction. Abstraction is a feature of language.

Anyone not with me so far? There’s a lot more. Abstraction can be performed on not just things we see, but on other ideas as well. Some abstractions are of other concepts alone, and not of objects that we experience in the material world. More on that later.

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Well, I reckon that’s clear to everyone. Of course, i don’t know who has read this, but i am left to wonder why anyone has made errors in this regard on another thread.

3

Perhaps because every word is yet another abstraction and you are trying to explain abstractions with abstractions. :sunglasses:

Intelligence and knowledge are no more than categorizing abstractions/concepts.

If they aren’t abstracting right (low intelligence), how are they to abstract your meaning? :confused:

…sometimes pictures help.
:text-worthless:

4

To me abstraction is allot like digestion of the senses, especially memories.
We add, we take away, we change, the ‘knowledge’. Then it is rendered into its primary format.
For some people, the digestion is flawed and it spoils the knowledge.
For other people, it makes life allot better and it works.
To me category is such a simple thing, but it seems like quite a few people are stuck on it.

5

I’m interested in the specific mistakes you’ve seen. Even if you’d rather not link to specific posts, at least give us an example of the kinds of mistakes being made.

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Are we saying that some people aren’t able to abstract properly, or that some people don’t know how to philosophize about the abstraction process properly?

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I’m saying ‘some people aren’t able to abstract properly’.
I’ve seen no shortage of insane people. I blame genes for the most part. I try not to feel upset about it.

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 Dan: therefore if you can't "abstract" properly, you have to be insane?  Of course I know what you mean, but would you grant, that besides the two modes of abstraction there is a third?  (Abstractions of abstractions.......is there a limit to referentiality? )

Meaning: how abstract can you get, before people will not know what you mean?

But shouldn’t philosophy be unconcerned about imminent meaning, and seek that which is beyond this field of immanence? Isn’t that was behind Plato’s idea? To posit an object beyond srutiny?

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That’s the abstraction of transcendence. Some people believe in it, some don’t.

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FJ

I see every mistake that it’s possible to make. Shockingly, I see people who do not understand the difference between an individual and a class when both have the same label. “Dog” as in “this particular dog” is different - is a logically different term - from “dog” as used as the label of the class of all dogs. Even when we add the “s” at the end of the second term, there is confusion.

It’s as if the they don’t teach basic set theory in school anymore. Because this is literally grade-school stuff.

So, “My dog has fleas” and “A dog may have fleas” are each employing a different sense of the word “dog”.

Really. Not shitting. Truth.

“My dog” is in fact equivalent to a proper noun (which many professional philosophers have spilled a lot of useless ink over) and “A dog” is not.

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Sounds like an inability to make second-level abstractions. Most people can talk about dogs in the abstract sense (as in “dogs are lovable animals”) without problem, but point out that “dog” in that statement denotes a set rather than a particular dog (which is to form an abstraction out of an abstraction), and they’re lost.

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The argument in the other thread was whether (geometrical) circles are real. Lots of things are commonly (and lazily) reified. Evolution, for example, or economics.

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isn’t this grammar 101…?

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Tab - yes. It is grammar 101. My general contentions were and are that many “philosophical” problems are problems of language, that you cannot begin to do philosophy until you have some mastery of language and that certain philosophical errors are really language errors.

This is partly because abstraction creates categories or classes. These classes occur “naturally” in thought and so in language. A formal system has been more or less worked out by logicians (and perhaps by proto-logicians). Even the logicians have been confused, and late 20th-Century logicians like Kripke have gone further astray than we were before they got their mitts on the issue.

To wit - the whole Hesperus and Phosphorus thing, which is a tempest in a teapot if ever there was one.

Now, Humean has brought up circles, which I was trying to avoid for the moment, because mathematics is sort of a special case, compared to doggies and kitties. That’s because mathematics utilizes a special case of language.

Geometry is “pure” or “perfect” abstraction. Here we have to get into “referents”.

Sometimes the referents of an abstraction are quite simple and clearly traced. Sometimes, not so much. While “dog” depends upon a real-world referent to even make sense, mathematics does not.

