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[A Poster He or I]

Chomsky has suggested that it is possible that mathematics may be an offshoot or as an "abstraction of linguistics operations..."

Again for anybody else who chafes at Chomsky's presumptions, I recommend Where Mathematics Comes From by Lakoff & Nunez. It is a compendium of empirically-based studies by cognitive scientists that suggest how wrong Chomsky may be. Cognitive science makes a clear case for how both language and mathematics are merely manifestations of the same underlying mechanisms responsible for all forms of cognition.

There is no empirical evidence for any such thing as an underlying universal grammar. In my opinion that is merely a Platonic chimera projected upon data to justify Platonic thinking, just like the belief in the Platonic existence of numbers. (I remember a grammar textbook I had as a school kid based on Chomsky that was actually called an introduction to "Cartesian Linguistics"!).

An animal like Koko the gorilla can be taught sign-language and generate her own original sentences, and certain rats can "count" up to 8 or 9, because abstraction is an emergent quality of standard cognitive operation. An underlying "template" is unnecessary.

[Bohm2]

In my opinion that is merely a Platonic chimera projected upon data to justify Platonic thinking, just like the belief in the Platonic existence of numbers.

What do you mean by this? Chomsky is not a Platonist in the sense you are arguing and I think people confuse the map/model/theory for the territory. Collins explains this part and the alleged issue of Platonism in linguistics by using analogy from theories used in physics:

Every theory, we may say, has an infinite import. This is because the very notion of explanation is modal insofar as it must support counterfactuals. Thus, a law does not describe phenomena but tells us what will occur under any conditions that satisfy the properties the theory posits. For example, Newton’s laws don’t purport to describe our solar system (unlike Kepler’s ‘laws’), but instead tell us what will occur in any circumstances that are covered by the concepts of classical mass and force, which our solar system happens to realize (within certain parameters — forget about twentieth century developments). In this sense, Newton’s laws tell us about infinitely many possible systems, even though our universe is finite (we presume). The same holds in the case of linguistics. A formal theory tells us about infinitely many possible states the human mind/brain can fall into, without committing itself to the idea that the mind/brain is infinite, or, of course, that there are infinitely many sentences anywhere at all, not even in Plato’s heaven. To be sure, we need to employ the notion of an infinity of expressions, in Chomsky’s sense, much as we are required to think about infinitely many states of any physical system (theorized, say, in terms of Lagrangians or Hamiltonians). My present point is merely that such notions, while essential in the modal sense explained above, don’t attract our ontological commitment, at least not if we are working within the theory (cf. Feferman’s 1998 position on the relation between science and mathematics). If all this is so, linguistics looks to be in the same boat as any other science.

A Question of Irresponsibility: Postal, Chomsky, and Gödel
http://www.biolinguistics.eu/index.php/ ... 12/showToc

Again for anybody else who chafes at Chomsky's presumptions, I recommend Where Mathematics Comes From by Lakoff & Nunez. It is a compendium of empirically-based studies by cognitive scientists that suggest how wrong Chomsky may be..

For a critical view of the alleged empirically-based studies by Lakoff you mention:

While this framework at first does not seem implausible, it can be questioned whether Lakoff and Nunez really describe how mathematical cognition actually works. The authors posit that cognition ultimately derives from direct bodily experience, an idea far from established in cognitive science (Goldin, 2001, 18). Yet, they present this theory as if it were generally accepted. To be sure, many cognitive scientists concur with the general view that cognition is embodied, i.e., the activity of the mind is grounded in mechanisms that evolved for interaction with the environment (see e.g., M. Wilson, 2002, for an overview of the many types of embodied cognition approaches in the current literature). However, it does not automatically follow from this that all mental processes are based on metaphors that are ultimately grounded in sensory-motor experiences. On the contrary, experimental psychological evidence seems to support the view that humans, including young children, explain physical, psychological and biological phenomena around them by positing unobservables...

Despite the heavy emphasis on cognition and cognitive science, Lakoff and Nunez hardly mention the substantial body of empirical evidence of how mathematics is actually represented in the brain. They also neglect to provide a detailed description of how metaphors function in mathematical practice. Instead, they apply their model of metaphors and blends to some examples of standard mathematical theorems found in textbooks and curricula. By doing this, Lakoff and Nunez are outsiders in the emerging field of cognitive science of mathematics.However, by failing to ground their model in the broader context of empirical research on mathematical cognition and of theoretical work in cognitive science, their work remains highly speculative and fundamentally unconvincing.

