Ramón Casares - Academia.edu (original) (raw)

Drafts by Ramón Casares

Following Post program, we will propose a linguistic and empirical interpretation of Gödel's inco... more Following Post program, we will propose a linguistic and empirical interpretation of Gödel's incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make "infinite use of finite means". The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our finitary tool, which is our complete language.

I defend that the main task of language is to deal with intended meanings, and therefore that lan... more I defend that the main task of language is to deal with intended meanings, and therefore that language should be centered on semantics and pragmatics. I propose a subjectivist program based on problem solving to achieve that conception of language. I argue that the predominant program of language, which is centered on syntax, is driving biolinguistics to a dead-end. In summary, this is a paper on the foundations of biolinguistics that proposes a new balance where semantics and pragmatics will weigh more and syntax less.

This is a review of the book "Why Only Us" by Berwick & Chomsky done from the point of view of co... more This is a review of the book "Why Only Us" by Berwick & Chomsky done from the point of view of computing. The main conclusions are: that the book uses the word 'recursion' with a meaning that does not correspond to the meaning used in mathematics, causing confusion, and that the theory presented in the book, that syntax can be reduced to Merge, does not translate sensibly to computing, because Merge by itself cannot even parse, and therefore it is not enough to explain the evolution of Merge to explain the evolution of language, as the book proposes.

Recursion in linguistics by Watumull et al. (2014) is compared with recursion in mathematics by T... more Recursion in linguistics by Watumull et al. (2014) is compared with recursion in mathematics by Turing (1937).

Turing (1937): "Computability and λ-Definability"; doi: 10.2307/2268280.

Watumull et al. (2014): "On Recursion"; doi: 10.3389/fpsyg.2013.01017.

A complete hierarchy of languages is introduced to defend the thesis that 'human language is a Tu... more A complete hierarchy of languages is introduced to defend the thesis that 'human language is a Turing complete language'. This complete hierarchy discriminates languages on computability, meaning mixability, generativity, decidability, and expressiveness. We show that our thesis is true and, using the complete hierarchy, that our thesis is more specific and then more significant than other truths about human language. The complete hierarchy explains the evolution of language on the assumption that it was driven by expressiveness, and consequently it explains that our language is complete because complete languages are the most expressive languages.

Language is the most distinctive feature of humans, but there is no consensus on what is characte... more Language is the most distinctive feature of humans, but there is no consensus on what is characteristic of language. From the point of view of computing, we argue that 'the human brain circuitry that implements language is Turing complete'. This thesis makes evolutionary sense and natural languages are expressive enough, but two issues against it remain: natural language syntax is decidable and not every possible language can be a natural language. We answer the first by showing that the syntax of a complete language can be decidable, and by blaming functional semantics for the undecidability, where functional semantics is the semantics of syntax. To answer the second, we distinguish native language, first language, and later languages, where all natural languages are first languages acquired during a critical period that eases the process by preventing some possibilities. The thesis supports the weak version of the linguistic relativity hypothesis, and explains the rôle played by language in the cognitive gap that separates our species from the rest.

To investigate the evolution of syntax, we need to ascertain the evolutionary rôle of syntax and,... more To investigate the evolution of syntax, we need to ascertain the evolutionary rôle of syntax and, before that, the very nature of syntax. Here, we will assume that syntax is computing. And then, since we are computationally Turing complete, we meet an evolutionary anomaly, the anomaly of syntax: we are syntactically too competent for syntax. Assuming that problem solving is computing, and realizing that the evolutionary advantage of Turing completeness is full problem solving and not syntactic proficiency, we explain the anomaly of syntax by postulating that syntax and problem solving co-evolved in humans towards Turing completeness. Examining the requirements that full problem solving impose on language, we find firstly that semantics is not sufficient and that syntax is necessary to represent problems. Our final conclusion is that full problem solving requires a functional semantics on an infinite tree-structured syntax. Besides these results, the introduction of Turing completeness and problem solving to explain the evolution of syntax should help us to fit the evolution of language within the evolution of cognition, giving us some new clues to understand the elusive relation between language and thinking.

