...but not in Chinese, perhaps.

Let me try a different approach. It probably won't help, but that's life.

If Moore's propositions or hinges cannot be known, it follows that there are no grounds/justification or reasons/evidence to say they are true. If it's nonsensical to claim that Moore can know "This is a hand," then it follows that it cannot be true either. It follows also that these basic beliefs cannot be confirmed or disconfirmed, i.e., they are arational beliefs or hinges.

If we know X, then at the very least we know they're true, but Wittgenstein is claiming that Moore's statements have no grounds to secure their truth, and thus they cannot be known. Hinges are fundamental arational beliefs that ground any talk about epistemology. They are a given, part of the reality around us. They are not ordinary propositions or statements.

Yes, I know I'm repeating myself.

I think a better approach would be to let go of Moore's hand for a moment and look at what was said about mathematical propositions.They are hinge propositions and true. If this is correct then it cannot be true that all hinge propositions are neither true nor false.

That is an important point and should not be overlooked.

If Moore's propositions or hinges cannot be known, it follows that there are no grounds/justification or reasons/evidence to say they are true. — Sam26

Wittgenstein points to many ways in which the term "know" is used and some ways it is misused. If Moore held up his hand as said: "This is a hand" we could look and confirm that it is indeed a hand. If he raised his hand and said instead: "This is a foot" we would know that it is not a foot. We have no difficulty distinguishing a hand and foot. We know what a hand is and what a foot is.

That Moore does not hold up his foot and say "This is a hand" is significant. He does, after all, know the difference.

We disagree and that's fine, but I'm moving on to continue the analysis.

Fooloso4 We disagree and that's fine, but I'm moving on to continue the analysis. — Sam26

Interpretative differences are to be expected, but there really should be no disagreement over whether it is true that 2x2=4. One interpretive rule I follow is that when my interpretation contradicts the text, the interpretation and not the text should be altered. But by all means continue in any way you see fit.

I could say the same thing, but it gets us nowhere.

Sam, 2x2=4 is not an interpretation.

If Moore held up his hand as said: "This is a hand" we could look and confirm that it is indeed a hand. If he raised his hand and said instead: "This is a foot" we would know that it is not a foot. — Fooloso4

I don't think that holds. We can justifiably deny that his foot is not a hand, but there is no way to be certain, and that's the key distinction, that what we see empirically is indeed a hand. Fake barns may look like real barns but we cannot under any circumstances be certain beyond some empirical probability. If the criterion for knowledge is certainty, which is not true for any science, then we cannot have empirical knowledge.

Obviously your interpretation is the correct interpretation. And yes, 2x2=4 is not an interpretation, but whether it's a hinge or not is. It seems to be more about ego with you than getting to the truth about what Wittgenstein is saying.

The axioms of math are!

And yes, 2x2=4 is not an interpretation, but whether it's a hinge or not is. — Sam26

Wittgenstein is clear:

"The mathematical proposition has, as it were officially, been given the stamp of incontestability. I.e.: 'Dispute about other things; this is immovable - it is a hinge on which your dispute can turn.'" (655)

It is also clear that 2x2=4 is a mathematical proposition (10) just as 12x12=144 is:

"In the first place there is the fact that "12x12 etc." is a mathematical proposition". (654)

I really do not want to get stuck on this point. I think this is clear and unambiguous. If you don't then there is nothing more I can say or show from the text.

We can justifiably deny that his foot is not a hand — magritte

I'm not sure I follow. Why would we deny that his foot is not a hand?

It seems to be more about ego with you than getting to the truth about what Wittgenstein is saying. — Sam26

It is actually the exact opposite. Given the hostility and resentment I think it best that I do what I had intended to do and leave.

If Moore held up his hand as said: "This is a hand" we could look and confirm that it is indeed a hand. — Fooloso4

What if he raised his arm and said "this is an arm"? How would that act of holding up his arm be different from the act of holding up his his hand? How do you propose that we could confirm whether he's actually holding up a hand, or an arm?

Of course it is true that 2+2=4. No one here doubts that.

What may be contentious is whether 2+2=4 can participate in the activity of deciding if it is true or false. Sam, Wittgenstein and I do not think that it can - and hence that it is a hinge statement. Fooloso4 night well agree.

Of course it is true that 2+2=4. No one here doubts that. — Banno

Did you change your opinion in the interim? Because you and Sam claimed earlier that mathematical propositions can be neither true nor false:

That 12x12=144 is not subject to doubt; it could not be false, and hence is outside our considerations of true and false... — Banno

I think Sam's earlier suggestion that @Fooloso4 should start his own analysis in another thread. instead of offering his interpretation in this discussion, needs to be seriously re-considered.

If you wish to understand, you might benefit from a wee bit of charity, instead of the tedious "gotcha".

Yes, it is true that 2+2=4; an it is true that 12x12=144 is not subject to doubt. It could not be false.

If you wish to understand, you might benefit from a wee bit of charity, instead of the tedious "gotcha". — Banno

The same charity that has been afforded to @Fooloso4, you mean?

I'm more interested in Sam's exposition than in tedious chitchat.

If you are keen, the related thread I started on the Grayling article awaits.

I'm more interested in Sam's exposition than in tedious chitchat. — Banno

I must have mistaken this for a philosophy forum discussion. I didn't realise it was Sam's blog.

I'm wondering, does my behavior show what I do not doubt, or what I cannot doubt?

