Language and Physics: A Discussion of Some Issues


“Many physicists have gone so long not understanding quantum physics that they think it is a mistake to even try”

               “The world doesn’t speak only we do” Richard Rorty

Facebook can be a great medium to think through various different scientific and philosophical issues. A while ago on Facebook a friend of mind Fabiola Soreng posted an interesting quote by Heisenberg:

“It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme — the quantum theory — which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies — the wave picture and the corpuscular picture.”

I had read this claim by Heisenberg many years ago in his book ‘Physics and Philosophy’. Over the years I have heard it repeated many times by various different physicists. Below is a nice discussion of the perils of trying to talk about physics when not being clear about language

When reading the post on Fabiola’s page I believed that these physicists including Heisenberg had inherited a logical positivist view on the nature of language, for example a Carnap/Ayer type view on language. I wondered if physicists today knew that few if any theorists would accept the simple picture theory of language that Ayer, following the early Wittgenstein, argued for. When I voiced these concerns Fabiola correctly informed me that a lot of physicists like Heisenberg were very critical of Logical Positivists and my historical understanding of the issue was deficient. That said I was still unclear as to what justification physicists had for their claim that language was incapable of describing the world of Quantum Mechanics etc. If they simply meant that in their experience language was a bad tool then there would be little issue. But if they on the other hand argued that language was structurally deficient then things would be different and they would need to provide some justification for their claims about the nature of language. So needless to say I was delighted to see that she tagged her friend physicist David Samuel Silverstein into our discussion. However before moving on to Silverstein I will first give a brief outline of Heisenberg’s reasons for thinking that language is inadequate to describe reality.

Heisenberg discusses language in his ‘Physics and Philosophy’ in the chapter ‘Language and Reality’. He argues that language is by its nature vague and that even if we try to define the terms of language we will have to rely on some basic concepts which are themselves vague. He claims that language is vague because of its evolutionary history. He gives various examples of what he sees as the primary difficulty with language, e.g. colour blind people who use the word red and green without having any idea of what the actual extension of these terms. He begins with a discussion of colour and appeals to the work of Socrates who in Plato’s dialogues showed the slippery nature of concepts that we think we have a handle of e.g. Justice, Equality, The Good, etc. He credits Aristotle with giving us tight definitions of concepts and says that Aristotle gave us our scientific language.

He then notes that Aristotle’s emphasis on logical analysis and syllogisms etc, while important doesn’t capture the actual vague pattern of ordinary language discourse. He then talks about how we develop a scientific language (through technical definitions) which is different from natural language. He argues that this technical language, prior to the theory of Relativity and Quantum Theory, could be employed consistently and without difficulty. With the mathematical and experimental discoveries of relativity and quantum theory things changed. He argued that since our language formed in a Newtonian world it would be of little use in describing non-Newtonian concepts.

He seems to think that with regard to language it gradually moulds itself around new theoretical developments. He notes that (scientific) language is now in line with Einstein’s notion of ‘simultaneity’. But he argues that there are unsurpassable difficulties when it comes to describing some aspects of physics in natural language:

“In the theory of general relativity the language by which we describe the general laws actually now follows the scientific language of the mathematics, and the descriptions of the experiments themselves we can use the ordinary concepts since Euclidean Geometry is valid with sufficient accuracy in small dimensionsThe most difficult problem, however, concerning the use of language arises in quantum theory. Here we have at first no simple guide for correlating the mathematical symbols with concepts of ordinary language; and the only thing we know from the start is the fact that our common concepts cannot be applied to the structure of atoms…But the problems of language here are really serious. We wish to speak in some way about the structure of the atoms and not only about the ‘facts’- the latter being for instance the black spots on a photographic plate or the water droplets in a cloud chamber. But we cannot speak about the atoms in ordinary language.” (ibid pp 78-79)

So above Heisenberg is arguing that Relativity theory is to some degree expressible in natural language but things are much more difficult with quantum theory. He goes on to note that there have been two alternative approaches to trying to describe quantum weirdness in ordinary language. The first approach is to speak vaguely (and poetically about) about the discoveries of quantum mechanics.


