Clear Language, Clear Mind

Wiki. Source.

Kennethamy:

Well, here is an example: in English we use the terms, “believe” and “know” very differently, from which we can infer that there is a difference between “believing” and “knowing”. For instance, we say, “Joe believes that La Paz is the capital of Ecuador, but he is wrong”. We never say, “Joe knows that La Paz is the capital of Ecuador, but he is wrong”. However, we have to be cautious. There are often extraneous circumstances which govern what we say so that if we attend only to what we say, will mislead us. A good example is that we do not say “It is raining, but I do not believe it is raining”. But that cannot show that it cannot be true that it is raining but I not believe it is raining. (Moore’s Paradox). Here is an interesting example of a sentence that may be true, but which, for extraneous factors not having to do with its semantics (meaning) it would make no sense to say.

Emil:

What is funny about “It is raining, but I do not believe it is raining” is that it is equivalent with “It is raining and Moore does not believe that it rains” (since “I” refers to Moore). However the latter one is not viewed as paradoxical. The difference seems to be that it is an implicit assumption in most communication contexts that the utterer (here Moore) believes what he claims. With that assumption in mind, we get the contradiction: It is raining, Moore does not believe that it is raining and (from the assumption and the utterance) Moore believes that it is raining. Thus, Moore believes and does not believe that it is raining. Voila!

Kennethamy:

(since “I” refers to Moore).

Why do you think that? Do you think that when Descartes wrote, “I think, therefore I exist” he was referring to Descartes? He was referring to no one in particular. The first person personal pronoun there is a very impersonal personal pronoun, just as when I say something like, “If you believe that the claim that a miracle has occurred is justifiable, then you are wrong”need not be addressed to anyone in particular. The “you” there just means the impersonal, “one”. (As in the French, “on” and the German, “Man”). But your explanation of the paradox is right. A person who makes a claim is assumed either to believe or know what he claims. (In fact, Moore pointed that out in a different context). But that fact about conversation is not about the semantics of what the person says, it is about the pragmatics of what he said. It does not seem to me that the person who says, “It is raining and I don’t believe it” is contradicting himself (and you did not say he was). But, as you said, from the premises that the person who says it is raining but that he does not believe it, together with the premise that he does believe it is raining, a contradiction can be derived. But that, to repeat, is no reason to think that the person is contradicting himself.

Emil:

Why do you think that?

I never heard of impersonal “I”‘s before. The pronoun “I” refers to the speaker, you defined it yourself in another thread.

Do you think that when Descartes wrote, “I think, therefore I exist” he was referring to Descartes?

Yes.

He was referring to no one in particular.

I disagree. I think he was referring to himself. But alas, the justification works equally well no matter who uses the argument. That does not imply that the “I” is impersonal.

The first person personal pronoun there is a very impersonal personal pronoun, just as when I say something like, “If you believe that the claim that a miracle has occurred is justifiable, then you are wrong”need not be addressed to anyone in particular. The “you” there just means the impersonal, “one”. (As in the French, “on” and the German, “Man”).

Or the danish “man”, (The german one isn’t capitalized, since “man” isn’t a noun but “Mann” is (means man). To avoid confusion with impersonal and personal pronouns in english, I try to always use “one” but it slips from time to time. You know, the bewitchment of our language.

But, as you said, from the premises that the person who says it is raining but that he does not believe it, together with the premise that he does believe it is raining, a contradiction can be derived. But that, to repeat, is no reason to think that the person is contradicting himself.

Right. Here is a more formal argument for the ‘contradiction’.

1. Moore utters “It is raining but I don’t believe it.”

2. For any person and any utterance, if the utterance is uttered in a truthful context, then the person believes all the propositions expressed by his utterance.

3. “It is raining but I don’t believe it.” was uttered in a truthful context.

Thus, 4. Moore believes all the propositions expressed by this utterance. (2, 3)

5. The propositions expressed by “It is raining but I don’t believe it.” are {that it is raining, that Moore doesn’t believe that it is raining}.

Thus, 6. Moore believes that it is raining. (4, 5)

Thus, 7. Moore believes that Moore doesn’t believe that it is raining. (4, 5)

This isn’t actually a contradiction, but it is somewhat paradoxical in a looser sense.

If we include the utterance (re-worded) as a premise. A contradiction follows:

8. It is raining and Moore doesn’t believe that it is raining.

Thus, 9. Moore doesn’t believe that it is raining. (8)

Thus, 10. Moore doesn’t believe that it is raining and Moore believes that it is raining. (6, 9)

Give it a read. It is divided into 4 parts:

My Take on the Liar Paradox (Part I of IV)
My Take on the Liar Paradox (Part II of IV)
My Take on the Liar Paradox (Part III of IV)
My Take on the Liar Paradox (Part IV of IV)
All four articles combine to a total of about 8,000 words, so it will not take long for a dedicated reader to read through it.

