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An Ideal Language For Philosophy & Reality?
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The best language to describe philosophy and reality is swearing.
Surprisingly there is no mention of Russell and Whitehead's Principia, or of Godel's critique, via the Incompleteness Theorem, of the whole project of constructing such a fully axiomatized, philosophical language (his implication being that if we can't even fully axiomatize mathematically statable knowledge, then all bets are off for knowledge claims statable via other language systems). Now that that seems to have been set aside, another manner of approaching the issue of some ultimate language for stating philosophical propositions with maximal clarity would be Chomskian research into a "universal grammar" of thought. If there is such a thing as a universal grammar (and this isn't yet another idle philosophical construct) then this would be the sturdiest basis for philosophical discourse. This would also manage to sidestep relativistic-contextualist critiques.
Though someone like Shakespeare with his queer sympathy for Tragically Wise Fools might side with the above proposal of swearing as the ultimate language.
Elena wrote: "Surprisingly there is no mention of Russell and Whitehead's Principia, or of Godel's critique (via the Incompleteness Theorem) of the whole project of constructing such a fully axiomatized, philoso..."
No language, including mathematics, is ever complete in itself.
No language, including mathematics, is ever complete in itself.
Probably not. But the best candidate for an "ultimate language for stating philosophical propositions with maximal clarity" would have to be the language that most closely approximates the working of human thought. Since the sciences of mind (including neuroscience) are still in their infancy, we'd need to amass something like centuries' worth of data from the various disciplines concerned with the nature of thought, from anthropology to AI, from neurolinguistics to sociopsychology, before we can discover the parameters that can guide the invention of such a language. And since languages aren't invented so much as they evolve, let us then have this discussion in, shall we say, 500 years or so?
Hmmm... I am currently re-reading Machiavelli's Prince, translated by Alvarez. I think my perspective (especially while reading this translation) is not so much which language is 'ideally' suited for philosophy, but rather how well a communicator can use whichever language is at his or her disposal to translate philosophical concepts.
Elena wrote: "Surprisingly there is no mention of Russell and Whitehead's Principia, or of Godel's critique, via the Incompleteness Theorem, of the whole project of constructing such a fully axiomatized, philoso..."Godel's theorem comes with an important set of conditions for it to apply
https://en.wikipedia.org/wiki/G%C3%B6...
First Incompleteness Theorem: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F."
Second Incompleteness Theorem: "Assume F is a consistent formalized system which contains elementary arithmetic. Then {\displaystyle F\not \vdash {\text{Cons}}(F)} {\displaystyle F\not \vdash {\text{Cons}}(F)}
"Philosophical Implications—Real and Alleged6.1 Philosophy of Mathematics
Of the various fields of philosophy, Gödel's theorems are obviously most immediately relevant for the philosophy of mathematics. To begin with, they pose, at least prima facie, serious problems for Hilbert's program (this issue is discussed in some detail in the section on the impact of incompleteness in the entry on Hilbert's Program). Then again, they have important consequences for intuitionism (see the entry on intuitionism in the philosophy of mathematics) (see also Gödel 1933, 1941; Raatikainen 2005).
There has been some dispute on the issue as to whether Gödel's theorems conclusively refute logicism (see the entry on logicism). Henkin (1962) and Musgrave (1977), for example, argue it does; Sternfeld (1976) and Rodríguez-Consuegra (1993) disagree (see also Hellman 1981; Raatikainen 2005).
Gödel himself developed an argument against the conventionalist philosophy of mathematics of logical positivism, and of Carnap's in particular, based on the incompleteness results (Gödel 1953/9). It is discussed in Goldfarb and Ricketts 1992; Ricketts 1995; Goldfarb 1995; Crocco 2003; Awodey & Carus 2003, 2004; Tennant 2008.
6.2 Self-evident and analytical truths
One can also give more general epistemological interpretations of Gödel's theorems. Quine and Ullian (1978), for example, consider the traditional philosophical picture that all truths could be proved by self-evident steps from self-evident truths and observation. They then point out that even the truths of elementary number theory are presumably not in general derivable by self-evident steps from self-evident truths (Quine & Ullian 1978: 64–65.) Hilary Putnam (1975) in turn submits that, under a certain natural understanding of “analytic”, there must be, by Gödel's theorems, synthetic truths in mathematics. In fact, Gödel himself made remarks in a very similar spirit that even the theory of integers is demonstrably non-analytic (Gödel 1944).
6.3 ‘Gödelian’ arguments against mechanism
There have been repeated attempts to apply Gödel's theorems to demonstrate that the powers of the human mind outrun any mechanism or formal system. Such a Gödelian argument against mechanism was considered, if only in order to refute it, already by Turing in the late 1940s (see Piccinini 2003). An unqualified anti-mechanist conclusion was drawn from the incompleteness theorems in a widely read popular exposition, Gödel's Theorem, by Nagel and Newman (1958). Shortly afterwards, J.R. Lucas (1961) famously proclaimed that Gödel's incompleteness theorem
proves that Mechanism is false, that is, that minds cannot be explained as machines.
