Category Archives: Other

Truth-uncertainty and meaning-uncertainty

Epistemic status: just a half-baked idea, which ought to be developed into something more complete, but since I’m probably not going to do that anytime soon I figured I’d publish it now just to get it out there.

Consider a statement such as (1) below.

(1) Cats are animals.

I’m used to interpreting statements such as (1) using a certain method which I’m going to call the “truth-functional method”. Its key characteristic is, as suggested by the name, that statements are supposed to be interpreted as truth functions, so that a hypothetical being which knew everything (had perfect information) would be able to assign a truth value—true or false—to every statement. There are two problems which prevent truth values being assigned straightforwardly to statements in practice.

The first is that nobody has perfect information. There is always some uncertainty of the sort which I’m going to call “truth-uncertainty”. Therefore, it’s often (or maybe even always) impossible to determine a statement’s truth value exactly. All one can do is have a “degree of belief” in the statement, though this degree of belief may be meaningfully said to be “close to truth” or “close to falsth1” or equally far from both. People disagree about how exactly degrees of belief should be thought about, but there’s a very influential school of thought (the Bayesian school of thought) which holds that degrees of belief are best thought about as probabilities, obeying the laws of probability theory. So, for a given statement and a given amount of available information, the goal for somebody practising the truth-functional method is to assign a degree of belief to the statement. At least inside the Bayesian school, there has been a lot of thought about how this process should work, so that truth-uncertainty is the relatively well-understood sort of uncertainty.

But there’s a second problem, which is that often (maybe even always) it’s unclear exactly what the statement means. To be more exact (the preceding sentence was an exemplification of itself), when you hear a statement, it’s often unclear exactly which truth function the statement is supposed to be interpreted as; and depended on which truth function it’s interpreted as, the degree of belief you assign to it will be different. This is the problem of meaning-uncertainty, and it seems to be rather less well-understood. Indeed, it’s probably not conventional to think about it as an uncertainty problem at all in the same way as truth-uncertainty. In the aforementioned scenario where you hear the statement carrying the meaning-uncertainty being made by somebody else, the typical reponse is to ask the statement-maker to clarify exactly what they mean (to operationalize, to use the technical term). There is of course an implicit assumption here that the statement-maker will always have a unique truth-function in their mind when they make their statement; meaning-uncertainty is a problem that exists only on the receiving end, due to imperfect linguistic encoding. If the statement-maker doesn’t have a unique truth function in mind, and they don’t care to invent one, then their statement is taken as content-free, and not engaged with.

I wonder if this is the right approach. My experience is that meaning-uncertainty exists not only on the recieving end, but also very much on the sending end too; I very often find myself saying things but not knowing quite what I would mean by them, but nevertheless feeling that they ought to be said, that making these statements does somehow contribute to the truth-seeking process. Now I could just be motivatedly deluded about the value of my utterances, but let’s run with the thought. One thing that makes me particularly inclined towards this stance is that sometimes I find myself resisting operationalizing my statements, like there’s something crucial being lost when I operationalize and restrict myself to just one truth function. If you draw the analogy with truth-uncertainty, operationalization is like just saying whether a statement is true or false, rather than giving the degree of belief. Now one of the great virtues of the Bayesian school of thought (although it would be shared by any similarly well-developed school of thought on what degrees of belief are exactly) is arguably that, by making it more clear exactly what degrees of belief are, it seems to make people a lot more comfortable with thinking about degrees of belief rather than just true vs. false, and thus dealing with truth-uncertainty. Perhaps, then, what’s needed is some sort of well-developed concept of “meaning distributions”, analogous to degrees of belief, that will allow everybody to get comfortable dealing with meaning-uncertainty. Or perhaps this analogy is a bad one; that’s a possibility.

Aside 1. Just as truth-uncertainty almost always exists to some degree, I’m fairly sure meaning-uncertainty almost always exists to some degree; operationalization is never entirely completely done. There’s a lot of meaning-uncertainty in statement (1), for example, and it doesn’t seem to completely go away no matter how much you operationalize.

