There must be a distinction between what I think is given in perception and what is actually given in perception, just as there is a distinction between what I think is on the menu at Sizzler and what is on the menu at Sizzler. What is actually given in perception is what you actually see. What is 'there' before your conscious awareness. What I think is given may be utterly different.

Still, I think we might agree. I say that perceiving a hand is sufficient to end a regress of sceptical questions. You say that the ostensive definition 'this is a hand' is sufficient. I am not sure the two views are really different. — PossibleAaran

It seems that you are talking about individual instances of perception; where mistakes can be made, to be sure. I'm talking about perception in general where mistakes get ironed out, and constitutive rules concerning what is given in everyday perception, i.e. the world of objects and things in general, become the implicit background against which all beliefs and doubts find their sense.

So, perception of a hand as a hand is only possible once this background is in place.

Because I drew a distinction between me being certain and it being certain.

I am certain that I will win the lottery tomorrow. That's about my attitude. But is it certain that I will win tomorrow? That has nothing to do with my attitude.

It could be dubitable. But first, you have to give me an example of what it means to doubt such a statement. Apparently, it should mean that there are indubitable statements. But what would be the definition of an indubitable statement? — Magnus Anderson

I dunno, mate. You said it. You tell me.

Is it really important? I think that this is nothing but distraction. @Banno's claim that analytic propositions are indubitable is also a form of distraction. Who cares? The central point remains whether or not he's right. I just thought it would be fun to write a quick draft on the subject "How 2 + 2 = 4 Can Turn Out to Be Wrong".

So you assert that no statement is indubitable (except that one?), then question what indubitable means, then claim a distraction? No, it's not important.

Because it's not important.

You said it!

What did I say? Don't confuse what you think I said with what I really said.

Suppose that a person is overcome with a severe illness causing delusion, and hallucinations, with the appearance of all sorts of phantasms, paranoia and suspicion of everyone and everything. This person would be completely unsure of what was real. Wouldn't this person doubt everything and know nothing? — Metaphysician Undercover

You are one describing this -- not the person you are referring to. How would he know he is hallucinating? Oh, I see. Because he would have an idea of what's not a hallucination. Just like you can't claim you're only dreaming if you have no idea of a not-dream world.

The word "indubitable" either has no meaning, in which case it is true that nothing is indubitable, or it simply means dubitable to a relatively low degree, in which case there are things that are indubitable.

If a million out of a million observed swans are white the statement "all swans are white" is dubitable to a very low degree because it would take quite a lot of new observations to reject this proposition. Forget Popper, he was a moron. A single black swan does not refute the claim. It makes it weaker, that is true, but if a million swans are white the impact is almost non-existent. Popper was an absolutist who lost faith in absolute positivity (verificationism) and sought a new one in absolute negativity (falsificationism.)

Because I drew a distinction between me being certain and it being certain. — Michael

Curious.

How is "It is certain that..." different from "It is true that..."?

I am beginning to suspect that Magnus and Humpty Dumpty would agree as to the theory of meaning.

Hereabouts, it is hard to come by a white swan, but the black ones are plentiful.

Why would you say that doubting the meaning of something is not a sensible form of doubt? — Metaphysician Undercover

That's not what I argued, Meta.

Do you doubt that twice two is four? Could you? And if you came across someone who could, what would you make of them?

If I've flipped a coin then it might be true that it landed heads up but it won't be certain that it landed heads up. As I said before, certainty in this context is to do with probability.

Because it isn't certain that it landed heads up then it would be unreasonable for you to be certain that it landed heads up. It would be reasonable to doubt (in the sense of "not certain") that it landed heads up.

OK. DO you remember why we are talking about probability? I don't.

To allow for a distinction between something being certain and something being necessary, were such a distinction required.

SO we have certain as a propositional attitude, certain as a mode, and certain as a probability. Three uses.

I'm interested in the first one. That seems to me to be what the thread is about.

This line of enquiry is apparently up a garden path. I'm going back to the playground.

I'm interested in the first one. That seems to me to be what the thread is about. — Banno

Sure. The issue is whether or not certainty as a propositional attitude is justified. If there's a 10% chance that something will happen, is it reasonable to be certain that it will happen? What if it's 99%? What if it's 100%? The claim MU and others are making is that if something isn't certain to be true then it is reasonable to be uncertain (doubt). Of course that's not to say that it's reasonable to believe that it's false, which is where I think there's been a misunderstanding between you and them.

I can strongly believe that something is the case and still have doubt. The skeptic can still believe all the same things you do; that this is a hand and that there's a cat on the mat.

To my eye you are just replacing Certainty/uncertainty with certainty/probably.

Words are our tools. We can't just assume that the word means the same in both uses.

Then let me rephrase it without the term "certainty".