He stated that
given any machine which is consistent and capable of doing simple arithmetic, there is a formula it is incapable of producing as being true … but which we can see to be true.
More recently, very similar claims have been put forward by Roger Penrose (1989, 1994). John Searle (1997) has joined the discussion and partly defended Penrose against his critics. Crispin Wright (1994, 1995) has endorsed related ideas from an intuitionistic point of view (for criticism, see Detlefsen 1995). They all insist that Gödel's theorems imply that the human mind infinitely surpasses the power of any finite machine or formal system.
These Gödelian anti-mechanist arguments are, however, problematic, and there is wide consensus that they fail. The standard response to this argument goes along the following lines (this objection goes back to Putnam 1960; see also Boolos 1968, Shapiro 1998): The argument assumes that for any formalized system, or a finite machine, there exists the Gödel sentence which is unprovable in that system, but which the human mind can see to be true. Yet Gödel's theorem has in reality a conditional form, and the alleged truth of the Gödel sentence of a system depends on the assumption of the consistency of the system. The anti-mechanist's argument thus also requires that the human mind can always see whether or not a given formalized theory is consistent. However, this is highly implausible (cf. Davis 1990). Lucas, Penrose and others have attempted to reply to such criticism (see, e.g., Lucas 1996; Penrose 1995, 1997). For detailed criticism of Penrose, see Boolos 1990; Davis 1990, 1993; Feferman 1995; Lindström 2001; Pudlák 1999; Shapiro 2003; many of these considerations are also relevant for what Lucas says).
6.4 Gödel and Benacerraf on Mechanism and Platonism
Interestingly, Gödel himself also presented an anti-mechanist argument although it was more cautious and only published posthumously (in his Collected Works, Vol. III, in 1995). That is, in his 1951 Gibbs lecture, Gödel drew the following disjunctive conclusion from the incompleteness theorems:
either … the human mind (even within the realm of pure mathematics) infinitely surpasses the power of any finite machine, or else there exist absolutely unsolvable diophantine problems.
Gödel speaks about this statement as a “mathematically established fact” (Gödel 1951; for more discussion on Gödel's disjunctive claim, see, e.g., Shapiro 1998). According to Gödel, the second alternative
seems to disprove the view that mathematics is only our own creation … that mathematical objects and facts … exist objectively and independently of our mental acts and decisions.
Gödel was nonetheless inclined to deny the possibility of absolutely unsolvable problems, and although he did believe in mathematical Platonism, his reasons for this conviction were different, and he did not maintain that the incompleteness theorems alone establish Platonism. Thus Gödel believed in the first disjunct, that the human mind infinitely surpasses the power of any finite machine. Still, this conclusion of Gödel follows, as Gödel himself clearly explains, only if one denies, as does Gödel, the possibility of humanly unsolvable problems. It is not a necessary consequence of incompleteness theorems.
Now Gödel was, unlike the later advocates of the so-called Gödelian anti-mechanist argument, sensitive enough to admit that both mechanism and the alternative that there are humanly absolutely unsolvable problems are consistent with his incompleteness theorems. His fundamental reasons for disliking the latter alternative are much more philosophical. Gödel thought in a somewhat Kantian way that human reason would be fatally irrational if it asked questions it could not answer (for critical discussion, see Kreisel 1967; Boolos 1995; Raatikainen 2005).
As a reaction to Lucas' argument, but before the publication of Gödel's Gibbs Lecture, Paul Benacerraf (1967) put forward more qualified conclusions that interestingly resemble some ideas of Gödel. He argued that it is consistent with all the facts that I am indeed a Turing machine, but that I cannot ascertain which one. For some critical discussion, see Chihara 1972 and Hanson 1971.
6.5 Mysticism and the existence of God?
Sometimes quite fantastic conclusions are drawn from Gödel's theorems. It has been even suggested that Gödel's theorems, if not exactly prove, at least give strong support for mysticism or the existence of God. These interpretations seem to assume one or more misunderstandings which have already been discussed above: it is either assumed that Gödel provided an absolutely unprovable sentence, or that Gödel's theorems imply Platonism, or anti-mechanism, or both. "
-https://plato.stanford.edu/entries/go...
Elena wrote: "Probably not. But the best candidate for an "ultimate language for stating philosophical propositions with maximal clarity" would have to be the language that most closely approximates the working ..."What you want, I think, are logical languages.https://mw.lojban.org/papri/logical_l...
There is already something that approaches this:
http://www.ithkuil.net/
https://en.wikipedia.org/wiki/Ithkuil
https://www.newyorker.com/magazine/20...