“In answer to the first question one may say that the concept of complementarily introduced by Bohr into the interpretation of quantum theory has encouraged the physicists to use an ambiguous rather than an unambiguous language, to use the classical concepts in a somewhat vague manner in conformity with the principle of uncertainty, to apply alternatively different classical concepts which would lead to contradictions if used simultaneously. In this way one speaks about electronic orbits, about matter waves and charge density, about energy and momentum, etc., always conscious that these concepts only have a limited range of applicability. When this vague and unsystematic language leads into difficulties, the physicist has to withdraw into the mathematical scheme and its unambiguous correlation with the experimental facts…In fact I believe the language actually used by physicists when they speak about atomic events produces in their minds similar notions as the concept ‘potentia’. The language has already adjusted itself, at least to some extent, to this true situation. But it is not a precise language in which one could use the normal logical patterns; it is a language that produces pictures in our minds, but together with the notions that pictures have only a vague connection with reality, that they represent only a tendency towards reality.” (ibid p. 80)


Here we see the curious approach repeated by Heisenberg that he used above when speaking about relativity theory. He begins by saying that language cannot capture the discoveries of relativity and a few paragraphs later speaks about language adjusting itself to the new facts of reality. Likewise he begins by saying that language cannot capture the facts about quantum reality, but he then moves on to say that language is adjusting itself to the new quantum reality, except in certain areas where we need some mathematical formalism to capture reality.

The other approach to describing quantum reality using language is designing a more precise technical language. Heisenberg describes this as follows:


“Weizsacker (Birkhoff and Neumann) have tried to create precise logical languages which can cope with the quantum world…The general logical pattern, the details of which cannot be described here, corresponds precisely to the logical formalism of quantum theory. It forms the basis of a precise language that can be used to describe the structure of the atom. But the application of such a language raises a number of different problems only two of which we can discuss here. The relation between the two different levels of language, and the consequences for the underlying ontology.” (ibid p. 81)


Heisenberg is correct to note that there are some technical difficulties with Weizacker’s formal language. Furthermore one wonders what advantage there is to be gained in developing a formal language to express the discoveries of quantum physics when we can understand them well enough in mathematics. Nonetheless I see no reason in principle why a more advanced version of Weizacker’s project cannot be developed. Hence I see no reason why we cannot express the discoveries of quantum mechanics in terms linguistic terms. From what I can see Heisenberg really showed little more than that language is not always a good tool for capturing physics not that it is structurally deficient.

When I discussed the issue of language and math with Silverstein he made some points which were different than Heisenberg’s. Silverstein made some interesting points and it is worth delving into our discussion to see where the brief dialectic led us. I began with the following question:

Firstly I should say I am not an expert in physics so I freely admit I could be badly wrong on this issue. That said I think it is worth discussing because I don’t understand the structural features of language that physicists are pre-supposing when they speak of the nature of language. You begin with the following claim:

“To a very large degree our verbal language is something that is limited due to the fact we as humans are hardwired and evolved within the macroscopic world where the laws of Newtonian mechanics apply. Because of this, the quantum world is something that is a complete breakdown of our intuition. When we even begin to attempt to intuitively describe what happens within quantum mechanics we find ourselves in the dark when we either use our current language or further modify it to something that makes little to no sense to us.”

You claim that because of the conditions of our linguistic evolution (a place where Newtonian Mechanics apply) our language fails us because of a misalliance between our folk intuitions about reality, and the strange facts about the quantum world. I think here when you talk about folk intuitions about reality, you are not speaking about language, but about our intuitive theories of the world. Humans do seem to be hardwired with folk psychological expectations about the behavior and mental states of other agents in the world, and the behavior of objects in the world. These are the domains of study of folk-psychology and folk-physics. When ethno scientists study folk physics and folk psychology they are not interested in the world per-se but in the cognitive processes of a particular species and their expectations (probably unconscious) of how the world works.

