It's logical in the sense that the sentence contains no contradiction. And given the facts, it's false. — Michael

Correspondence theory would have that "P is true" simply means P, not "I believe that P". — Isaac

If we're to accept this, then there should be no absurdity. There is absurdity, so we must reject this. Wittgenstein, Moore and Ramsey all reject it in different ways, but the point of the paradox is to get us to reject it somehow. — Isaac

There are lots of reasons that someone might lie. But what does their reason for lying have to do with the supposed absurdity of the assertion? — Michael

My name is Andrew. The Moon is made of cheese. Liquorice is delicious.

There are many reasons that one might assert something that they don't believe to be true. But what does the motivation of the speaker have to do with it? — Michael

The claim I have made is that the meaning and truth of the sentence "it is raining outside" has nothing to do with the speaker's belief, and that it is possible to believe that it is not raining outside even if it in fact is. Therefore there is no logical contradiction in the sentence "it is raining outside but I believe that it is not raining outside". — Michael

So why does it matter if "one cannot believe both that it is raining and that it is not at the same time"? — Michael

(M) I went to the pictures last Tuesday, but I don’t believe that I did.[...]

The common explanation of Moore’s absurdity is that the speaker has managed to contradict himself without uttering a contradiction. So the sentence is odd because it is a counterexample to the generalization that anyone who contradicts himself utters a contradiction.

The more fundamental way of setting up the problem starts from the following three premises:

It can be true at a particular time both that P, and that I do not believe that P.
I can assert or believe one of the two at a particular time.
It is absurd to assert or believe both of them at the same time.

[Additionally, the absurdity arises only when stated as a first-person, present-tensed belief; e.g.] "It is raining, and I don't believe that it is raining. — Wikipedia

No, "1" is a symbol. So long as each 1 represents a different object there is no problem to add 1+1 and get 2. — Metaphysician Undercover

Isn't this obvious to you? If I count the object as "1" at time x, then I count the very same object as 2 at time y, this is a faulty count, counting the same object twice. Two instances of seeing the very same object, therefore a faulty count if I say there's two objects. — Metaphysician Undercover

if "1" refers to an object called "a number", then "2" cannot refer to two distinct occurrences of that same number, or else we would not have two, but only one still. — Metaphysician Undercover

If "1'" refers to an object called a number, then "1+1" indicates two distinct instances of the same object, which is still just the same object. So "1+1" would signify only 1 object if this were the case. — Metaphysician Undercover

Therefore, to remain consistent with common usage and adhere to true principles of numerology, we must accept the conclusion that "1" does not refer to a mathematical object called a number because this would allow the representation of two distinct instances of the same object "1" to be the same as "2". But according to common usage in counting, "2" cannot refer to a second instance of the same thing. — Metaphysician Undercover

No, that's clearly wrong, mathematics has to do with the desire to count and measure things. Counting and measuring are desirable things. Therefore contrary to your ignorant assertion, assigning a quantitative value to things is the result of the desirability of something, counting and measuring, because these are desirable things to do, there's a purpose to them. — Metaphysician Undercover

In general, a mathematical value may be any definite mathematical object. In elementary mathematics, this is most often a number – for example, a real number such as π or an integer such as 42.

— The value of a variable or a constant is any number or other mathematical object assigned to it.
— The value of a mathematical expression is the result of the computation described by this expression when the variables and constants in it are assigned values.
— The value of a function, given the value(s) assigned to its argument(s), is the value assumed by the function for these argument values.

For example, if the function f is defined by f(x) = 2x^2 – 3x + 1, then assigning the value 3 to its argument x yields the function value 10, since f(3) = 2·3^2 – 3·3 + 1 = 10.

And as I explained in the last post, if "1" refers to an object called "a number", then "2" cannot refer to two distinct occurrences of that same number, or else we would not have two, but only one still. — Metaphysician Undercover

Therefore that act of counting independent of counting something, is just an exercise in remembering an arbitrary ordering of symbols — Metaphysician Undercover

The point is that it is relative to something. Whether it is relative to my own personal decision, or agreed upon decision (convention), does not change the nature of what a value is, itself. — Metaphysician Undercover

there you go again with your uncharitable interpretation for the sake of straw manning. You, yourself, introduced ambiguity onto the meaning of "value", trying to distance your use of "value" from my use of value, for the sake of your straw man, when no such separation is warranted. — Metaphysician Undercover

