Clear Language, Clear Mind

August 25, 2011

Example of how one’s language influences one’s thinking: Calculating with different bases in math

Filed under: Language — Tags: , , , — Emil O. W. Kirkegaard @ 18:23

Read this exchange.

Calculating in non-base 10 is so very hard, even for bright individuals. However, it has not always been like this.

I think that I will rite a computer program (in free pascal) that can calculate different bases, just to train me to think in a non-standard way.

December 5, 2009

Quote: Archibald A. Hill (maybe)

Filed under: Language — Tags: , , , — Emil O. W. Kirkegaard @ 09:14

“A speaker of the language should be able to pronounce correctly any sequence of letters that he may meet, even if they were previously unknown, and secondarily, to be able to spell any phonemic sequence, again even if previously unknown.” -Archibald A. Hill, distinguished U.S. linguist.

I have not been able to confirm the source. A google search reveals only two pages that mention the quote. Even if it is a misquote, is it still a good principle.

Worth reading: Mark Twain, “The Awful German Language”

Filed under: Uncategorized — Tags: , , , , — Emil O. W. Kirkegaard @ 08:11

This essay on the german language is definitely worth reading. Especially if one has ever taken a german class as I recently have.

I found the text here. I made a nice pdf version Mark Twain, The Awful German Language.

November 17, 2009

“Stop raping language!”

Filed under: Uncategorized — Tags: , , — Emil O. W. Kirkegaard @ 16:33

I love when people use the phrase “Stop raping language!”. It’s a bloody inconsistent performative.

October 28, 2009

Semantic Analysis and meaning

Filed under: Language — Tags: , , , , , , , — Emil O. W. Kirkegaard @ 22:53

Again I’m quoting Paul Ziff’s Semantic Analysis:

41. […]

Consequently, if my contention about meaning is correct, then the first ‘do’ in ‘Please do not do it!’, unlike the second ‘do’, does not have meaning. This is testified to by the fact that generally the first ‘do’ in ‘Please do not do it!’, unlike the second ‘do’, will not admit of being stressed. Thus ‘Please do not do it!’ unlike ‘Please do not do it!’ is somewhat odd. Again, notice that the same is true of ‘to’ and ‘through’ in ‘I want to go through Istanbul.’. There is nothing odd about ‘I want to go through Istanbul.’ but ‘I want to to go through Istanbul.’ is generally quite odd. And this should not be surprising: if an element does not have meaning in an utterance, stressing the element is not likely to be, and indeed can hardly be, significant.

(There is a case, however, in which the ‘to’ in question will bear a stress. If I say ‘I want to go through Istanbul.’ and someone says ‘You want not to through Intanbul?’, I may reply ‘I want to go through Istanbul.’. An explanation of this is not hard to find. If I say ‘I want him to go.’ and someone says ‘You want them to go?’, I may reply ‘I want him to go.’, stressing the word after the verb for that was the point at which the utterance was misunderstood. But if I say ‘I want to go through Istanbul.’ and someone says ‘You want not to go through Istanbul.’, the confusion is owning to the insertion of ‘not’ after the verb. Thus in reply one is likely to stress whatever occurs over the segment immediately after the verb. Thus not ‘to’ but the stress it bears is significant in ‘I want to go through Istanbul.’: the stress contrasts with ‘not’ in the previous sentence.)

Meaning and meaningful words in sentences

Why do I quote this passage? Because I sometimes suggest this thesis in discussions:

1. A sentence is meaningful ⇔ Every word in that sentence is meaningful.1

This might seem obvious to some and it seems interesting to me. There is an, perhaps, obvious type of possible counter-example too. Here are a couple:

2a. kjjd is not meaningful.

2b. The word “kjjd” is not meaningful.

(2a) appears to be a counter-example to (1) since there is a word2 in it that is not meaningful. However, (2a) is an unclear sentence and perhaps grammatically incorrect.3 A more refined version is (2b) where it is clear that the sentence is about some word. There are a couple of solutions or explanations that spring to my mind about this.

One, one could see “the word “kjjd”” as a noun phrase that refers to the word “kjjd”. This seems unproblematic to me.

Two, one could try to limit (1) to some particular subset of sentences. One idea is to exclude sentences that are about words or phrases (meta-language). Though this seems excessive to me.

Three, one could exclude words that start and end with quotation marks (“) or whatever character is used to mark words or phrases. (Some people, like Ziff above, use apostrophes (‘).)

I favor the noun phrase theory or some similar theory. If that theory is true, then sentences like (2a) are not a problem for my thesis, that is, (1).