This will be quite shocking to the “a beer can is a cylinder” crowd, but it is, indeed, the case. That’s where real trouble starts. It’s not that we, as mathematicians, do not ‘see’ a cylinder when we look at a beer can. It’s that a mathematical cylinder has no empirical referent. The empirical referent has been completely removed from the concept of the cylinder. I’ll need some more coffee to explain why this is so. I will obtain this coffee from a cylindrical can, if anyone is wondering.

15

Are you sure about that, Faust? Don’t numbers at least refer to certain quantities of objects–4 dogs, 3 beer cans? Or am I confusing the cause of our abstractions with their referents?

Coffee comes in a can now? Like a coke can? Is it cold?

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gib - Coffee does indeed come in a can. It is neither wet nor cold. It comes in the form of ground coffee beans. A foil wrapped brick is also often available.

Well, no. One of the assumptions required to define “number” (as in natural numbers) is zero. I fear that I cannot fully answer without resort to Peano’s axioms. The first of which is that zero is a natural number.

This is actually a requirement in defining “number” even though most or all primitive arithmetical systems did not include any conception of zero as a number.

Here’s the problem - it’s often possible to produce a thing or a system without understanding all the “parts” involved. For instance, it’s perfectly possible to be fluent in your native tongue without knowing any formal grammar. It’s possible to do math without knowing the definition of “number” and in fact, almost no one does know this definition.

So we can draw a triangle without knowing any math. That, sadly, does not mean that we understand the abstraction involved. And for most purposes, we do not have to, but it’s not because we know the referent, it’s because there isn’t one.

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Are you sure about that, Faust? Don’t numbers at least refer to certain quantities of objects–4 dogs, 3 beer cans? Or am I confusing the cause of our abstractions with their referents?

The number 4 is pretty much that which 4 dogs and 4 beer cans and 4 grandparents and 4 rainclouds (etc…) have in common. To me, that’s a pure abstraction.

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Improperly removed!

Now you have this absurd situation:

Look at 5 dogs. Abstract the concept ‘dog’ out of the specific dogs. Apply the abstraction to each of the original dogs. You conclude that each of the original dogs is a ‘dog’.

Look at 5 cylinders(or circles, etc) . Abstract the concept ‘cylinder’ out of the specific cylinders. Apply the abstraction to each of the original cylinders. You conclude that none of the original cylinders is a ‘cylinder’. Cylinders don’t exist. #-o

You have taken an abstraction and warped it by making it conform to a physically impossible geometric definition.

That is also done to other abstractions. You look human behavior, abstract out ‘love’ and then create a concept of ‘perfect love’ which nobody can live up to.
Perfect omnipotent, omniscient, completely benevolent God.

The abstraction becomes the standard by which reality is judged. :open_mouth:

19

Oh, that kind of can.

I’m familiar with Peano–well, sort of: I know he formalized the definition of number in a way that would make sense to logicians and mathematicians.

I don’t know if you’d consider this a tangent of this thread, but would you say that if we don’t know the formal definition of “number” (something like Peano’s definition), then we don’t understand what a number is? I don’t think so. I think we can understand what a number is without knowing what that understanding involves–i.e. in terms of a more complex analysis of the understanding (i.e. the concept, the idea) consisting of a whole system or structure of more basic ideas or concepts. I think most of our understandings of concepts (maybe all) that we don’t necessarily have a more detailed or complex definition for are better thought of as fundamental rather than not understood (similar to how an electron is considered a fundamental particle–just because it doesn’t break up into more elementary particles doesn’t mean we don’t know what an electron is). Furthermore, we could say that such fundamental concepts or understandings are only fundamental until we can invent a more basic and complex definition through some kind of analytical process (which doesn’t entail inventing it willy-nilly, keep in mind). This is what Peano did. It would seem odd to say that we never understood what a number was until Peano came along; it seems (to me) to make more sense to say that we always understood, but Peano deepened our understanding.

Right, so you get rid of the real-world referent. This means that the relation between the pure concepts of numbers and the actual quantities of things in the world is characterized more by a causal connection than a referential one. So experiencing things in world as coming in different quantities eventually causes us to abstract the concept of “number” out of those experiences.

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Sorry, Humean. They do refer to quantities, but since those objects could be angels as well as dogs, there is no empirical referent, which is what i meant and what i should have stated.