Putnam proved that "every ordinary open system is a realization of every abstract finite automato... more Putnam proved that "every ordinary open system is a realization of every abstract finite automaton", showing that computing is meaningless. Analyzing a simpler version of his proof, we conclude that giving a meaning to a computation requires computing, which is meaningless, starting a recursion.

The Turing machine, as it was presented by Turing himself, models the calculations done by a per... more The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here is why, Why are we Turing complete?

Being Turing complete also means that somehow our brain implements the function that a universal Turing machine implements. The point is that evolution achieved Turing completeness, and then the explanation should be evolutionary, but our explanation is mathematical. The trick is to introduce a mathematical theory of problems, under the basic assumption that solving more problems provides more survival opportunities.

So we build a problem theory by fusing set and computing theories. Then we construct a series of resolvers, where each resolver is defined by its computing capacity, that exhibits the following property: all problems solved by a resolver are also solved by the next resolver in the series if certain condition is satisfied. The last of the conditions is to be Turing complete.

This series defines a resolvers hierarchy that could be seen as a framework for the evolution of cognition. Then the answer to our question would be: to solve most problems. By the way, the problem theory defines adaptation, perception, and learning, and it shows that there are just three ways to resolve any problem: routine, trial, and analogy. And, most importantly, this theory demonstrates how problems can be used to found mathematics and computing on biology.

We prove that if our calculating capability is limited to that of a universal Turing machine with... more We prove that if our calculating capability is limited to that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.

For Putnam in "Representation and Reality", there cannot be any intentional science, thus dooming... more For Putnam in "Representation and Reality", there cannot be any intentional science, thus dooming cognitive science. His argument is that intentional concepts are functional, and that functionalism cannot explain anything because "everything has every functional organization", providing a proof. Analyzing his proof, we find that Putnam is assuming an ideal interpreting subject who can compute effortlessly and who is not intentional. But the subject doing science is a human being, and we are not that way. Therefore, in order to save cognitive science, we propose to replace the ideal subject with a real and intentional human subject, and we propose to model intentionality by using a problem theory which is an intuitionist set theory where the resolving subject is a computing device. We are intentional because we are living beings, where life is the intention of not to die, so we are embodied intentions designed by evolution. We are real and then we have to compute our resolutions to the survival problem, and fortuitously we are computationally Turing complete, so our language is complete and then full and self referable. In summary, evolutionary subjectivism modeled as problem solving by computing should save cognitive science. Or, in other words, we are proposing to update Kant with Darwin and Turing.

Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of ... more Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of our success as species is that we, Homo sapiens, are the first and the only Turing complete species. Turing completeness is the capacity of some hardware to compute by software whatever hardware can compute. To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing is for solving problems, and software is much cheaper than hardware, resulting that Turing completeness is evolutionarily disruptive. This conclusion, together with the fact that we are the only Turing complete species, is the reason that explains why we are so many. Most of our unique cognitive characteristics as humans can be derived from being Turing complete, as for example our complete language and our problem solving creativity.

Papers by Ramón Casares

ArXiv, 2015

To investigate the evolution of syntax, we need to ascertain the evolutionary r\^ole of syntax an... more To investigate the evolution of syntax, we need to ascertain the evolutionary r\^ole of syntax and, before that, the very nature of syntax. Here, we will assume that syntax is computing. And then, since we are computationally Turing complete, we meet an evolutionary anomaly, the anomaly of sytax: we are syntactically too competent for syntax. Assuming that problem solving is computing, and realizing that the evolutionary advantage of Turing completeness is full problem solving and not syntactic proficiency, we explain the anomaly of syntax by postulating that syntax and problem solving co-evolved in humans towards Turing completeness. Examining the requirements that full problem solving impose on language, we find firstly that semantics is not sufficient and that syntax is necessary to represent problems. Our final conclusion is that full problem solving requires a functional semantics on an infinite tree-structured syntax. Besides these results, the introduction of Turing completen...