Meaningless words in meaningful sentences without metalanguage

In the quoted paragraph Ziff argues that some words in some meaningful sentences are not meaningful. His two examples are:

3a. Please do not do it!

3b. I want to go through Istanbul.

I think that it is uncontroversial whether these sentences are meaningful, they clearly are.4

Ziff thinks that:

4. A word in a sentence does not admit of being stressed without it being odd ⇒ That word does not have meaning.

This seems somewhat plausible and it is a problem for my thesis, that is, (1). Since (1) implies that all words in (3a) and in (3b) are meaningful but (4) implies that there is at least one word in (3a) and in (3b) that is not meaningful. How might one resolve this? Obviously one can simply deny that Ziff’s claim is true though it does seem rather intuitive to me, and I guess to many other people too.

Tokens and types

One might try to fix the problem by introducing the token-type distinction.5 Is (1) about types or tokens?:

1a. A sentence is meaningful ⇔ Every word token in that sentence is meaningful.

1b. A sentence is meaningful ⇔ Every word type in that sentence is meaningful.

Is (4) about tokens or types?:

4a. A word in a sentence does not admit of being stressed without it being odd ⇒ That word token does not have meaning.

4b. A word in a sentence does not admit of being stressed without it being odd ⇒ That word type does not have meaning.

The relationships between (1)’s and (4)’s are less clear. Let’s examine them in turn.

One, (1a) and (4a)

This appears to be the same situation as before.

Two, (1b) and (4a)

(1b) seems true to me but it is rather unclear what it means to say that a word type is meaningful. They do not seem inconsistent; The word type “to” is meaningful in (3b) and there is according to (4a) both a meaningful and a meaningless word token of “to” in that sentence. It is curious that some type can be meaningful yet tokens can be both meaningful and meaningless. (In the same language of course.)

Three, (1a) and (4b)

(4b) is false. Consider examples similar to the (3)’s, (4b) materially implies that the word type “to” and the word type “do” is both meaningful and meaningful. Contradiction.

Four, (1b) and (4b)

This is even worse than the case above. (4b) is false for the same reason as above, and (1b) materially implies not-(4b).

The type-token distinction did not help much, even though it clarified some things. (4b) is to be avoided, and (1a) and (1b) are interesting and problematic.

Meaningful phrases

An idea is to reject (1) but accept some similar thesis:

1c. A sentence is meaningful ⇔ Every word token in that sentence is meaningful or is part of a meaningful phrase token in that sentence.

This seems more plausible than the other (1)’s so far to me. It also seems consistent with Ziff’s examples since the meaningless “to” tokens are part of a meaningful phrase token “want to”.

It also avoids the question of what it means to say that a type is meaningful.

Stress and word-parts

Notice that in the above paragraph that it is not odd to stress parts of words. (I stressed “less” and “ful”. “Less” functions as a logical negation in this case and many others.) Is this an indication that word parts are sometimes meaningful too? It doesn’t follow from (4)’s but if we created general principle out of (4):

4c. A language part is able to be stressed with it being odd. ⇒ That language part is meaningful.

(4c) materially implies that word parts (morphemes) are sometimes meaningful too.

Chomskyan counter-examples

And yet, there are still other counter-examples (1c). Consider this famous sentence:

5. Colorless green ideas sleep furiously.6

(5) is clearly a counter-example to (1c) since all the words in this sentence are meaningful, and yet the sentence itself is meaningless. Perhaps another thesis similar to (1) is needed:

1d. A sentence is meaningful ⇔ Every word in that sentence is meaningful or is part of a meaningful phrase in that sentence, and all words are meaningful in the relation they are stand in or are part of a phrase that is in a meaningful relation.

This seems to effectively deal with sentences similar to (5).


1“⇔” means is logically with.

2I use the word “word “ here in a less strict sense. It is sometimes defined like “(linguistics) A distinct unit of language (sounds in speech or written letters) with a particular meaning, composed of one or more morphemes, and also of one or more phonemes that determine its sound pattern.” By “word” here I mean something like a string of latin characters (without spaces). The strict definition above is taken from Wiktionary.

3It seems unusually hard to judge whether it is grammatically incorrect or not in this case.

4Though it is curious how to best establish that a specific sentence is meaningful or meaningless in a specific language. I suppose that if the vast majority of the native speakers of language L understands sentence S, then S is meaningful in L. But there are problems with this. I will not discuss them in this essay.