In an earlier essay I mentioned that that meaninglessness is contagious with respect to sentences. One can pretty easily formulate the principle in normal english – if a sentence is meaningless, then so is any more complex sentence of which it is a part of. To get a proper, formal formulation of this we may simply think of the rules in logic systems used to form well-formed formulas (=wff’s) and then formulate some similar principles for the meaninglessness of sentences. Here’s what I have in mind:

Negation. For all sentences, iff it is not the case that a sentence is meaningful, then it is not the case that the negation of that sentence is meaningful.

(∀S)(¬M(S)↔¬M(¬S)

Conjunction part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the conjunction of that sentence with another sentence is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S∧Z)¹

Disjunction part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the disjunction of that sentence with another sentence is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S∨Z)

Implication/conditional part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the implication of the first sentence to the second is meaningful, and it is not the case that the implication of the second sentence to the first is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S→Z)∧¬M(Z→S))

Bi-implication/bi-conditional part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the bi-implication of the first sentence to the second is meaningful, and it is not the case that the bi-implication of the second sentence to the first is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S↔Z)∧¬M(Z↔S))

This should cover propositional logic. It is left to the reader can invent the relevant principles for modal logics and predicate logic.

Notes

By sentence theory I just mean a theory of truth carriers that implies that some sentences are true or some are false. Not necessarily a monist sentence theory (=theory that implies that sentences are the only kind of truth carriers) or a theory of sentences as primary truth carriers (=theory that implies that sentences are the primary truth carriers). For more about these terms, see my earlier writings on the subject.

Anyway, I read the newest post on my favorite logic blog (Blog&~Blog). It dealt with the sentences which I have given incredibly clever names (in footnotes):

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is true.

NMNT.¹ (∀S)(¬M(S)→T(S))

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is false.

NMNF.² (∀S)(¬M(S)→F(S))

With the obvious interpretation keys.

This seems like plausible sentences to many when faced with sentences such as the Chomsky:

C. Colorless green ideas sleep furiously.

Which Ben, btw, got wrong as he forgot the first word.

Let’s also agree that:

1. It is not the case that C is meaningful.

¬M(C)

However, this along with some other sentences is inconsistent (=implies a contradiction). First sentence bivalence:

SB.³ For all sentences, it is either true or it is false.

(∀S)(T(S)∨F(S))

The contradiction is easy to derive here:

2. ¬T(C) [from 1, NMNT, MP]

3. ¬F(C) [from 1, NMNF, MP]

4. T(C) [from 3, SB, DS]

5. T(C) ∧¬T(C) [from 2, 4, conj.]

Contradiction! So this doesn’t work. Here I told Ben (author of the blog) that I would drop SB.⁴ However that apparently doesn’t work either.

Say hi to the T-schema, or the semantic theory of truth:

TS1. For all sentences, iff it is true, then it is the case.

(∀S)(T(S)↔S)

TS2. For all sentences, iff it is false, then it is not the case.

(∀S)(F(S)↔¬S)

Now these are obvious to most people. Not something is that plausible to deny unless the alternatives are really bad. However from these one can get their contra-positional versions:

TS1-CP. For all sentences, iff it is not the case, then it is not the case that it is true.

(∀S)(¬S↔¬T(S))

TS2-CP. For all sentences, iff it is not the case that it is not the case, then it is not the case that it is false.

(∀S)(¬¬S↔¬F(S))

And from these, we can derive their converses (and we can do that because these are bi-conditionals that can be conversed without problems). Do the same for TS1 and TS2:

TS1-CP-C. For all sentences, iff it is not the case that it is true, then it is not the case.

(∀S)(¬T(S)↔¬S)

TS2-CP-C. For all sentences, iff it is not the case that it is false, then it is not the case that it is not the case

(∀S)(¬F(S)↔¬¬S)

TS1-C. For all sentences, iff it is the case, then it is true.

(∀S)(S↔T(S))

TS2-C. For all sentences, iff it is not the case, then it is false.

(∀S)(¬S↔F(S))

And these actually need to be simplified too before I can use them, but I’m too lazy to do that, so I’ll just add a simp. step. No big deal.

Now:

6. ¬C [from 2, TS1-CP-C, simp., MP]

7. F(C) [from 6, TS2-C, simp., MP]

8. F(C)∧¬F(C) [from 3, 7, conj.]

Contradiction. And I didn’t need to use double negation to get it though one could do that too with TS2-CP-C, and of course I didn’t use SB either. It seems to me that this is terrible and the best way out of the contradiction is to deny NMNT and NMNF, and believe instead that sentences like C cannot even meaningfully be said to be true or false, nor can they meaningfully be said to be not true or not false. Any complex sentence with a meaningless part is itself meaningless.⁵

There is a tendency for people to conflate denial of properties with the denial of the meaningful application of these properties to things. This seems to be the case here too. So instead of saying things like:

Meaningless sentences are not true.