If something could be false then it is reasonable to lack a full conviction that it is true.

Still looks like mixed use. Is the could modal or probable?

I'm not sure. Does it make a difference? Neither have anything to do with one's attitude, which is the main point.

Neither have anything to do with one's attitude, which is the main point. — Michael

So do we agree that it's got nothing to do with the main topic, which is belief as a propositional attitude?

I think you have helpedset out a nice distinction. Cheers.

So do we agree that it's got nothing to do with the main topic, which is belief as a propositional attitude? — Banno

That must be an intentional misread. The meaning of "could" in that sentence has nothing to do with our propositional attitude, but whether or not something could be false does have something to do with whether or not our propositional attitude is justified.

So take the sentence either way:

If something is possibly (modal) false then it is reasonable to lack a full conviction that it is true.

If something has a non-zero probability of being false then it is reasonable to lack a full conviction that it is true.

What?

You are one describing this -- not the person you are referring to. How would he know he is hallucinating? — Caldwell

He wouldn't, but that's exactly what doubt is, being unsure.

Do you doubt that twice two is four? Could you? — Banno

In general practise, I do not doubt "2+2=4", I use these mathematical principles all the time, without doubt that they help me achieve what I use them for.

However, I have doubted the truth of this statement in the past, and I have found it curiously contradictory. There is a problem with the meaning of "=", equivalence, which is inconsistent with the meaning of "unit" . Units are what the numerals represent to me, "2" signifying a unit of two, "4" signifying a unit of four.

On the left side of the equivalence signifier, we have two units of two, with a sign for addition. On the right side we have one unit of four. What is signified is that the two units on the left side are equivalent to the one unit on the right side. Initially, this appears as an impossibility, to say that two distinct units are the same, or equivalent, to one. It would require either a very odd definition of "equivalent", or some further standard, such as size, or weight, to say that the two units are equivalent to the one unit.

But I haven't yet taken into account the "+", and it is by means of the "+" that the two are said to be equivalent. The "+" signifies an action, addition. And it is by means of this action, adding, that the two are said to be equivalent. So the two units on the left are not equivalent to the one on the right, until the action of addition is performed. They become equivalent through this activity.

Now here's the problem. Before the action of addition is carried out, there are two separate units of two. After the action of addition is carried out there is one unit of four. So the equivalence which is signified by "=" is dependent on this action. Therefore "=" does not signify that "2+2" coexists with "4" as two equivalent things, it signifies that "4" negates "2+2" by means of that action. Because "two units" and "one unit" is inherently contradictory, they cannot coexist as equivalent things, the action negates one to bring about the existence of the other.

And if you came across someone who could, what would you make of them? — Banno

Doubting this was very useful two me. It helped me to justify the belief that Platonic Realism is not a good ontology. So I think that anyone who doubts this is a good, diligent philosopher. Anyone philosopher who does not doubt these fundamental rules is probably stuck within the confines of a Platonic Realism ontology.

In short, to doubt the rules is the only way that we're going to get through, toward an understanding of what type of existence these rules have. We can assume, take for granted, the existence of the rules, and follow them without doubt, but this will not give us an ontology. That would be a case of accepting the existing ontology. Ontology being the game which provides the rules for epistemology. So we must take the rules, doubt them, rip them apart in analysis, in order to see what supports their existence if we want a good ontology. Then the epistemology is built on the ontology. If you're happy with the belief that the rules are necessary then keep your Platonic Realism. if you do not believe that they are necessary then why not doubt them? Doubting them will only increase your understanding of fundamental ontological principles.

Is there a difference between doubting that 2 + 2 = 4 and doubting that "4" is the numeral that refers to the sum of 2 and 2?

I am inclined to say that I cannot really doubt that 2+2 = 4. What I mean, specifically, is that I cannot imagine any way in which 2+2 does not equal 4. Sure, I can imagine that "4" does not mean the following number of distinct units:

I I I I

I can imagine that "4", in my language, means this many distinct units:

I I I

And I can imagine that, if that were true, 2+2 = 4, assuming that "2", in my language, means this many distinct units:

I I

I can also doubt that "2" means that many distinct units. But, holding the meaning of the symbols fixed, I cannot imagine that 2+2 is not 4. I cannot imagine that putting these units:

I I

with these units:

I I

would give me anything other than these units:

I I I I

Thus, there is a sense in which I couldn't really doubt that 2+2=4.

Best,
PA

Your point is basically "if you accept that the premises are true and that the logic is valid then the conclusion is necessarily true". That amounts to saying "if you choose not to question something then you cannot question that something".

But, holding the meaning of the symbols fixed, I cannot imagine that 2+2 is not 4. — PossibleAaran

That's exactly the same as saying "but, assuming that the future mimics the past, I cannot imagine the existence of zombies". You can't do something if you resist doing it.