This keynote abstract presents the definitions of Fregean concepts and the concept by Johnson and Lakof and discusses their conceptual relationship. Although, in ordinary conversation, we talk about concepts without feeling any need to define what they are, many philosophers and scientists have tried to give precise explanations of their nature. But such explanations vary greatly in what they say or imply regarding what is referred to by the word 'concept'. In other words, there are many diferent conceptions of concepts.
• mental entities that correspond directly to physical material or structures or processes in the brain, • mental entities that are formed from the interaction between an (embodied) agent and its environment.
Much analysis could be carried out clarifying, refining and contrasting the variety of conceptualisations of concepts. Although such meta-level considerations may seem abstruse to some, I believe that they are necessary if one wishes to integrate the insights of diverse modes of investigation.
Two of the most distinct notions of concepts are those associated with the logician Gottlob
Frege [
Oppositions between fundamental characteristics attributed to concepts according to their views are summarised in the following table:
2.1. Fregean Concepts
For Frege (see e.g. [
Frege also believed that every concept has precise criteria of membership. He argued that it would not be possible to share and make efective use of concepts unless they were precise. If concepts were vague or variable this would mean that proofs, which always involve multiple references to the same concept would be unreliable. This would be especially problematic in cases where concepts were applied to information coming from diferent sources, since consistent use of the concepts would require consistent criteria for the application. 1It is a simplification to assume that Lakof and Johnson always express a single view. But I believe this is reasonable given the course granularity of the current discussion.
A final aspect of Frege’s conception of concepts, that is very important to note, is his view that concepts are only indirectly and imperfectly correlated with human words and ideas. Although we ‘grasp’ concepts that are precise and eternal, our means of grasping by means of words and ideas is far from perfect. 2.2. Concepts according to Lakof and Johnson Given the context of the talk (Image Schema Day), a detailed exposition of the views of Lakof and Johnson would be out of place. Sufice it to say, they vigourously expound the idea that thought and the concepts it employ arise from the embodied interaction between an agent and its environment. They suggest that conceptual primitives (‘image schemas’) arise from significant regularities of embodied perception; and, from these basic constituents, concepts are developed and manipulated by means of principles they describe as based on metaphor. For example, a basic notion of ‘container’ can form a semantic ingredient of higher-level concepts such as ‘jug’ and ‘jail’.
For Lakof and Johnson, both basic image schemas and the higher-level concepts derived
from them are considered to be malleable, open ended and applicable to many purposes. They
are also subject to many influences and can have diverse connotations dependent on context or
purpose. In this respect they difer significantly from Frege’s precise platonic concepts.
2.3. Supposed implausibility of Fregean concepts
As emphasised in several works of Lakof and Johnson, there are several respects in which the
Fregean conception of concepts may be questioned and doubted:
1. The concepts that we humans use, seem to be far from precise.
2. The notion of abstract concepts that are grasped (imperfectly) by humans is not compatible
with modern (materialist) science.
3. Certain ways of using and combining concepts in natural languages seem to be hard to
explain in terms of Fregean concepts.
2.4. The Power of Fregean Concepts
Despite the concerns raised in the previous section, it must be admitted that Frege created an
extremely powerful and robust apparatus for carrying out logical inference [
Although Frege thought that predicates must correspond to precise concepts in order for his system to work, this is a somewhat over-strict requirement. The actual requirement is that the applicability of each predicate (that is whether it applies or does not apply to any given object) is consistent across all occurrences of the predicate within a given reasoning context (e.g. in all the assumptions and derived formulae that constitute a particular proof). We would certainly expect a completely precise concept to have consistent criteria of applicability. But the robustness of logical reasoning arises because we consider an argument correct if would hold under any precise specification of predicate meanings. We do not actually have to fix a particular precise meaning of the predicates or even assume that there is a single precise meaning. It is enough to convince us if we can see that under any precise interpretation the inference would follow.2
Given the stark diferences and outright contradictions between Frege’s and Lakof/Johnson’s views of concepts, it may seem unlikely that they could be reconciled and assimilated within a more general understanding. Yet we have already considered a phenomenon that can often explain diferent viewpoints: the indeterminacy of a word in relation to its meaning.
(In my keynote talk I presented various approaches that have been taken to explaining
semantic indeterminacy ranging from Wittgenstein’s notion of family resemblance [
Whereas Frege considers concepts to be possible precise referents of words or ideas, Lakof and Johnson consider concepts to be ‘mental’ correlates of words (with the ‘mental’ for them being associated with perceptual patterns arising in embodied experience) .
The figure on the left illustrates the Fregean view of indeterminacy of the meanings of words and the content of ideas. Here, C1, C2, C3 and C4 correspond to diferent precise concepts that could correspond to some word or idea. Since linguistic and mental entities can be imprecise 2This is closely related to the more widely recognised insight that the validity of an argument does not require that its assumptions are true. Validity just requires that if the assumptions are true then the conclusion must be true. and indeterminate they may correspond to many diferent precise concepts. On the right we have the picture of the relation between words and concepts that seems to be assumed by Lakof and Johnson. On this view it is the concept that is vague an indeterminate
The two explanations of the evident indeterminacy in the correspondence between words and ideas can be summarised by the following contrasting statements: Frege:
Lak/John: Words refer to indefinite concepts.
Yet another way of explaining the diference is to say that what Lakof and Johnson call a ‘concept’, would be regarded by Frege as an ‘idea’ that is associated with cluster of precise concepts. Lakof and Johnson do not really have a term for what Frege is calls a ‘concept’, but they might describe it as ‘an artificially precise interpretation of a concept’. 3.2. Ambiguity of Ontological Status and Existence In the previous section, I argued that an ambiguity in the meaning of ‘concept’ may explain opposing views as to whether concepts are indefinite or precise. However, one who accepts that argument may still consider that the Frege and Lakof/Johnson views of concepts are irreconcilable, since they ascribe incompatible ontological status to the entities referred to as concepts. How can the word ‘concept’ be ambiguous in such a dramatic way as to refer to things that are as completely diferent as, on the one hand, platonic forms, and, on the other hand, patterns arising in the perceptions of embodied agents. Surely, if ‘concept’ has such distinct meanings, we would be aware or this ambiguity.
Surprising as it may seem, it is actually quite common for count noun words to exhibit quite
radical polysemy with respect to the category of entity that they denote. This phenomenon
is studied in relation to the phenomenon of copredication (see for example [
Frege regarded any psychological ideas about concepts as irrelevant to his study. Lakof considered Frege’s platonic view of concepts to be archaic and deeply misguided. But were they even talking about the same thing? For Frege’s powerful logic to work at all, he must assume that each occurrence of the same predicate symbol denotes something that is associated with a precise, consistent membership function. He calls this abstract referent of the predicate symbol a ‘concept’. Lakof and Johnson, referring to the complex imprecise assemblage of associations and influences associated with words and ideas, also use the word ‘concept’. The word ‘concept’ is ambiguous in many ways.