In the sentence for example:
This book would also interest intelligent students with a taste for abstract ideas and theoretical arguments.
What does the phrase "abstract ideas" mean? I looked up the word in dictionary and it seems to have meanings such as something which not a material object and which exists as an idea. What does it generally mean?
An idea separated from a complex object, or from other ideas which naturally accompany it; as the solidity of marble when contemplated apart from its color or figure. --Wikipedia
An abstract idea is an idea that can be interpreted in many different ways. Some examples include:
Betrayal, Charity, Courage, Cowardice, Cruelty, Forgiveness, Truth, Love, Anger, Fear, Grief, Happiness, Jealously, Sympathy, Insanity, Knowldege, Wisdom, Right/Wrong, Duty, Fame, Justice, Liberty, Friendship, Greed, Innocence, Rules, Social Norm, and Religion. Usually these abstract terms are difficult to define alone, but easier when in context. For example: What is Right? vs. What is the right answer to this math equation? For most people it will be easier to answer the second question, because it is in context.
In OP's context, it seems the reference (along with theoretical arguments) is to concepts of philosophy.
Abstract ideas are concepts that need to be visualized, as they cannot be illustrated through concrete (real) examples. In a simple way, explaining the progression of logic in a (computer) program will be possible only if the reader can correctly visualize (imagine) it in his mind.
existing in thought or as an idea but not having a physical or concrete existence:
abstract concepts such as love or beauty
dealing with ideas rather than events:
the novel was too abstract and esoteric to sustain much attention
Besides the above definition, loosely put, an abstract idea is like a concept. A Ferrari sports-car is something concrete. The beauty of its lines is more abstract. Similarly, unlike the brain, the mind is an abstract idea.
In the example you provide, an "abstract idea" is probably meant to be an idea that is not applied to particular examples in the context in which it is discussed, and is not of immediate practical relevance, but which could provide a theoretical foundation for understanding and exploring a phenomenon, process, etc.
Alternatively, an "abstract idea" can refer to the result of "abstracting" (i.e., separating) a representation of something from the context it has in reality. For example, a thermodynamic model of a car in terms of energy inputs, outputs and transformations can amount to an "abstract idea" of a car since the model can "abstract from" various details of the car, like what the car is made of, the number of pistons in the engine, etc.
Abstract ideas refers to the ideas which are not concerned with worldly things. eg. education, knowledge, happiness, cowardice, freedom, self expression, peace of mind etc. They are the things that you cannot touch but you can feel them. Hope that helps.