Aside 2. The concept of meaning-uncertainty doesn’t seem to be as necessarily tied up with the truth-functional model to me as that of truth-uncertainty; one can imagine statements being modelled as some other sort of thing, but you’d still have to deal with exactly which example of the other sort of thing any given statement was, so there’d still be meaning-uncertainty of a sort. For example, even if you don’t see ought-statements as truth-functional, as opposed to is-statements, you can still talk about the meaning-uncertainty of an ought-statement, if not its truth-uncertainty.

Aside 3. Another way of dealing with meaning-uncertainty might be to go around the problem, and interpret statements using something other than the truth-functional method.

Footnotes

^ I’m inventing this word by analogy with “truth” because I get fed up with always having to decide whether to use “falsehood” or “falsity”.

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Selections from Tumblr

I have a Tumblr blog which I use for writing short-form things that aren’t necessarily of any lasting value. But occasionally things do end up there that might be worth reading, so I intend to make an organized list of links to Tumblr posts that might be interesting to readers of this blog every year or so. The last time I did this was in December 2015 (here on WordPress and here on Tumblr), and I have been posting on Tumblr at a higher rate since then, so the list in this post is rather long, and I’ve organized it into subsections to make it more manageable. Only posts from December 2015 are included; for earlier posts, see the earlier lists.

Linguistics

Theoretical linguistics

  1. On where my interests lie in linguistics
  2. On some nonsense about “recursion”
  3. A defense of Chomsky

Phonetics and phonology

  1. On homophone-substitution errors in writing
  2. Nonce phonemes (phonemes that only appear in one morpheme) in Mako, Latin, Bintulu and Amuzgo
  3. On random word generation for conlanging
  4. On learning to pronounce foreign sounds
  5. On the alterability of idiolect phonology
  6. On liaison phenomena in languages other than French (more)
  7. On aspiration
  8. On breathy voice and voiced aspiration
  9. On word-initial sonorant-obstruent clusters
  10. On Mandarin tones

Morphology and syntax

  1. On the isolating-agglutinative-fusional cycle (more)
  2. On weather verbs
  3. On case-marking prefixes
  4. On verbal argument indexing
  5. On inflecting nouns for person (more)
  6. On marking the positive rather than the negative
  7. On overt coding of animacy

Semantics

  1. On presupposition accommodation in St’át’imcets
  2. On mereologies (prompted by this)
  3. On the denotation of plural nouns (more, yet more)
  4. On affective adpositions

English phonology and grammar

  1. On grammatical gender in English
  2. On the pronunciation of television
  3. On checked vowels and yeah
  4. On the pronunciation of err
  5. On the pronunciation of one
  6. On contraction of let us
  7. On the superiority of northern English accents
  8. On final st-reduction in the Caribbean
  9. My pronunciation of anxiety
  10. On breaking before /l/
  11. On circumstances in which contraction is impossible (more, more)
  12. On double /t/ in eighteen
  13. On /k/ in length and /t/ in prince
  14. A complicated English syntax question to do with possessive NPs and number agreement
  15. On smew and English phonotactics
  16. On not all and all … not
  17. On weird pronunciations of interjections
  18. On English dual pronouns (more)
  19. My English spelling reform proposal, and various anonymous message-sender’s proposals: 1, 2, 3, amusing follow-up
  20. On reduced vowels in my accent of English
  21. On English’s one geminate consonant
  22. Tense and lax short a in American English
  23. On the most distinctive characteristic of American English
  24. A discussion on the pronunciation of English short a
  25. On the English voiced and voiceless dental fricatives