5See Wikipedia for an explanation. but see SEP’s article on it for a more thorough explanation

October 20, 2009

Quote: Paul Ziff

Filed under: Language — Tags: , , , , — Emil O. W. Kirkegaard @ 18:07

[Discussing the type/token distinction or ambiguity]

“I shall not in general try to eliminate these ambiguities by explicitly stating which sense is intended. Sometimes both senses are intended, sometimes not. In general the context is sufficient to indicate what is meant. I shall be more specific only when there is need to be so; if everything had to be spelled out, nothing could be said.” Paul Ziff, Semantic Analysis, §14, 1960.

I am especially happy for the last sentence.

October 19, 2009

Negating sentences in english

Filed under: Language,Logic — Tags: , , , , , , , — Emil O. W. Kirkegaard @ 23:01


I invent and explore a terminology about degrees of sentences, I explore how to negate sentences and sentence parts in english, I distinguish between verbs that can be used in sup-sentence parts and verbs that cannot, I discuss some problems with the verb “ought”, and lastly I explore the relationship between this terminology and predicate logic.

Negating sentences in english (PDF, 15 pages)

September 28, 2009

Language, the modal fallacy and the symbolic representation of a conditional

Filed under: Language — Tags: , , , , — Emil O. W. Kirkegaard @ 15:22

“[W]hat follows from a true premiss must be true” (The Problems of Philosophy, p. 60, link)

Wrote Russell as an example of a principle of logic that is more self-evident than the inductive principle. If we were to formalize this we would perhaps write it like this:

E1. □[([∀P][Q∧Q⇒P])→P]1

Or perhaps just just in propositional logic:

E2. □(P→Q) where “P” means P is true and P implies Q.

As the reader of my blog should know by now, the modal fallacy consists of trusting language and placing the modal operator of necessity in the consequence instead of before the conditional:

E3. P→□Q

However we could also put the modal operator somewhere else in our formalization:

E5. P□→Q

Operators solely ‘work on’ whatever is to the right of them.2 Thus the modal operator in (E5) works on the material conditional and not the proposition to the left of it. Similarly in (E2) the modal operator works on the parentheses-set which is treated as a single entity.

(E5) is closer to normal english (and danish) than (E2) which we can express in normal english like this:

E4. Necessarily, if P follows from Q and Q is true, then P is true.

Consider the sentence:

E5. If P follows from Q and Q is true, then P must be true.

(E5) is a reformulation of (E2). (E5) is worded like it would be by a normal english speaking person. In (E5) it may seem as though the modal operator is intended to work on the consequent. Indeed some people think this and commit the modal fallacy.

However the modal operator may also be thought of as working on the second part of the “if, then” clause, that is, the “then” part. The only problem with this interpretation that I know of, is that it makes the operator work on something that is to the left of it instead of to the right of it: Because “then” is to the left of “must” in (E5).


1Ignoring the complexities of bivalance.

2Monadic operators. Not dyadic operators like implication, consistency etc.

July 24, 2009

Language, truth makers and truth guides

Filed under: Language — Tags: , , , , , , , — Emil O. W. Kirkegaard @ 20:33

The issue is what the truth maker is of a certain type (subset), L, of propositions. A proposition belongs to L iff it has the form “X is the correct way to spell the word.”.

Truth makers and truth guides

A truth maker is what makes something true. ‘makes’ here is a semantic relation. What makes the proposition ‘it is raining outside’ true is the fact that it is raining outside. Another way to put it is to ask under which conditions the proposition ‘It is raining outside’ is true. And the answer is exactly when it is raining outside. Such a condition is called the truth condition.

A truth guide is a way to discover what the truth is. Asking your math teacher what the solution to an equation is, is probably a good way to discover the truth. However it is not that the teacher thinks the answer is x that makes it true that the answer is x. And if the teacher is not infallible, and no teachers are, then he might be wrong. It may be hard to distinguish between an infallible truth guide and the truth maker but we need not concern ourselves with this since it is never the case that a truth guide in infallible.

Language claims about spelling

I’m trying to discover what the truth maker is of L-type propositions. So far a number of possibilities have been suggested to me:

  1. How the majority of the general population uses the word.
  2. What the majority of the general population thinks is the correct way to spell the word.
  3. What some special dictionary says is the correct way to spell it.
  4. What the majority of dictionaries say is the correct way to spell it.
  5. How the majority of some subset of the general population uses the word.
    1. How the majority of fluent, educated speakers use the word.
    2. How the majority of fluent, educated speakers and serious writers use the word.
    3. How the majority of serious writers use the word.