Now what is interesting here is that empirical studies into the folk physics of children, indicates that they have an implicit theory about how the world should work prior to acquiring any language. These studies are typically done by tracking the expectations of children; children are habituated to a particular stimulus and when something surprising happens (from the child’s perspective); the child will stare at the stimulus longer. Using this technique psychologists have found that children have detailed expectations of the way the world should work months before they even begin to acquire a language. Spelke (1990) describes some of this data:

“Bower’s studies have yielded four findings that seem to have provided evidence for object permanence in infants well below 9 months. First, 7 week old Infants were found to discriminate between disappearances that signalled the continued existence of an object (e.g. Gradual Occlusion), and disappearances that did not (e.g. gradual dissolution or sudden implosion). Second, 2 month old infants were found to anticipate the reappearance of an object that stopped behind the screen, ‘looking to that half of the movement path the object would have reached had it not stopped’ Third, five month old infants were found to show disruptions in their tracking when an object was altered while passing behind the screen: they tended to look back at the screen, as though in search of the original object. Finally, 5-month-old-infants were found to reach for an object that had been hidden by darkening the room. (1985, 195)”

Now there was admittedly some debate in the literature on the significance of Bower’s results; Piaget and Quine both in their different ways, argued that Bower over interpreted the data. But since then Spelke, Baillargeon, Markman, Carey, Bloom and many others have replicated these studies and responded to both Piaget and Quine’s objections. For a more detailed explication of these topics see my: . The important point here is that children typically begin developing their language from about 12 months as they learn their first words, and start triangulating on shared objects of experience with others, and this is months after they have developed their folk physics. So difficulties in describing the quantum world may as you suggest stem from a discontinuity between our folk physics and the actual structure of reality. But I don’t see how this can be traced to a problem in the structure of language as opposed to a problem with people expecting the world to fit their a priori intuitions.

Silverstein replied to my point as follows:

“ First off I would like to point out that this isn’t specifically with respect to our linguistic evolution, but to the very hard-wiring of our brain itself. However because of that, of course language is still going to play a role regardless, yet if we focus particularly on language alone that really is something that I feel will really mask the issue as a whole. Once again this does reflect on language yet to get at the very roots of language I feel one first needs to look and focus on understanding and comprehension. So to elaborate further one needs to look at and see how the world works first even before comprehension. Now that is some very interesting information you shared with me with regards to the psychological studies done with children. Yet this is something which really does show how we are hardwired to the Newtonian world, and because of that it is something that is extremely intuitive to us even at a very young age. Once again I feel what we have to do is look more at the root or as Fabiola said, a common denominator, and that really has to do with our understanding of the physical world.”

I am not entirely sure I fully understand the reply of Silverstein. On one level we seem to be in agreement that the conditions under which humans evolved resulted in hardwired intuitions which make understanding quantum mechanics difficult from an intuitive point of view. I would add that a slight amendment; studies in folk physics intuitions show that children seem to intuitively accept a kind of Cartesian contact mechanics. It is for this reason that people, including Newton, found some aspects of Newtonian physics puzzling. That said it seems that Silverstein and I are in agreement that our intuitive folk physics can be an impediment to understanding the real world.

What I am slightly confused about is his claim that we need to look at and understand the world ‘before our comprehension’. To some degree this seems like arguing that our eyes to some degree effect how we see the world, so to see things in a theory neutral way we should rip out our eyes and see the world as it is. When Silverstein argues that we need to understand the world ‘before our comprehension’ what he seems to mean is that we should carefully observe and mathematically describe the world as it is before theorising about it. I think, and pretty much all brain science and developmental psychology would back me up on this, pure theory neutral description is impossible we are always using an implicit theory to interpret data. Now things may not seem like that from the point of view of the theorist doing the observing but it is none the less a fact (see Wittgenstein 1953, Quine 1960 for more details). From the point of view of a working physicist these implicit assumptions may be so close to home that they are not even aware of them. The working assumptions typically do no harm so a physicist who thinks he is engaging in theory neutral observation and typically will not run him into trouble. Nonetheless it is important that we give as accurate description of what is going on as is possible if we as external observers are to understand the nature of the scientific enterprise.