Innate Ideas as a Naturalistic Sourceof Mathematical Knowledge

http://www.academia.edu/230866/Innate_i ... athematics

[A Poster He or I]

Chomsky is not a Platonist in the sense you are arguing and I think people confuse the map/model/theory for the territory. Collins explains this part and the alleged issue of Platonism in linguistics by using analogy from theories used in physics...

Your excerpt from Collins strikes me as supportive of my own position against Chomsky, not as supporting Chomsky. As an anti-realist myself I don't frankly care whether Chomsky thinks his UG has a "real" existence in the Platosphere or is just a very useful model. I'm interested in how well it models the phenomenon of language in use. Cognitive models such as used by Lakoff/Johnson, Talmy, Fillmore, Langacker, et al. are more illuminating in my opinion. And incidentally the UG model is Platonic in its very premises, as is any conception of "innate" capabilities, broadly speaking.

However, it does not automatically follow from this that all mental processes are based on metaphors that are ultimately grounded in sensory-motor experiences.

Correct but what is the significance here? Of course ALL mental processes do not follow from metaphors. Metaphors themselves are mostly-unconscious constructs. They in themselves are not fundamental.

On the contrary, experimental psychological evidence seems to support the view that humans, including young children, explain physical, psychological and biological phenomena around them by positing unobservables...

And this is supposed to be antithetical to metaphor-based reasoning because..........?????

However, by failing to ground their model in the broader context of empirical research on mathematical cognition and of theoretical work in cognitive science, their work remains highly speculative and fundamentally unconvincing.

Yes, it's speculative. Just as all reasoning about the ontology of consciousness. Just like all interpretations of quantum mechanics such as Bohmian Mechanics. The speculative nature of Bohmian Mechanics doesn't stop anybody from questioning the hubris of naive realism, nor should it. Likewise, Cognitive Linguistics should be making any intellectually responsible person seriously question Chomsky whose conclusions rest on far less empirical evidence than Lakoff's.

[Bohm2]

Likewise, Cognitive Linguistics should be making any intellectually responsible person seriously question Chomsky whose conclusions rest on far less empirical evidence than Lakoff's.

I'm not sure about that claim as I'm not a linguist but from what I've read, I doubt that, particularly if one is concerned with 'I-language'. The critical paper previously posted by Mcdoodle summarizes some of Chomsky's reasons for eschewing some of the research in this area:

On the other side, Ernest Rutherford (physicist, 1871–1937) disdained mere description, saying "All science is either physics or stamp collecting." Chomsky stands with him: "You can also collect butterflies and make many observations. If you like butterflies, that's fine; but such work must not be confounded with research, which is concerned to discover explanatory principles."...Finally, one more reason why Chomsky dislikes statistical models is that they tend to make linguistics an empirical science (a science about how people actually use language) rather than a mathematical science (an investigation of the mathematical properties of models of formal language). Chomsky prefers the later, as evidenced by his statement in Aspects of the Theory of Syntax (1965): "Linguistic theory is mentalistic, since it is concerned with discovering a mental reality underlying actual behavior. Observed use of language ... may provide evidence ... but surely cannot constitute the subject-matter of linguistics, if this is to be a serious discipline."

Norvig then goes on to criticize this view by arguing the following:

I can't imagine Laplace saying that observations of the planets cannot constitute the subject-matter of orbital mechanics, or Maxwell saying that observations of electrical charge cannot constitute the subject-matter of electromagnetism. It is true that physics considers idealizations that are abstractions from the messy real world. For example, a class of mechanics problems ignores friction. But that doesn't mean that friction is not considered part of the subject-matter of physics.

But as I tried to show above, Norvig misses the point:

For example, to simply specify correctly the motion of a body with a certain mass and distance from the sun in terms of elliptical space-time orbit is not to explain the earth's revolving around the sun but rather to redescribe that state of affairs in a mathematically precise way. What remains to be explained is how it is that the earth revolves around the sun in that way, and within classical mechanics, Newton's law of universal gravitation and second law provide that explanation.

Chomsky and other biolinguists taking that route are attempting to discover the language analogue of gravity while the rest are still doing stamp-collecting. That is the just of the argument as I understand it.

