Consider the following sentence: "A glacier is a river of ice."

This is metaphorical. In some sense, a glacier isn't actually a river. A "literal" river has flowing liquid water, not ice.

Let a river(1) be defined to be an archetypal flowing-water river. A glacier isn't a river(1). Rather, a glacier shares some structure in common with a river(1). We may define river(2) to mean some broader category, of things that flow like a river(1), such as:

  • A glacier
  • A flowing of earth matter in a landslide
  • A flowing of chemicals down an incline in a factory

and so on.

A river(2) is a concept by metaphorically extending river(1). It is, in fact, easier to explain the concept of river(2) by first clearly delineating what a river(1) is. A child will have trouble grasping the metaphorical language of "a glacier is a river of ice" until understanding what a river(1) is, such that the notion of flow that generates river(2) can be pointed to with concrete examples.

Formally, we could think of metaphorical extensions in terms of generative probabilistic models: river(2) is formed by taking some generator behind river(1) (namely, the generator of flowing substance) and applying it elsewhere. But, such formalization isn't necessary to get the idea intuitively. See also the picture theory of language; language draws pictures in others' minds, and those pictures are formed generatively/recursively out of different structures; see also generative grammar, the idea that sentences are formed out of lawful recursive structures.

Is ice a form of water?

Consider the sentence: "Ice is a form of water."

What does that mean? Suppose that, by definition, ice is frozen water. Then, the sentence is tautological.

However, the sentence may be new information to a child. What's going on?

Suppose the child has seen liquid water, which we will call water(1). The child has also seen ice, in the form of ice cubes; call the ice of ice cubes ice(1). It is new information to this child that ice(1) is a form of water(1). Concretely, you can get ice(1) by reducing the temperature of water(1) sufficiently and waiting.

At some point, water(1) is metaphorically extended into water(2) to include ice, liquid water, and water vapor. Tautologically, ice(1) is water(2). It is not strange for someone to say "The tank contains water, and some of it is frozen." However, the water(1) concept is still sometimes used, as in the sentence "Water is a liquid."

The water/ice example is, in many ways, much like the river/glacier example (and not just because both are about liquid/solid water): water(1) is metaphorically extended into water(2).

(An etymology question: why do we say that ice is a form of water, not that water is a form of ice? A philosophy question: what would be the difference between the two?)

While I've focused on extensions, other conceptual/metaphorical refinements are also possible; note that the preformal concept of temperature (temperature(1)) which means approximately "things that feel hot, make things melt/boil, and heat up nearby things" is refined into the physics definition of temperature(2) as "average kinetic energy per molecule".

Figure-ground inversion

A special case of metaphorical extension is a figure-ground inversion. Consider the following statements:

  • All is nature (naturalism).
  • All is material (materialism).
  • All is physical (physicalism).
  • All is mental (idealism).
  • All is God (pantheism).
  • All is one (monism).
  • All is meaningless (nihilism).

Let's examine naturalism first. A child has a preformal concept of nature (nature(1)) from concrete acquaintance with trees, forests, wild animals, rocks, oceans, etc. Nature(1) doesn't include plastic, computers, thoughts, etc.

According to naturalism, all is nature. But, clearly, not all is nature(1). Trivially, plastic isn't nature(1).

However, it is possible to see an important sense in which all is nature(2) (things produces by the same causal laws that produce nature(1)). After all, even humans are animals (note, this is also an extension!), and the activities of humans, including the production of artifacts such as plastic, are the activities of animals, which happen according to the causal laws of the universe.

Naturalism is a kind of figure-ground inversion. We start with nature(1), initially constituting a particular part of reality (trees, rocks, etc). Then, nature(1) is metaphorically extended into nature(2), a "universal generator" than encompasses all of reality, such that even plastic is a form of nature(2). What starts as figure in the ground, becomes the ground in which all figures exist.

And, even after performing this extension, the nature(1) concept remains useful, for delineating what it delineates. While (according to naturalism) all is nature(2), some nature(2) is natural(1), while other nature(2) is unnatural(1). In fact, the nature(2) concept is mostly only useful for pointing at the way in which everything can be generated by metaphorically extending nature(1); after this extension happens, nature(2) is simply the totality, and does not need to be delineated from anything else.

Similarly, materialism extends material(1) (wood, brick, stone, water, etc) to material(2) (things that have substance and occupy space) such that material(2) encompasses all of reality. Notably, materialism is, in a sense, compatible with naturalism, in that perhaps all of reality can be formed out of the nature(2) generator, and all of reality can be formed out of the material(2) generator.

The other cases are left as exercises for the reader.

(thanks to Cassandra McClure for coming up with the terminology of figure-ground inversions applied to concepts)

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I’m not sure I buy the glacier example (nor any similar ones).