SSRN Electronic Journal, 2014

Universal Grammar Is a universal grammar by Ramón Casares Universal Grammar is a universal gramma... more Universal Grammar Is a universal grammar by Ramón Casares Universal Grammar is a universal grammar, because the human brain circuitry that implements the faculty of language is Turing complete.

SSRN Electronic Journal, 2017

Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of o... more Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of our success as species is that we, Homo sapiens, are the first and the only Turing complete species. Turing completeness is the capacity of some hardware to compute by software whatever hardware can compute. To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing is for solving problems, and software is much cheaper than hardware, resulting that Turing completeness is evolutionarily disruptive. This conclusion, together with the fact that we are the only Turing complete species, is the reason that explains why we are so many. Most of our unique cognitive characteristics as humans can be derived from being Turing complete, as for example our complete language and our problem solving creativity.

When the error rate is not absolutely zero, infinite computations are necessarily erroneous, rend... more When the error rate is not absolutely zero, infinite computations are necessarily erroneous, rendering them uninformative. This restricts the practical value of those hypercomputers that perform infinite computations.

For Putnam in Representation and Reality, there cannot be any intentional science, thus dooming c... more For Putnam in Representation and Reality, there cannot be any intentional science, thus dooming cognitive science. His argument is that intentional concepts are functional, and that functionalism cannot explain anything because “everything has every functional organization”, providing a proof. Analyzing his proof, we find that Putnam is assuming an ideal interpreting subject who can compute effortlessly and who is not intentional. But the subject doing science is a human being, and we are not that way. Therefore, in order to save cognitive science, we propose to replace the ideal subject with a real and intentional human subject, and we propose to model intentionality by using a problem theory which is an intuitionist set theory where the resolving subject is a computing device. We are intentional because we are living beings, where life is the intention of not to die, so we are embodied intentions designed by evolution. We are real and then we have to compute our resolutions to the...

We prove that if our calculating capability is that of a universal Turing machine with a finite t... more We prove that if our calculating capability is that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.

We define a problem theory from first principles. We investigate the objects of this theory: prob... more We define a problem theory from first principles. We investigate the objects of this theory: problems, resolutions, and solutions. We relate problem theory with set theory and with computing theory. We find taxonomies for resolutions and for problems. We build a hierarchy of resolvers: mechanism, adaptor, internalizer, learner, and subject. We show that the problem theory is complete, that is, that there are just three ways to resolve any problem: routine, trial, and analogy. Finally, we propose a thesis: We are Turing complete subjects because we are the result of an evolution of resolvers of the survival problem.

Physicalism is the default position in science and in the philosophy of mind, but it should not b... more Physicalism is the default position in science and in the philosophy of mind, but it should not be, I argue, because of two errors. By its epistemological error, physicalism tries to explain theoretically what is evident. Only what I experience in first person is certain, so pain does not need a theoretical explanation. Physics itself is based on first person perception, avoiding the epistemological error, and then physics can progress, even changing its own ontology. However, physicalism imposes the ontology of physics on every science, and in physics everything is causal. By its ontological error, physicalism tries to explain causally what is intentional. And it happens that causality and intentionality are mutually exclusive, showing that the ontology of physics is insufficient wherever intentions are present. This ontological insufficiency prevents that physicalism can repeat the success of physics with any science where intentions play a rôle, and thus it is blocking the advance of both the social sciences and the philosophy of mind. To overcome this obstacle, I propose to go back to the essentials: we should consider again the transcendental problem raised by Descartes and its solutions by Hume and Kant. On top of this subjectivist solution, we should take advantage of Darwin and Turing, and we should extend our ontology beyond causality to include intentionality, and here my proposal is problem solving. Then you could join our Post-Kantian subjectivism and say with me: The world is not a huge machine, as physicalism proposes, but an enigmatic problem.

Turing (1937): "Computability and λ-Definability"; doi: 10.2307/2268280.

Watumull et al. (2014): "On Recursion"; doi: 10.3389/fpsyg.2013.01017.

ArXiv, 2015

SSRN Electronic Journal, 2014

SSRN Electronic Journal, 2017