Take any of the usual examples you like -- object permanence seems an obvious choice. As I type here, it's clear that I do not doubt the continuing existence of my laptop, blah blah blah.

Is there some behavior I could engage in that would show that I cannot doubt such a thing? What does that look like, to behave as if I cannot doubt something? How does it differ from behaving as if I simply do not doubt it? -- That is to say, behaving as if I am content to accept it as so.

I've no idea. What do you think?

What if he raised his arm and said "this is an arm"? How would that act of holding up his arm be different from the act of holding up his his hand? How do you propose that we could confirm whether he's actually holding up a hand, or an arm? — Metaphysician Undercover

This is also correct. The rules for empirical knowledge are different than those for deductive mathematics. Empirically we can never ever be certain because nature and our senses are incorrigibly open to interpretive vagueness as well as to physical and sensory illusions.

Of course it is true that 2+2=4. No one here doubts that. — Banno

I do hold to the idea that if a proposition is basic or hinge, then to say that it's true is just as mistaken as saying "I know this is a hand." So yes I'm saying that Banno. My interpretation of OC is not unique, there have been many papers written on this subject. However, I'm not saying there aren't instances where it makes sense to say that 2+2=4 is true. The thing about hinges is that they depend on context. If I'm teaching someone how to use the word hand in English, then I might say "I know this is a hand," i.e., I've learned that this is what I call a hand. So, in this case "I know..." means that I have learned how to use the word hand. The same can be said of 2+2=4, in some contexts it can makes sense to say it's true, other contexts not so much. I don't know what Wittgenstein would say about this. OC 10 doesn't give enough information. Moreover, Wittgenstein never edited his thoughts in OC, it's just a rough draft.

The fact that it doesn't make sense to doubt Moore's propositions, seems to also hold for the mathematical proposition 2+2=4. Can I doubt that it's true that 2+2=4. It seems senseless to doubt it.

Ya, I was a bit harsh on Fooloso4.

So, in this case "I know..." means that I have learned how to use the word hand. The same can be said of 2+2=4, in some contexts it can makes sense to say it's true, other contexts not so much. I don't know what Wittgenstein would say about this. OC 10 doesn't give enough information. — Sam26

I find no ambiguity in OC 10 regarding this. Wittgenstein plainly states that "2x2=4" is a true proposition, irrespective of any and all contexts (occasions, times):

is "2x2=4"...not a proposition of arithmetic, apart from particular occasions? "2x2=4" is a true proposition of arithmetic—not [only] "on particular occasions" nor "always"

Moreover, Wittgenstein never edited his thoughts in OC, it's just a rough draft. — Sam26

It's easy to disregard the parts that don't fit with your interpretation, but that's not very charitable to Wittgenstein. At any rate, it seems unusually specific to be classed as a careless error. Taken as what W intended to say, it also appears consistent with (and perhaps a precursor to) his latter remarks on mathematical propositions, e.g. 340, 350, 651-658.

The fact that it doesn't make sense to doubt Moore's propositions, seems to also hold for the mathematical proposition 2+2=4. Can I doubt that it's true that 2+2=4. It seems senseless to doubt it. — Sam26

If it were the result of Wittgenstein's philosophy that hinge propositions are neither true nor false, have you considered that this might not be because they are indubitable, but because they are usually non-propositional (except for W's exposition of them)? If memory serves, I believe that Daniele Moyal-Sharrock regards hinges as non-propositional.

If it were the result of Wittgenstein's philosophy that hinge propositions are neither true nor false, have you considered that this might not be because they are indubitable, but because they are usually non-propositional (except for W's exposition of them)? If memory serves, I believe that Daniele Moyal-Sharrock regards hinges as non-propositional. — Luke

I do think of hinges as basic beliefs, and that they are non-propositional. I said this earlier in my posts. It might be that indubitable is the wrong word. I very seldom use the word indubitable, but on occasion I have. It seems to me that any system of belief, must have basic beliefs, including mathematics.

Ah, well, perhaps we part here on our understanding of the text.

For OC10 leads to

12. - For "I know" seems to describe a state of affairs which guarantees what is known, guarantees it as a fact. One always forgets the expression "I thought I knew".

A child though they knew 12x12 = 128. Where did they go wrong? There can be no justification here apart from understanding how to calculate; had they simply mis-remembered? Perhaps. It remains that it is not true that 12x12 = 128.

I'll just suggest that you are here over egging the cake. Let's leave it at that.

So, you don't think there are mathematical hinges? No one is saying that there are instances where one can doubt a mathematical proposition. Just as there are instances where you can doubt that "This is a hand." Let's say I'm in the context that Moore is in, and I say, "It's true that 2+2=4." Isn't it just as out of place as, "I know this is a hand?" A doubt in that situation is just as silly.

Of course if you change the context you make sense of the doubt. The point is that there is an inherited background that allows you to distinguish between true and false.

So, you don't think there are mathematical hinges? — Sam26

I am saying that when you treat a statement as a hinge in the relevant way, it is not subject to doubt, and hence cannot participate in the game of assigning either truth or falsehood to it, because being false cannot be assigned to it. Despite this, hinge propositions are to be counted as true.

I'm doing this because to follow your view, that hinge statements are not true, leads to the conclusion that no mathematical statements are true. While I see that for you this may be a grammatical convenience, it's too odd a locution to be helpful.