Look, it is completely arbitrary that the symbol "2" represents the quantitative value which we call "two". To remove the arbitrariness we might assume an object, a number, which "2" and "two" refer to. — Metaphysician Undercover

That two distinct things are equal, and therefore have the same value, is inherently arbitrary, but that they are distinct individuals, allowing us to number, or count them individually, is grounded in real difference. — Metaphysician Undercover

Therefore that value is "relative" to that system. — Metaphysician Undercover

Otherwise I could arbitrarily say that a chair and a table have the same value to me, therefore they are the same intelligible object. — Metaphysician Undercover

Do you even know what "value" means? It refers to the desirability of a thing, or what a thing is worth. — Metaphysician Undercover

The principles that the system is based in, the arbitrariness of the system, is a further matter. — Metaphysician Undercover

That's simply the nature of a value, because value is relative there is a degree of arbitrariness. — Metaphysician Undercover

I just can't see how the fact that a specific variable can be assigned different values, is at all relevant. That's simply the nature of a value, because value is relative there is a degree of arbitrariness. One dollar appears to be a constant value, but when considered within the context of the international market, it is variable. — Metaphysician Undercover

And, if I say "2+2", you could infer that I am taking about the quantity represented by "4", but in no way am I talking about the quantity represented by "4". You simply apply some logical premise and make that conclusion. — Metaphysician Undercover

MY point is that "different expressions of the same value" refer to different things. — Metaphysician Undercover

"Ten dimes" refers to something different than "four quarters". — Metaphysician Undercover

This is how I represent "one dollar", like that or like this, $1. Something equal to a dollar is "ten dimes", or "four quarters". I really do not believe that you can't see the difference, I think you're in denial. — Metaphysician Undercover

If you cannot see the difference between representing the value "one dollar", (which is represented as $!), and representing something equal to a dollar ("four quarters", or "ten dimes"), then I think you've got a problem. — Metaphysician Undercover

Moral realism (in the robust sense; cf. moral universalism for the minimalist sense) holds that such propositions are about robust or mind-independent facts, that is, not facts about any person or group's subjective opinion, but about objective features of the world. — Meta-ethics

So, "2+2" does not represent a value, it represents two distinct values related with "+", and we say that this is equal to the value of "4". — Metaphysician Undercover

If it is true that "4" expresses a value, then "2+2" does not express a value. — Metaphysician Undercover

Do you see that if "4" is an example of an expression of value, then in "2+2" there are two distinct values expressed, "2" and "2" whereas only one value "4" is expressed with "4"? — Metaphysician Undercover

That's because we qualified value with "quantitative" value. — Metaphysician Undercover

1. Epistemological: the identity of mind adherent has to claim that Jack, in the scenario, is referring to a brain state. But Jack doesn't know anything about brains, let alone brain states. Does it make sense to say that someone who doesn't know they're referring to brain states is really referring to brain states when they talk about being in pain? If that's true, shouldn't the person be aware they're communicating all this brain-state information to another person when they talk of pain? — RogueAI

By the way, in case I didn't make this clear last time, I consider "different expressions of the same value" to be ambiguous nonsense, and "different ways of expressing the same value" does very little to clarify what you could possibly mean. Do you even know what "value" means? It refers to the desirability of a thing, or what a thing is worth. How do you apprehend "2+2", or "4", as an expression of what a thing is worth? — Metaphysician Undercover

It is only by assigning equality to distinct things that we are able to count them One apple is equal to an orange, and then we count them, 1,2. So apprehending different things as having an equal value allows us to count them, 1,2,3,4.... — Metaphysician Undercover

Quite obviously,"2 apples + 2 apples" signifies two distinct groups of two apples, and the "+" represents an operation of putting the two groups of two apples together into one group. — Metaphysician Undercover

There is no such two distinct groups of two, nor the operation of addition signified by "4 apples". — Metaphysician Undercover

We cannot count apples and oranges unless we say that an apple is equal to an orange. It is only by assigning equality to distinct things that we are able to count them One apple is equal to an orange, and then we count them, 1,2. So apprehending different things as having an equal value allows us to count them, 1,2,3,4.... — Metaphysician Undercover

The real discovery is the one which enables me to stop doing philosophy when I want to. The one that gives philosophy peace, so that it is no longer tormented by questions which bring itself into question. — Wittgenstein PI § 133

I don't deny that two plus two equals four.

I only assert the obvious, that "2+2", which represents an operation of addition, does not represent the same thing as "4", — Metaphysician Undercover