The list goes on but I believe the above captures some of the good initial guesses. What makes it so hard to determine is, I think, that even though there is only one truth maker all the possibilities function as truth guides.

Analyzing (1) and (2)

(1) seemed like a good proposal to me, that is, for all I knew it might be true. However when analyzed closer it becomes clear that (1) is not a good proposal at all. All we have to do to see this is to ask ourselves what ‘general population’ we’re talking about. Suppose we’re talking about the  danish language. The general population seems to be danes. But then how about other people that can speak danish? Danish is taught in schools in other countries like Greenland. And how about danes that can’t speak danish? Presumably some people have managed to become citizens of Denmark without being able to speak danish. Do they belong to the general population? It seems not. The general population then is not a good idea at all because it is unclear what this refers to, and if it refers to speakers of danish, then it is equivalent to (5).

Similarly (2) becomes an extended version of some (5)-type proposal.

Analyzing (3) and (4)

(3) also seemed a good proposal to me but again when analyzed closer it loses its status. When I proposed the theory Pyrrho wrote:

“You also have the oddity of there being, according to your theory, no right way to speak or write before dictionaries were invented, which is very curious indeed. Was there not a difference between fluent speakers of English and those who were not before the invention of dictionaries? Was there not a difference between being very literate and not so literate before the invention of dictionaries?”[1]

That is a curious implication indeed. One way to fix it is to say that the truth maker of L-type propositions changed some time after dictionaries were invented. This is obviously an ad hoc assertion and makes the theory less simple.

Another oddity arises for (3), as Pyrrho writes:

“Yet another oddity of saying a particular dictionary is the “truth maker” is that it would mean that there could be no such thing as a misprint, as it being in the dictionary, according to that theory, is what makes it true. It is a very odd theory that postulates the impossibility of a misprint.”[2]

Indeed that is a very odd implication. Clearly it is not impossible to misprint and thus (3) is false.

Analyzing (5)

One obvious problem is to discover what the necessary and sufficient conditions are for a given person to belong to the group of people’s who makes L-type propositions true.

A ‘Fluent’ speaker means a speaker who is “able to speak a language accurately and confidently.”[3] It is unclear why fluent speakers have anything to do with L-type propositions since they do not necessarily write anything. Most people do not write much but speak a lot and most speak fluently too. Why does it matter how they spell a particular word when they rarely write it?

It is unclear what ‘educated’ refers to in this case. Educated about what? The language? Are we talking about a formal education or will an informal doo? Most of one’s first language is probably not learned via any formal education but by mimicking parents and other people around one. ‘Educated’ is too vague to be a useful condition.

It is also unclear what a ‘serious writer’ is. Perhaps it’s just someone who writes a lot. It would be odd if only how a minority of writers wrote was the truth maker. How does one decide if the writer is serious in that sense? It seems that disposing of the unclear ‘serious’ is a good idea and just settle on ‘mere’ writers of the language.

Another trouble is how to deal with the majority thing. Suppose that there are n writers that write a particular word in one way and there are n writers that write the same word another way. Suppose further that n+n is equal to the whole population of writers. Which way is the correct way? There seems to be no answer to that question. Indeed the best idea seems to be to reject the question and say that there are two correct ways. Suppose we accept that. Again it can be asked what the correct way to write a particular word is if the group of writers is exactly divided into three groups. Again one might answer that there are three correct ways. However if we continue this way we will reach the conclusion that if all writers wrote it in their own way, they would all be correct. This is a curious implication.

However in practice this is not a problem since it is never the case that writers are that divided. In reality is suffices to say that if writers are divided somewhat equal into, say, five groups, then all these are acceptable and that they ought to find a particular way to spell the word to avoid confusion.

One thing remains to discuss about (5) and that is whether it is how writers use the word or how they think it is spelled correctly that is the truth maker. I know of no way to decide this question since they correlate so much: Writers write the way they think is correct and writers think the way they write is correct. It doesn’t seem like an important question to settle this.


The majority of dictionaries theory (4) and the majority of writers theory (5d) seem to be equal in explanatory power but since the writer theory is more simple, then we ought to prefer it.




September 15, 2008

Nonsensical English

Filed under: Humor,Language — Tags: , — Emil O. W. Kirkegaard @ 22:42

Imagine that John complains to Peter that he did not sleep well last night. He then says that he will attempt to sleep weller the next time. This sentence fails.

Imagine that John complains to Peter that he did not sleep good last night. He then says that he will attempt to sleep gooder the next time. This sentence also fails.

Where is my simplified English language? I have to do a project about it later.

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