On Chomsky and the Two Cultures of Statistical Learning
http://norvig.com/chomsky.html

Not that I buy his arguments but another recent set of critical papers on Chomsky's position are the following papers by Postal:

This paper analyzes recent remarks by Noam Chomsky in effect admitting that his biolinguistics framework is incoherent. This is done in the context of a brief discussion of the incoherence independent of the admission, documenting various contradictions in Chomsky's foundational writings. It briefly draws some ethical and sociological conclusions.

Chomsky's Foundational Admission
http://ling.auf.net/lingbuzz/001569

The Incoherence of Chomsky’s ‘Biolinguistic’ Ontology
http://ling.auf.net/lingbuzz/001608

-- Updated April 10th, 2013, 9:01 pm to add the following --

I thought this is interesting paper that recently was published and kind of relevant to this topic:

A new study from the University of Pennsylvania has shown that children as young as 2 understand basic grammar rules when they first learn to speak and are not simply imitating adults....This suggests that true language learning is-so far-a uniquely human trait, and that it is present very early in development. "The idea that children are only imitating adults' language is very intuitive, so it's seen a revival over the last few years," Yang said. "But this is strong statistical evidence in favor of the idea that children actually know a lot about abstract grammar from an early age."

Young Children Have Grammar and Chimpanzees Don't
http://www.sciencedaily.com/releases/20 ... 131327.htm

Finally, the quantitative demonstration that children but not primates use a rule-based grammar has implications for research into the origin of language. Young children spontaneously acquire rules within a short period, whereas chimpanzees appear to show only patterns of imitation even after years of extensive training. The continuity between the ontogeny and phylogeny of language, frequently alluded to in the gradualist account of language evolution, is not supported by the empirical data. Theories that postulate a sharp discontinuity in syntactic abilities across species appear more plausible.

Ontogeny and phylogeny of language
http://www.ling.upenn.edu/~ycharles/PNAS-2013-final.pdf

-- Updated April 17th, 2013, 7:43 pm to add the following --

For a recent lecture by Chomsky on the idea that language has little to do with communication, externalism, etc. It's bit long/boring but well worth the effort if one is interested in understanding the internalist argument that language is the expression of thought,etc:

[Satyr]

I don't know if someone already said this but language according to Evolutionary Psychologists, is a sophistication of grooming.

It's basic method is to symbolize, first with vocalizations and then with codes (numbers, letters), mental abstractions.

Controlling language or what emotions and phenomena, particular words refer to, is a sure way of controlling the minds that use them.

In the area of philosophy, for example, the language acquires a specialized form, deferring to the authorities that invent them and then come to dominant the intellectual discourse. Though the subject matter, reality, the world, is all around all of us, when we speak of philosophy, in our time, it must go through the academic spectrum of definitions and texts.

The very usage of words, such as autopoesis, will, ego, modernity, nihilism, must refer to the proper anchorites and adhere to the most popular definitions, or else you are dismissed and ignored. This makes discussions an endless debate over who got which authority right and who supports which specialists perspective the best; a gossipy, discussion over cadavers. In the process each participant senses his own place within the intellectual sub-grouping.

Like all specializations a very technical terminology evolves as being an indication of belonging to this select group of "regurgitating" thinkers". The first test is in how you know the lingo. The next establishes how loyal you are to the shared, yet often unstated, moral framework. If the above criteria are not met, then a casual dismissal follows.

And like all specialized groupings, each member must justify and validate the time and effort he has put into belonging to the group. If not the appropriate credentials then the appropriate deference is expected.

[VYCanisMajoris]

At the age of 1, I remember being in a photo room where my parents wanted to take formal pictures of my brother and me. I remember seeing a dark brownish-grey-purplish (colour) projection sheet on the wall in the centre of the room, which formed the background colour image of our photos, with the rest of the wall on both sides unmarked. It was a room which was very simple and unique. I recognized its shape: it was square. And I definitely took note of its colour. However I do not remember the actual photo being taken or entering or leaving the room. Perhaps there was too much going on.. too many shapes of by the complexity of the camera, and a lot of movement thereafter.

This to me, on inspection 21 years later, is how we form language:

When you see something enough times, you form a mental image of it in your head, make associations, and never forget it.