Cars are not true.

We should say things like:

Meaningless sentences cannot meaningfully be said to be true.

Cars cannot meaningfully be said to be not true.

Maybe some people sometimes, confusingly, use the first versions as a shorthand for the second. If they do and really mean what the second ones mean, then they should use them.

In a web of beliefs approach one could set up an inconsistent set of sentences and see which one is the least plausible. I figure that my readers can do that in their heads without I needing to write it out in this case. Maybe the readers will agree with me that NMNT and NMNF are the least plausible ones in the set.

Notes

For some reason some people get these wrong.

And so on for a great deal of other concrete entities. However for abstract objects it becomes more difficult to translate into believe-that phrases. Consider:

I believe in democracy

What are we to translate this into? Some ideas:

I believe that democracy is good

I believe that democracy is the best

Other examples include:

I believe in freedom of speech

I believe in myself

I believe in you (this does not mean anything similar to the above even though the phrases are quite similar, the object of belief is a personal pronoun)

I believe in love

Is it worth reading if you are interested in meaningfulness, contradictions, names and ontological arguments.

W.v.O. Quine – On what there is

Consider the phrase in the title in this paragraph:

“each has a thumb, followed in order by four fingers: the index (or forefinger), the middle, the third, and the so-called little finger.” (Swartz, Beyond Experience, pp. 204-205)

What are the conditions for its correct use? (Correct use is how it is commonly used by fluent speakers of english.) It is funny that I, as a fluent speaker of english, asks this question since I can and do use the phrase correctly. It is often the case that we can use a word correctly without being consciously aware of the conditions of its use. Some people call this usage intuitive. One could speculate that the pattern mechanisms in the brain that makes it possible to use such phrases correctly do not share their information with the consciousness.

As for the above phrase, I propose a theory for its use: A necessary and sufficient condition for its use is that the speaker/writer considers the name mentioned after the phrase questionable in a broad sense. In relation to the example above, presumably Swartz thought when writing that paragraph that that name of the little finger is somehow questionable. Perhaps little finger is a slang name or was at the time that book was written and Swartz preferred the non-slang name. I have not found a counter-example to this theory yet.

From Beyond Experience, p. 157:

“The term “ things ” here is meant in a very broad, inclusive sense. On this interpretation,  “ things ” will include, of course, the most familiar things of all, namely physical objects, but will include as well all sorts of nonphysical things, e.g. minds (if indeed they are nonphysical), supernatural beings, numbers, classes, colors, pains, mathematical theorems, places, and events. In short, “ things ” is being used here as a general name for any sort of thing (!) whatsoever that can be named or described.”

This is strikingly similar to what I have earlier written about the onniword “thing”.

“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.

“In sharp contrast, men more than women tended to rate egoistic dominant acts as more socially desirable, including “Managing to get one’s own way,” “Flattering to get one’s own way,” “Complaining about having to do a favor for someone,” “Blaming others when things went wrong.” Men appear to regard more selfish dominant acts as more desirable, or less undesirable , than do women.” (David M. Buss, Evolutionary Psychology, 1999, p. 353)

Notice how the author uses the phrase “less undesirable”. Does it serve a good purpose? That is the question I want to answer.

It seems to me that the author thought that in some cases it is correct to use “more desirable” and in other cases it is correct to use “less undesirable”. I imagine that the kind of cases where he thinks that the latter phrasing is correct are cases where both the things considered have a negative value.

To illustrate: Think of an infinitely long vertical line that is numbered every centimeter with increasing numbers upwards and decreasing numbers downwards. The numbers correspond to desirability. Now imagine two points, A and B, that represent two items and are on that line at two negative numbers, -2 and -5 respectively. Do we need to say “A is less undesirable than B” or can we do fine with “A is more desirable than B”? As far as I can tell the second phrase is fine. Recall the truth condition for the proposition: D(A)>D(B) where D(A) means the desirability of A. Is that condition met? Yes, because -2 is larger than -5. If so, then it seems to me that there is nothing wrong with the sentence “A is more desirable than B”. It is not the case that the proposition implies that A is desirable. It neither implies that B is desirable. A thing is desirable iff the dot representing it has a positive value on the vertical line. Neither A or B are desirable, but A is more desirable than B. I see no problem with this wording.

So when do we need the other sentence, that is, “A is less undesirable than B”? Perhaps when we want to imply (not a logical implication but implicature [Wiki, SEP]) that both A and B are undesirable, that is, have a negative value. Perhaps the author above added the secondary phrase just in case some readers thought that A and B have negative values. This seems unnecessary to me. Worse, it lengthens the text which should be avoided.

Another use of the “less undesirable” phrase is that of intended confusion. It involves a double negative which is good for confusing matters. As a general principle double negatives should be avoided for the sake of clarity.