Back to the issue of language I do agree with Silverstein that it has its deficiencies. Natural language can be vague there is no doubt about this. But people like Quine (1960) have worked on modifying our natural language to at least minimise this vagueness where necessary. There is a huge literature of Vagueness (Timothy Williamson has done great work on this) in natural language that can help in discovering where exactly natural language breaks down and examining this literature can probably help in the process of making language more precise in order to express the weird world of Quantum mechanics.

People like Ladyman and Ross in their ‘Everything Must Go’ attack the philosophical need to tame the world as revealed by contemporary physics. They note that attempts to make quantum mechanics more intuitive, by the lights of our folk intuitions, simply ends up falsifying the data. For this reason they argue we should treat the mathematical structure of the various theories as real and ignore the other aspects of the theory as mere window dressing. To some degree I think they have a point. Nonetheless I think understanding precisely how our folk intuitions differ from what science tells us about the world can greatly increase our understanding. So, for example, with a greater appreciation of what our intuitions are about how the physical world works, we can understand why we find some scientific theory radically unintuitive. This works in simple areas like probability, we have a good working understanding of how people intuitively think about probability, we can also explain why people’s intuitive probability goes wrong in certain areas. This helps us explain to children why certain facts seem intuitive to them and shows them the unreliable nature of their intuitions on some topics (some philosophers haven’t taken this simple fact on board: Thomas Nagel take a bow).

Similar situations arise in the study of consciousness where people use intuition pumps to get others to think that certain aspects of consciousness will never be amenable to a scientific analysis. But none of this is the fault of language as far as I can see, but is the fault of taking our intuitions more seriously than we should on a variety of different topics. Silverstein replied to my above comments as follows:

“As for differentiating our folk intuitions verses what science actually tells us; well that is something that we have been doing within the scientific community for centuries and it is still something we are differentiating today. Consciousness is something that is extremely mysterious due to the fact that we have such an ill understanding of what it is, however that is something that really isn’t something which we need to focus on language first, but once again need to look more at the big picture which is being able to understand it first. When it comes to talking about language I really don’t think that it is so important to specify on a particular nature of language they are using.”

Again here I think there are large areas of agreement with Silverstein and I. We are in agreement that science has been differentiating our folk intuitions from what sciences tells us for centuries. The evidence I gave about our deficient folk intuitions was scientific evidence. I am not presenting some alternative to science as the best tool for understanding reality, there is no alternative that I know of. On the issue of Consciousness I think he misunderstands me to some degree. I don’t think we need to focus on language first in order to understand consciousness. Rather what I was pointing towards was the fact that people have intuitions which make them think of consciousness in a certain way. These ways of thinking sometimes lead to pessimism about a science of consciousness. People like Dennett use language (analogies, metaphors, intuition pumps) to get people to think differently about consciousness. This is not a replacement of the experimental approach rather a helping hand in getting people be less guided by their a priori intuitions about the way we should or should not approach consciousness.

On the issue of language I do worry about the way physicists think about it. When physicists talk about language they typically (but by no means always) don’t specify what their theory of the nature of language is, rather they seem to rely on their own intuitive view on its nature. Relying on one’s own intuition is bad practice for physicists thinking about linguistics as much as it for linguists thinking about physics.

I think that it is necessary if language is being discussed for the person to give some indication of what they mean by the word ‘Language’. There are debates within linguistics about the degree to which language is an innate domain specific entity genetically programmed or whether is developed culturally and learned by each individual using domain general innate architecture. I think it is important to take a stance on these issues as if you are going to talk about language being limited in ways x or y you need to justify this with empirical data about the nature of language. There is a big debate on the extent to which natural language consists of universals that are wired into the subject and if a theorist is arguing that language is hardwired to do x or y then they owe us an account of what they think are the universals in natural language and some commentary on the anthropological and linguistic data offered by people like Everett, Sampson, Pullum, Evans, Behme, Cowie, Clark etc who argue that these supposed universals don’t actually exist.