Imagine not knowing a single word. You were born and raised to fend for yourself in a forest. You recognize that a tree is different from everything around it: the grainy ground, the sky above, the passive motion around the sides of it, the colour and shape of the tree itself. Instead of gawping at every tree as though it was new and something to consider, you see every tree as the same when you walk by them. That is one problem out of the way. This makes life a little easier, doesn't it? This identity can be given any association: a colour, a shape, or in a way that your kin can mutually understand, a physical utterance. The mockery of a tree's sound blowing in the wind turned into a simple utterance sounds, in our language, like "pffffffffff", which can be altered and enunciated as "phuuu" or to shorten it further "phu". In your own developed language, this sound can be interpreted in your own devised language by the letters you invent which I will lend English's: "buolp".

You walk by several buolp (Our English: phu). Then you see a little woodpecker and notice its features. Its vast complexity is noted and this physical complexity can only be interpreted as a living thing like your own physical complexity. However it was different from the tiger that was chasing you last night because it is small, can fly and makes a weird sound on the buolp. It sounds in our language like, "Tk tk tk tk tk tk"; for you it sounds like "mo mo mo mo mo" and you call the bird "mo" (Our English: tik); and you combine this new identity of a woodpecker on a buolp: "muolp" (Our English: thu)--a hybrid of the sound of buolps and the sound of a mo. You share this utterance to your other little humanoids. In your mind, you look for the one brown liney thing with a little red on it that makes the sound "mo mo mo mo mo". Because the mo was valued as a good need-satisfier, you identify in the field of buolp the one muolp that you will climb and grab the mo to make you sated.

But you see other little birds on the buolp, not necessarily the mo. How confusing! The birds make a weird sound which sounds to us like "he", in your language "la". While the mo itself remains mo, the concept of tiny, flying complexities are called "moa" (Our English: tee); a hybrid of mo and la. And a buolp with any bird on it, including the mo, is called "molalp" (Our English: tee); a hybrid of la, mo, and buolp. In your own head, you project the image of a liney brown tall thing with a green top with not just a little red on it, but other colors and shapes and sizes too. Muolps will be hard to spot with all of these moa. In the field of buolps, you will look for the all of the molalps for a muolp to eat the mo.

The point I'm trying to make is, we take our senses and define any given object by our related sensory associations to it. A word or mental impression encompasses the identity or perfect example of it which you form and can readily identify upon first glance. Even though every tree is different, you have thought the epitome of one as one which defines the rest--or, "tree-ness".

In my case, I took the square of the sheet on the wall and associated that shape to other instances where I see the shape, but of different objects. These objects have their own purpose and common occurrence and thus have their own name, but the shape has its own purpose and common occurrence and thus has its own name--in other words, we give an identity, like a tree, or a tree with a woodpecker, or a tree with all birds, and isolate it, and describe it in a way that is all-encompassing to form one identity, or that picture you form in your head. You could also see one sentence as one giant identity; an identity which is very specific and thus requires a great deal of enunciation instead of "boo" or "gop" to express. It makes life so much easier.

Sorry for all of the editing. I'm trying to make the story of your mo shorter and a little easier to grasp.

[3uGH7D4MLj]

The point I'm trying to make is, we take our senses and define any given object by our related sensory associations to it. This word or impression encompasses the identity of the entity which you form. Even though every tree is different, you have thought the epitome of one as one which defines the rest--or, "tree-ness".

In my case, I took the square of the sheet on the wall and associated that shape to other instances where I see the shape, but of different objects. These objects have their own purpose and common occurrence and thus has their own name, but the shape has its own purpose and common occurrence and thus has its own name--in other words, we give an identity, like a tree, or a tree with a woodpecker, or a tree with all birds, and isolate it, and describe it in a way that is all-encompassing to form one identity. You could also see one sentence as one giant entity, an entity which is a more sophisticated and complex entity of more specific ideas. It makes like so much easier.

I like this picture you've painted. Fun to think about this. What about this: Proto humans were pretty intelligent in the ways of their environment. They knew volumes about plants, animals, and were skilled in knowledge and use of their own bodies and were sharpeyed, fast, and accurate with a thrown stone. Their world was vision and sound and smell and they had it covered. They recognized not only the trees but all the different species of tree in their area, their leaves and bark, strength, taste of the sap, and they had a full and successful life without talking that much, or identifying objects with words. The generalization, "tree," went without saying. : )

Maybe you don't need words to know all these things. I don't think that language is a way of thinking, or necessary for thinking. Early humans could have had a large memory for sights and sounds, they could have thought in movies (like I do). I think language was for communication. It probably came from the fun of mimicry like you say, and from the desire and need to tell the others what's going on where I was today.

Pretty cool remembering back to age 1.