Abstract concept versus literal concept When we throw a stone we develop a mental structure that is the concept of throwing a stone. When we run from a bear we develop a mental structure of the concept of running from a bear. These are literal (experiential, actual) concepts. What is an abstract concept? I think that a sentence or a paragraph might be good analogies for abstract concept. Think of words as being literal concepts and think of sentence or paragraph as being an abstract concept. The words are organized by the imagination to develop a sentence or paragraph. The coherence of the sentence or paragraph is dependent upon how well the imagination has formed it. A good sentence, like a good abstract concept, makes sense and will stand up to the empirical test of validity. Cognitive science, as delineated in “Philosophy in the Flesh” by Lakoff and Johnson, presents a new paradigm for cognitive science. This new paradigm might be called the “conceptual metaphor” paradigm. The theory is that experiences form into concepts and some of these concepts are called “primary metaphors”. These ‘primary metaphors’ are often unconsciously mapped from the originating mental space onto another mental space that is a subjective concept, i.e. abstract concept. Many years ago, before ‘self-service’, it was common to pull into a gas station and when the attendant came to the car the motorist would say “Fillerup”. “More is up” is a common metaphor. I think of it every time I pour milk into a measuring cup when baking cornbread. The subjective judgment is quantity, the sensorimotor domain is vertical orientation, and the primary experience is the rise and fall of vertical levels as fluid is added or subtracted and objects are piled on top of or removed from a collection. We can see (know is see) by this mechanism that we equate vertical motion in the spatial domain with quantity; we use the vertical domain to reason about quantity. We have a vast experience in vertical space domain reasoning and thus we derive this great experience to help us in reasoning about quantity; no doubt a very useful thing when first learning arithmetic. Teachers of mathematics, I suspect, depend upon this storehouse of knowledge to make abstract mathematical reasoning for children more comprehensible. In a metaphor the source domain, ‘up’, is mapped onto the target domain ‘more’. The neural structure of the sensorimotor domain, the primary metaphor, is mapped onto the subjective domain ‘more’. Reasoning about the vertical motion in the spatial domain is mapped onto reasoning about the quantity domain. This is a one-way movement; reasoning about quantity is not mapped onto spatial domain reasoning. The direction of inference indicates which the source is and which the target domain is. Physical experiences of all kinds lead to conceptual metaphors from which perhaps hundreds of ‘primary metaphors’, which are neural structures resulting from sensorimotor experiences, are created. These primary metaphors provide the ‘seed bed’ for the judgments and subjective experiences in life. “Conceptual metaphor is pervasive in both thought and language.” It is hard to think of a common subjective experience that is not conventionally conceptualized in terms of metaphor.