Upon reading my reply to Silverstein my friend Fabiola responded by posting a meme from Feynman: in which Feynman argued that making language too precise as some philosophers do can actually be counterproductive and bad for science. Below is my reply to her:

Fabiola I am not sure I agree with you on Feynman. It seems to me that physicists say diverse things about language and don’t really justify them with empirical evidence. One physicist Pete Morrison claims that the problem is that language is too vague and cannot be used to make the precise predictions in the way that mathematics can. In the Feynman quote he complains that philosophers use language in too precise a manner. Heisenberg claims that language is deficient because we need to form mental images when using language whereas mathematics is more abstract. Einstein on the other hand argued that language was a bad tool for thinking and he preferred to think in mental imagery (so is he making the opposite claim to Heisenberg?)

So different physicists seem (from a cursory glance) to have vague and not always consistent views on what is so deficient about language as a tool for explaining the world. If they are making claims about the structure of language they need to deal with the structures revealed by linguistics. On the other hand if they are merely saying that language is a tool that is not very useful for them then we can just ignore the issue. I don’t think Feynman really addresses any real issue above it would be helpful if he cited particular philosophers who are guilty of this behaviour. Then I could see if he understands them correctly, if he did I may agree with his characterisation. Furthermore as Heisenberg showed above it is not just philosophers who try to improve language to make it a more precise tool to explain reality. Weizsacker, Birkhoff, and Neumann, have all tried to develop formal language for this purpose as well. I wonder what Feynman would make of their work?

I am not arguing that physicists need a theory of meaning to do their science. It is one of the most flourishing scientific fields there is, and needs no help from ignorant outsiders like me. I am more concerned with their views on language and whether I can make sense of them. In my view Linguistics is a flourishing science, if physicists want to talk about language they need to understand the science of language. Otherwise they can just choose to ignore the issue, (a perfectly sensible approach) but empirical claims about the nature of language require empirical evidence. I mean if a theorist decides to speak about quantum mechanics then presumably they need to know something about quantum mechanics and maths. Why does a physicist get to make vague claims about the nature of language while systematically ignoring the science of language? Just because a scientist has expertise in physics doesn’t make them an expert on language. It seems to me that some physicists make a mish-mash of claims; e.g., language is too vague to do x, we shouldn’t try to make language too precise because it leads to paralysis, we need to form a mental picture to use words. These claims are never justified with any evidence. I agree that if you want to understand cosmology physics is the only place to look (although philosophers like Maudlin and Ladyman, Ross, Albert etc have written interesting stuff). My concern is to understand whether there are structural features of language that make it unsuitable to understanding the world. And if there are why it cannot be modified to fill this void?. It is clearly the case that physicists find mathematics the best tool for explaining and understanding the world. But this tells us nothing about the semantic power of language or its limits. Silverstein commented on my reply to Fabiola as follows:

“To be frank it seems like it should be something that is self explanatory with regards to what language we are using. Yes I am one of those people that relay far more on my own intuitive view. This is my honest opinion when it comes to language and it is not only something that I feel is true but I would say that about at least 99% of the physics community of the past and present agree with. I cannot give any fancy linguistic argument since it is not my field, however I did express my opinion earlier and I hope this further illuminated it.”

More than anything he said, in our discussion, I am in strong disagreement with Silverstein’s above claim about language. If a theorist wants to make claims about the structure of language they need to provide empirical evidence to support these claims. The fact that 99 percent of physicists agree with him on this fact is not relevant at all. Furthermore this 99 percent of physicists seem to be in disagreement about what it is about language that makes it so deficient; is it too vague, is it too precise? Heisenberg seems to think that the problem with language is that we need to connect our words to mental images in order to give them content. This claim is simply false; some people are extremely poor mental imagers and don’t use mental imagery in using their words at all (see Kosslyn et al 2006, and Galton 1880). I have discussed mental imagery and how assumptions that all people have the same degree of mental imagery leads to theoretical mistakes in my blog post: . I think that physicists can claim that they don’t find language a useful tool and that is fine as far as it goes. But when they argue that language cannot express x or y they need to provide real empirical evidence to support their claim and neither Fabiola or David Silverstein have provided this evidence.