The sentence “A glacier is a river of ice” may also be read as shorthand for “A glacier is a river, except of ice”. This is itself still a sort of shorthand; the full and precise formulation would be: “A glacier is like a river in all important respects, except that instead of being made of water, as actual rivers are, it is made out of ice.”

Under this interpretation, if I say “A glacier is a river of ice”, I am not actually saying that a glacier is a river; in other words, the following implication does not hold (or at least, I am not claiming, nor implying, that it holds):

“A glacier is a river of ice” -> “A glacier is a river”

Or, to put it in yet another way, “river” is one sort of thing, and “river of ice” is another sort of thing, and the latter is not simply a particular kind of the former.

So I am not extending the concept of “river”, you see. Under this interpretation, what I am doing instead is a sort of one-time generalization, where I take some named concept (in this case, “river”), and I generalize it—without, however, naming the more general concept, because I do not necessarily intend to re-use it to generate other analogues. (By analogy with certain programming concepts, we might say that I am creating a “locally-scoped anonymous template”.)

Other examples:

  • An open-faced sandwich is a sandwich, except without one of the bread layers. (It is not the case that an open-faced sandwich is a sandwich.)

  • A cobbler is a pie, except without the bottom crust. (It is not the case that a cobbler is a pie.)

  • A tricycle is a bicycle, except with three wheels. (It is not the case that a tricycle is a bicycle.)

  • Hearing aids are eyeglasses, except for hearing. (It is not the case that hearing aids are eyeglasses.)

  • A dishwasher is a washing machine, except for dishes. (It is not the case that a dishwasher is a washing machine.)

Note that under this interpretation, no “general” or “extended” version of the concept is ever created (the template is anonymous, and is discarded as soon as it “goes out of scope”—which is to say, as soon as it has been used to create the new concept). There is thus no need to ask the questions of what this new, “general”/“extended” concept means, to what else it may or may not apply, how to differentiate between uses of it and any specific version, etc.

EDIT: To add to what I say above: I think it is likely that this account more realistically describes how people form new concepts. Actual generalization—which is to say, the creation of a persistent, named generalized version of some concrete concept—is, I suspect, more rare than this sort of “concept cloning”.

The concept cloning you talk about is definitely a thing. It's a good fit for the river/glacier example.

I think there is a general form of the "river of X" concept, such that people know what you mean if you say "river of (new substance)" (and can reuse their intuitions about other rivers(2)), but this form isn't named.

There are cases where "river" is used metaphorically without modifying it to "river of X". Consider: "The glacier is a river flowing slowly down the mountain". It's poetic/metaphorical language, not considered to be literally true, but considered to be true in some metaphorical sense.

The water/ice example is a case where ice is considered to be, literally, a kind of water. In the case of adoptive/biological parents, the "parent" concept is metaphorically extended to include adoptive parents, with the original being renamed to "biological parent". These are examples of the kind of extensions I'm talking about, where the extended one becomes a canonical concept.

I think both of this and the above post are treating concepts as more platonic than they are in practice. Take for instance "one legged duck", it has the same structure as "open faced sandwich" but most people would say it is in fact still a duck, even though ducks have two legs. I think language concepts are often pointing at fuzzy categories, and so it's natural to not be sure how far they extend, to extend them in ways that stretch further than other people's extensions, etc.

Some people's boundary for river includes water, but some people's doesn't, etc. The dictionary definition is a good starting place, but rarely sufficient for how humans use language.

Take for instance “one legged duck”, it has the same structure as “open faced sandwich” but most people would say it is in fact still a duck, even though ducks have two legs.

Yes, of course. I didn’t say anything that would contradict that, even by implication. I certainly wouldn’t claim that all concepts which might be described with the same very general syntactic structure behave in the way I described; that would be a rather bizarre claim, wouldn’t it?


The dictionary definition is a good starting place, but rarely sufficient for how humans use language.

I made no reference to the dictionary definition of anything, though.

The point I was trying to make was that for instance in your open faced sandwich example, there are many people who would say it's still obviously a sandwich, just like the duck is still a duck.

However, I realized I don't know enough about the philosophy of language to meaningfully contribute to the discussion, so I'm going to bow out.

Whether or not Lakoff is right in a strong sense (all language is metaphors!), it seems relevant to this discussion that most things we talk about that are not part of very simple, direct experiences are done so metaphorically, and even much of direct experience is still talked about metaphorically. For example, English and many languages have only metaphors for talking about time such that there are few to no ways to talk about time as itself rather than as a metaphor for something else (distance, size, finite resource, etc.), yet time would seem to be something we have direct experience with.

If everything is metaphors, then it seems likely that we should expect to be able to switch metaphors and thus equivocate by changing what a word means by changing the metaphors that support it.

Also, the "everything is chemicals!" argument against organic food and such.