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"It is raining."

"'It is raining' is true."

Does "is true" make any difference? Thanks.

This link gives context to this question and testify that I'm not a nut (yet).

George Chen
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    The second contains a veridical statement, and is almost certainly in a logical register. The first can have different meanings, and, unless 'man' is emphasised (= real man), sounds peculiar without context. – Edwin Ashworth Jan 19 '14 at 11:12
  • Why are you asking us to do this? – Barrie England Jan 19 '14 at 11:19
  • Here is the original question. http://math.stackexchange.com/questions/643160/what-is-the-difference-between-asserting-phia-and-asserting-phia-is – George Chen Jan 19 '14 at 11:22
  • I think I'm supposed to feel the difference. – George Chen Jan 19 '14 at 11:24
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    The article is primarily looking at logic, which is off-topic on this site. The first sentence makes a statement (one assumes it is definitively testable, but you'd have to point out we're not talking about Fred's cat Socrates). It is true or false. The second sentence claims that the first sentence is true rather than false. It is supporting the claim. However, it too may be false as well as true. – Edwin Ashworth Jan 19 '14 at 11:32
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    @GeorgeChen - I expressed this elsewhere, but you have conducted your own experiment and had it answered already. The logical conclusion is: among respondants to your post, one person expressed emotion, and the rest experienced recognition of a familiar logical argument. There was little feeling involved, except for emotions most would rather not name. – anongoodnurse Jan 19 '14 at 11:40
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    Susan has just kicked Fred's cat. – Edwin Ashworth Jan 19 '14 at 11:47
  • @Susan. My current understanding of the difference is like an ESL speaker's understanding of articles, which just a mechanical habit and no understanding at all. – George Chen Jan 19 '14 at 11:50
  • @EdwinAshworth - please explain is this a nidiom? ;) – anongoodnurse Jan 19 '14 at 11:52
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    Looking out of my window, I know that "'It is raining' is true" is false. – Damkerng T. Jan 19 '14 at 12:08
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    @DamkerngT. "It is raining" is false also. – George Chen Jan 19 '14 at 12:11
  • I added your comments to the answer. Thanks @Edwin. – George Chen Jan 19 '14 at 12:46
  • @Susan: No. It was a logical hypothesis after your mentioning your 'emotions most would rather not name', but is probably not a true statement. – Edwin Ashworth Jan 19 '14 at 13:05
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    This question appears to be off-topic because it is soliciting impressions rather than requesting the examining of usage; it would also be more fitted to a logic site. – Edwin Ashworth Jan 19 '14 at 13:11
  • @Edwin, when a sentence is significant, it creates a mental state; otherwise, there is no mental state. That is why I'm soliciting impressions. I really appreciate your patience. – George Chen Jan 19 '14 at 13:16
  • @Edwin, I added a link to give context to this question – George Chen Jan 19 '14 at 13:18
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    @EdwinAshworth: imho, this question is an excellent one when you know the context OP is asking it in. And yes, it might be suitable to sweep the question aside and move it to a philosophy or linguistics or logic or artificial intelligence site. But at the end of the day, the formal problem OP (and Russel, for that matter) had derives from internal contradictions within a language (in this case English). – Denis de Bernardy Jan 19 '14 at 13:41
  • Sorry @Barrie. I'll provide appropriate context next time. I hope this passage page 179 can explain why I think the distinction is worth brooding on. – George Chen Jan 19 '14 at 22:55

2 Answers2

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The two sentences have a very different meaning, especially in light of the context you gave.

Betrand Russel was a high profile mathematician who, alongside a few of his contemporary peers (Whitehead, Turing, Gödel and a couple of others), were actively investigating one of the list of open mathematical questions that David Hilbert gave at the opening of the 20th century. Namely, whether there existed a set of axioms that we could build arithmetics on, in such a way that any proposition could be either true or false without permitting any internal contradictions.

Getting back to your statement:

  • "It is raining" is a statement (on the weather).
  • "'It is raining' is true" is a statement on the 'It is raining' statement.

Note the subtlety here, in light of the above-mentioned context: the first has a meaning in the sense that it has semantical implications. Namely on the state of the weather. The second also has meaning, but this time in the context of a logical grammar.

Here's a more convoluted example to illustrate how it is problematic when you assume that these two types of meaning (or implication) are congruent:

  • This statement is false
  • 'This statement is false' is true

See where we're heading in the above?

The answer to Hilbert's question and how the above should be dealt with came in the form of Kurt Gödel's incompleteness theorem in the early 1930s: arithmetics cannot prove itself internally consistent. (Ergo, you cannot prove that there is one Truth, and ergo you shouldn't confuse logical truth with semantic truth.)

Denis de Bernardy
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  • Thanks, @Denis, for mentioning semantics. According to Meaning and Truth, the first one is supposed to invoke a mental image; the second one is mostly verbal. The book asserts that most of educated knowledge (as opposed to personal experiences) are actually of the second type, that is, merely verbal, although its true form looks rather unusual. – George Chen Jan 19 '14 at 22:40
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    Mental vs verbal is a good way to think of it, though personally, I prefer meaning vs structure. In formal grammars (think Turing machines), a proposition can be syntactically correct or not (structure), while being utterly meaningless. But be wary of what Russel asserts, since the book (I haven't read it) dates back from a time when the debate was ongoing -- and indeed raging -- in philosophical spheres, and where opinions changed widely. See for instance Russel's buddy Wittgenstein. – Denis de Bernardy Jan 19 '14 at 23:04
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As @EdwinAshworth stated, this is most likely the beginning of a deductive logical argument which takes the form

  1. P -> Q.
  2. P (hypothesis)
  3. therefore Q (deduction)

The most common example is:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

To reach a logical conclusion, each statement (or premise) must be true. So one must accept as true the premise that Socrates is a man.

Socrates is a man. is logically different that 'Socrates is a man' is true.

anongoodnurse
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  • Thanks, @Suan. But if we analyse it, we really missed the point. – George Chen Jan 19 '14 at 11:31
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    @GeorgeChen - Oh, my apologies! You wanted to ask us for our impressions to this set of statements? I see. Then my answer is: This is the beginning of a logical argument. I don't feel anything when I see this because the argument is too familiar. Again, my apologies. – anongoodnurse Jan 19 '14 at 11:35
  • I see your point. @Susan. It is true "Socrates is a man" is so conditioned by logic that most people would think logic right away. – George Chen Jan 19 '14 at 11:41
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    @GeorgeChen - I wanted to thank you. You have given me a rather unexpected and interesting little experience. :) – anongoodnurse Jan 19 '14 at 11:46
  • Thank you @Susan for sharing your perspective. I'll be sensitive next time. – George Chen Jan 19 '14 at 12:01
  • If I may nitpick on the term, it's actually syntactically different, in the context of a formal grammar (or whatever those are called in English), rather than logically different. – Denis de Bernardy Jan 19 '14 at 13:34