On the issue of mathematics Silverstein’s claims are interesting but again I think they need to be qualified. He argued:

Now mathematics is something which is not so limited because with mathematics we are writing down natures laws which is something that automatically comes to us, and no matter how it comes out, it is something that we write down and describe not with verbal language but the language of the cosmos. Hence we are not limited to inventing ways of describing things, when we are discovering the endless and different amount of ways the laws of nature comes to us. This is regardless if it is something that at first makes sense to us or not and no matter how paradoxical it may seem, the only thing we are looking for is truth, no matter how it may show its face to us.”

Firstly I think the metaphor of the language of the cosmos needs to be expanded on a bit. The universe doesn’t speak any language, it is us (and perhaps other creatures) that uses language or math to describe the universe, but does it really make sense to say that the universe speaks? I think it would be more expedient to say that so far mathematics has proven the most efficacious tool we have for describing the universe.

When he speaks of mathematics being used to understand the universe he argues that because of the fact that the universe speaks mathematics we don’t have to invent symbols to describe it. You just describe the universe in its own language; the language of mathematics. Assuming that he doesn’t think that the universe is a conscious agent who has a language, there are two ways I could parse his claims (1) As meaning that the universe at its most fundamental level is nothing more than a series of mathematical entities and their relation to each other. (2) That mathematics is the most useful tool we have for understanding the universe?

Silverstein replied to this question as follows:

“When I talk about the language of the cosmos and language of nature, you even stated that it does appear to be a metaphor. Indeed this is a metaphor and it doesn’t literally mean that the universe is literally speaking. I would like to add that I don’t see mathematics as a mere tool but I actually see mathematics as a discovery and artifact that we are uncovering. This is something that I truly do feel that makes it different than language which is something that really does appear to be something that is invented and is not something universal. To be very direct I’m going to put language and mathematics in two different categories and I don’t see the universe as a self aware conscious agent. To a very large degree, I will say that at the most fundamental level. Earlier I was not emphasizing language being hardwired into us; I was talking about the hard-wiring of our minds as a whole which gives us a physical understanding which then LEADS to language.”

Silverstein’s reply in so far as I understand it is an expression of some kind of Platonism. Language is a tool developed over our evolutionary history but mathematics is something that exists independent of our contingent biology and is a universal feature of the universe. I partly agree with him here but I think he ignores the degree to which our mathematical abilities are innately structured because of our evolutionary history. To develop the point a bit we can assume mathematical Platonism but still think that us as contingent biological entities may be incapable of grasping all of these truths and our innate mathematical sense may only partially correspond with the mind independent world. Silverstein who believes that maths puts us in direct contact with reality may not agree with my pessimism on this point.

When Silverstein speaks of the fact that “We discover the way the laws of nature come to us no matter whether they make sense to us, we accept it no matter how paradoxical it may seem, because we are after truth; no matter how it may show its face to us.” Here I think he definitely needs to expand on what he is claiming. Sure you can and should modify your theory on the basis of unexpected experimental results. But an experimental result doesn’t come with a label ‘I must be interpreted this way’. When an anomalous experimental result occurs and it cannot be made sense of in light of previous theories. Different theorists ALL of whom presumably want to discover the truth no matter what its face may disagree on how to account for this new experimental result. Different mathematical formalisms may be tried which at least agree with the current experimental result and can account for it in light of a modified previous theory and a variety of different experiments will be proposed to test the various new formalisms and theories. I think the way he describes things air brushes the fact that we are sometimes at a loss with how to cope with anomalous experimental data. Theorists disagree, and hopefully as we do more and more tests we can get an interpretation which is more in line with the facts. But such results are rarely the result of simply accepting some revealed truths but rather as a result of interpretation, theorizing, and testing these theories as rigorously as possible.

Silverstein replied as follows:

“With regards to how nature shows itself, I am saying that regardless if we comprehend it or not, it is something that we write down regardless. As I stated before there are things that observation plays a key role in the picture and regardless if what we are observing cannot be understand and if there are no words to describe it in the dictionary we write down the mathematics regardless, and when it comes to labeling yes it does indeed come with a label, we simply just need to decipher what it is telling us. Yes different mathematical formalism often is tried, but very often we are discovering a brand new axiom of mathematics, something physical which is which is describing our results.”

