What is thinking in the "abstract" in symbolic logic?

Question

A book I've been reading stresses the importance of "abstractionism" and " the ability of thinking in the abstract". What does this exactly mean. Im ahving a difficult time interpretating the meaning the author is trying to convey. Please, do not make the answer to scholary. One thing Ive noticed about a lot of philosphers and logicians is that the tend to be more concerned with their vocabulary and intellectual self-image than truly assisting people. Ive also noticed how studying this has effected me. Its important for me to teach people, not teach them how to recognize how "intelligent" I can be. Thanks.

Answer 1

In ordinary life, if I have thought about a cat, I am simply noticing things about the cat. For example, I may simply notice "Hey, there is a cat sitting on the couch" or "Gosh! That sure is a fluffy cat!" or "I have a cat that looks just like that one" and so on. But philosophical thought tends to get a bit more weird. A philosopher might pay special attention to the fact that there are many different kinds of cats, but they all have something in common, namely, that fact that they are all cats. What is it that ALL cats have in common? We say there is a category "catness" and all particular cats fall into this category. But what is a category? It is obvious that cats exist; I can see cats, pet them, etc. If someone is skeptical about the existence of cats, I can show them a cat and let them pet it for themselves. But do categories exits? If someone says "categories don't exist" then what can I do to prove them wrong? I can't show them the category of "catness" in the same way that I can show them a particular cat. If I want them to understand what a "category" is, I need to encourage them to think in a different way. I will never be able to get my dog to think about the category of "catness" because dogs do don't think "that way". What is it that we humans do that dogs can't do? The answer: we can think abstractly. Dogs only experience particular things – objects in the world that they can see, smell, taste, etc., but human have experiences that don't seem to be about particular objects in the world. Both my dog and I can have an experience of seeing two donuts on the floor, and we can both respond in a way that shows that we in some sense understand that there are two donuts, not one or three. But in addition to experiencing two donuts, I can think about the number two itself. I can think "If I broke each donut in half, then there would be four things." My dog can't think this way because the number two is an abstraction, and I can only think about the number two if I am able to think abstractly – which is to say, I can think in terms of categories or generalities. And I can think about a category AS IF it were a thing. So, for example, I can compare categories to other categories. I can think of categories as being "sets" and say that the set of all black cats is smaller than the set of all cats. How can one thing be smaller than another unless the two things "exist" in some way? So even though I can see or touch the "set of all cat" it seems that "the set of all cats" does exist in some way. This ability to think about categories and compare them to each other as if they were ordinary objects even though they are not ordinary objects – this ability is the ability to engage in abstract thought.

Answer 2

In asking your question, you have stated the obvious answer to your own.....abstract means to gain a visual of what you have not seen, or to extract ideas from what you are given and make them your own,..(.i would suggest to you(knowing I cannot)that you take any thought you have on any subject you are given and extrapolate(define in your own terms) any answer that immediately comes to mind. you think for yourself, therefore you are your own reality. I'm sorry, but I cannot come up with a more simple way to say what I know to be an absolute truth. You have to decide for yourself what is or isn't in reality......this is the truist example of abstract.