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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).

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closed as off-topic by Edwin Ashworth, MrHen, aedia λ, Kristina Lopez, tchrist Jan 24 at 23:39

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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 at 11:12
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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 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. –  medica Jan 19 at 11:40
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Susan has just kicked Fred's cat. –  Edwin Ashworth Jan 19 at 11:47
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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 at 13:11

2 Answers 2

up vote 2 down vote accepted

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.)

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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 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 at 23:04

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.

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Thanks, @Suan. But if we analyse it, we really missed the point. –  George Chen Jan 19 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. –  medica Jan 19 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 at 11:41
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@GeorgeChen - I wanted to thank you. You have given me a rather unexpected and interesting little experience. :) –  medica Jan 19 at 11:46
    
Thank you @Susan for sharing your perspective. I'll be sensitive next time. –  George Chen Jan 19 at 12:01

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