Here again he seems to be emphasising the importance of pure observation and not letting our theories force us to ignore inconvenient or seemingly bizarre data. I think it is worth reflecting on the degree to which our minds enter into our interpretative process when we are collecting data. Chomsky has written about the fact that we are creatures created by natural selection not angels so we shouldn’t be so sure we are always directly in touch with reality at all times. I have written on this topic and though I am very critical of it, it is worth thinking through his logic in thinking about whether our brain engages a science forming faculty which to some degree influences how we interpret the world . There is a long standing debate between people like Kuhn and those like Weinberg and Sokal on the degree to which observation is theory laden. I don’t think Kuhn is necessarily correct on this issue but I do think that Silverstein is beginning with the assumption that Kuhn is wrong and hasn’t provided much evidence to support this a-priori intuition of his.

When Silverstein talked about the evolution of language he noted that it developed in our Newtonian Environment. But he spoke about mathematics as something we discover and read off Nature’s language. To some degree I agree with him on this, I think Frege and Husserl both conclusively showed that mathematics cannot be entirely reduced to psychology. That said some of our implicit mathematical abilities are shared with other animals, Dogs, Crows, non-human Primates Etc. There is good evidence that we have an innate number sense which we use to acquire our more complex mathematical abilities. See for example:

Above Susan Carey discusses the evidence for an innate number sense. In a different direction Ian Hacking and George Lakoff have discussed the role of embodiment in the type of mathematical structures we develop:

Above is a talk by Hacking on mathematics development and Lakoff on embodied cognition. None of this in my opinion shows that mathematics can be reduced to cognitive/embodied processes in my opinion. But it does show that if we are going to discuss the nature of mathematics and language we need to pay attention to cognitive science to justify our positions. We do know that in the brain there are different areas which specialise in language and math. We know through brain damage that the areas are dissociated from each other. A person after a stroke can have much of their mathematical abilities spared, while losing the ability to speak and understand language (and vice-versa). But I don’t think this really demonstrates much about the structure of maths and the structure of language and how they can be developed, modified, and inter translated.

Silverstein responded to the above points as follows:

“Yet with mathematics what we are doing is that we are doing something that is rather different. Even before we can understand what it is we are writing, we are writing down our observations; something which we very often are forced to come up with entire new names because of what that very observation is telling us. While with the mathematics it is indeed something that is already there; and indeed being a physical phenomenon, it was something that already existed before our prior knowledge. To be direct, we don’t invent words such as gauge invariance, Lorentz Transformations, Chern-Simon forms and topological explicit and spontaneous symmetry breaking prior to the mathematics and that is used to describe our daily lives. This is something that comes to us first from the mathematics and then we are forced to invent new words for them.”

I think here I should note that Silverstein is presenting a particular philosophy of mathematics called realism. In their ‘The Grand Design’ Stephen Hawking and Leonard Mlodinow espoused a kind of model dependent realism, while people like Penrose prefer a form of Platonism. Different physicists hold different philosophies of science. So a physicist who says that this is the philosophical views held by physicists needs to at least debate with the competing scientists who hold different philosophies of science whether pragmatist, Platonist etc.

An important point to note when speaking of natural language (and the degree to which it can express mathematical truths) is that natural language is typically explained interms of mathematics by linguists. Linguists typically explicate syntax in terms of a kind of quasi set theory; semantics in some quarters is explicated in terms of ‘Tarski’s theory of truth’. There are mathematical studies of the statistical features of words being used and correlated with the probability of a child hearing things like nouns, verbs etc in their linguistic environment. Some theorists like Katz actually think of language as an abstract object like math. I think if physicists want to make large scale claims about the semantic powers of math (or lack thereof). They need to provide empirical evidence to support their claims.

I found the discussion with Fabiola and David Silverstein very interesting and informative. But I am not sure that I fully understand their positions. So I decided to post it in blog-post form to see if others had any views on the differences between natural language and mathematics and could perhaps help us to further clarify the issues. As a non-expert on these issues I hope to gain further insight by engaging with thinkers who have thought about this issue deeper than I have.

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