Here is a good book that I think might be applicable to this discussion: https://www.goodreads.com/book/show/9...."Whether all human languages are fundamentally the same or different has been a subject of debate for ages. This problem has deep philosophical implications: If languages are all the same, it implies a fundamental commonality--and thus mutual intelligibility--of human thought.We are now on the verge of solving this problem. Using a twenty-year-old theory proposed by the world's greatest living linguist, Noam Chomsky, researchers have found that the similarities among languages are more profound than the differences. Languages whose grammars seem completely incompatible may in fact be structurally almost identical, except for a difference in one simple rule. The discovery of these rules and how they may vary promises to yield a linguistic equivalent of the Periodic Table of the Elements: a single framework by which we can understand the fundamental structure of all human language. This is a landmark breakthrough both within linguistics, which will herewith finally become a full-fledged science, and in our understanding of the human mind."
Zachary wrote: "Here is a good book that I think might be applicable to this discussion: https://www.goodreads.com/book/show/9...."Whether all human languages are fundamentally the same o..."
An interesting idea that I thought of this morning, could formal Logic be represented within a "Preiodic Table of [linguistic] Elements" a la Chomsky? Logic has its limits a la Kurt Gödel. Perhaps the above table of elements could account for and systematize this since human language can express illogical fuzzy abstract statements as well. Note: I am only beginning my study of Logic now, and I am just a layperson reading about linguistics. Anyway, the idea of formal Logic being a subset of a deeper more illogical, yet very structured, language is a fascinating idea to me.
For fuzzy statements ( e.g. When does a crack in a road become a pothole?If you keep removing grains of sand from a sand heap, when does it stop being a heap of sand?) we have fuzzy logic.
https://www.google.com/url?sa=t&s...-
"A philosophical language is any constructed language that is constructed from first principles, like a logical language, but may entail a strong claim of absolute perfection or transcendent or even mystical truth rather than satisfaction of pragmatic goals. Philosophical languages were popular in Early Modern times, partly motivated by the goal of recovering the lost Adamic or Divine language. The term ideal language is sometimes used near-synonymously, though more modern philosophical languages such as Toki Pona are less likely to involve such an exalted claim of perfection. It may be known as a language of pure ideology. The axioms and grammars of the languages together differ from commonly spoken languages today.
In most older philosophical languages, and some newer ones, words are constructed from a limited set of morphemes that are treated as "elemental" or fundamental. "Philosophical language" is sometimes used synonymously with "taxonomic language", though more recently there have been several conlangs constructed on philosophical principles which are not taxonomic. Vocabularies of oligosynthetic languages are made of compound words, which are coined from a small (theoretically minimal) set of morphemes; oligoisolating languages, such as Toki Pona, similarly use a limited set of root words but produce phrases which remain series of distinct words.
Láadan is designed to lexicalize and grammaticalize the concepts and distinctions important to women, based on muted group theory. Toki Pona is based on minimalistic simplicity, incorporating elements of Taoism.
A priori languages are constructed languages where the vocabulary is invented directly, rather than being derived from other existing languages (as with Esperanto or Ido). Philosophical languages are almost all a priori languages, but most a priori languages are not philosophical languages. For example, Quenya, Sindarin, and Klingon are all a priori but not philosophical languages: they are meant to seem like natural languages, even though they have no genetic relation to any natural languages.
History[edit]
Work on philosophical languages was pioneered by Francis Lodwick (A Common Writing, 1647; The Groundwork or Foundation laid (or So Intended) for the Framing of a New Perfect Language and a Universal Common Writing, 1652), Sir Thomas Urquhart (Logopandecteision, 1652), George Dalgarno (Ars signorum, 1661), and John Wilkins (An Essay towards a Real Character, and a Philosophical Language, 1668). Those were systems of hierarchical classification that were intended to result in both spoken and written expression. In 1855, English writer George Edmonds modified Wilkins' system, leaving its taxonomy intact, but changing the grammar, orthography and pronunciation of the language in an effort to make it easier to speak and to read.[1]
Gottfried Leibniz created lingua generalis (or lingua universalis) in 1678, aiming to create a lexicon of characters upon which the user might perform calculations that would yield true propositions automatically; as a side effect he developed binary calculus.[2]
These projects aimed not only to reduce or model grammar, but also to arrange all human knowledge into "characters" or hierarchies. This idea ultimately led to the Encyclopédie, in the Age of Enlightenment. Leibniz and the encyclopedists realized that it is impossible to organize human knowledge unequivocally as a tree, and so impossible to construct an a priori language based on such a classification of concepts. Under the entry Charactère, D'Alembert critically reviewed the projects of philosophical languages of the preceding century.
After the Encyclopédie, projects for a priori languages moved more and more to the fringe. Individual authors, typically unaware of the history of the idea, continued to propose taxonomic philosophical languages until the early 20th century (for example, Ro). More recent philosophical languages have usually moved away from taxonomic schemata, such as 21st century Ithkuil by John Quijada."