Historical linguistics

  1. On the evolution of the French reflexive
  2. On a possible Hurro-Urartian-Etruscan clade
  3. On the grammaticalization of pronouns as copulas (more)
  4. On the weirdness of the Proto-Indo-European stop system
  5. On the early development of the Indo-Aryan languages
  6. On fronting of postalveolar sibilants
  7. On fricativization of voiceless unaspirated stops (more)
  8. On regular sound change’s capability to produce apparent suppletion
  9. A discussion on various Proto-Indo-European topics
  10. On metathesis of clusters with sibilants
  11. On Lydian (more)
  12. On the conditioning of changes in vowel height
  13. On the Proto-Indo-European velar series
  14. On possible unidirectionality of OV to VO word order shifts (more, yet more)
  15. On resources on Iranian historical phonology
  16. On dl variation in Latin
  17. On the existence of Proto-Anatolian

English historical phonology

  1. On irregularity in English historical phonology
  2. On it’s and ’tis
  3. On there being no /t/ in the word moisten
  4. On the digraph wh pronounced /h/ in English

Etymology

  1. On Geordie
  2. On Latin trahere
  3. English place names including OE wicga ‘beetle’ as an element
  4. On hang (erratum)
  5. On cuckold and cuckoo (more)
  6. On sibling (more)
  7. On cognacy of ‘food’ and ‘corpse’
  8. On prince
  9. Obscure English words beginning with gn- (more)
  10. On ostrich
  11. On the alleged cognacy of child with a word for ‘vulva’
  12. The meaning of race
  13. On the city Ur and the prefix ur-

Miscellaneous

  1. On language’s untidiness
  2. On the femininity and masculinity of linguistic varieties
  3. On sign languages interacting with spoken languages
  4. The lewdest language
  5. On linguistic prescriptivism

Mathematics

  1. The pumping lemma as a statement about integers
  2. On continued fractions
  3. A theorem on rational approximation
  4. On non-intersective adjectives in mathematical terminology
  5. On Big-O and little-o notation
  6. Why you can’t integrate 1/x from -1 to 1
  7. On bets and probabilities
  8. On Riemann-Stieltjes integration by parts
  9. On dividing by zero
  10. On two meanings of ‘the’ in mathematical writing
  11. On a binomial coefficient identity
  12. On continuous entropy
  13. On generating terrain

Sociology and anthropology

  1. On sacrifice
  2. “High gods” in various societies
  3. A defense of Jared Diamond
  4. On the Lengua’s conceptions of personality (not my own writing)
  5. On the origin of religion
  6. On agnosticism/atheism in ancient India (not my own writing)
  7. On the development of kinship systems
  8. The secret girdles of Ainu women
  9. On Dene-Yeniseian and the settlement of the Americas
  10. On lactase persistence
  11. On the Ashvamedha (more)
  12. On the Solubba
  13. On “guess culture”

Zoology

  1. The curious story of the inquisitive shrew-mole and roving economist Hayden Castagno
  2. On the Orkney vole (more)
  3. Comparison of the wild mammal fauna of Britain and America (plus responses to replies: 1, 2, 3, 4)

Philosophy

  1. On human nature and morality
  2. On Gongsun Long’s argument that people have three ears

Politics

  1. My (wrong) prediction on the EU referendum
  2. On the horribleness of American universities
  3. On the acceptability of not voting
  4. On Labor, the Conversatives and the Literal Democrats
  5. On the House of Lords
  6. Highlights from Wikipedia’s list of incidents of grave disorder in the House of Commons
  7. On British and European identity (more)

History

  1. On sea silk
  2. List of phrases of the form numeral-noun in Chinese history
  3. On Robert Tombs’ The English and their History
  4. YouTube videos on historical figures or events with Coldplay’s “Viva La Vida” as the background music

Art and literature

  1. On the meaning of songs
  2. On surrealism in art
  3. On V. S. Naipaul

Personal history

  1. On religious education in the UK
  2. On my local identity
  3. Dreams: 1, 2, 3, 4, 5
  4. On memories of dreams
  5. On historical events in my lifetime
  6. An important life update
  7. What I learnt from school history classes

Miscellaneous

  1. German folktales: 1, 2 (reply 1, reply 2), 3
  2. Tang Yang’s advice to the Song Emperor
  3. On dreams (notes from a lecture)
  4. On an interestingly bad joke
  5. On “anischerality”