No, I don't. I don't own any of Wittgenstein's books. I made an attempt to understand Tractatus once but without much luck. I find Bertrand Russell to be more interesting.

The next step is belief revision. The belief I am revising is "the subject of this thread is . . ."

I also agree with what you say about taking such possibilities seriously. Really, that is the whole point. I guess where we disagree is that you seem to believe that otherwise reasonable people are capable of genuinely doubting the kinds of things we have been discussing (which would mean taking such possibilities seriously) whereas I see no reason to believe that they are any more capable of doing that than I am. — Janus

Let's make it simple. If you agree that it is possible that our memories can turn out to be wrong, we are on the same page. Because that's all I am saying.

While non impossible, it is, I submit, nonsensical to doubt that you have hands while you are engaged in typing.

OR can you provide a sensible account of how tis might come about? — Banno

My point is that you can question your memory. For example, I remember the sensation of my fingers hitting the keys on my keyboard just a few moments ago. My point is that this memory can be questioned. Perhaps no such experience took place. Perhaps there is nothing but an imagination of such an experience. That's all I am saying.

But what am I to think of you if refuse to acknowledge that you have hands, if you claim to genuinely doubt that, and yet continue to type your responses on your keyboard? Do you really want to claim that I should take you seriously? — Janus

I think I have to state this in order to clarify my position. I do not refuse to acknowlede that I have hands. I do have hands. I don't doubt that. What I am saying is that the reason I don't doubt that statement is not because it is impossible or non-sensical to doubt such a statement but because I choose, for one reason or another, not to do so.

You appear to be arguing that it makes no sense to doubt our memories. I don't understand that. You think it's impossible for us to wake up one day and realize that we've been dreaming all along?

Again, I share @Banno's sentiment that we should not take such possibilities seriously. It's possible that I am a centaur who's dreaming of being a human but that does not mean that I should take such a possibility seriously. I personally don't. I think I am a human and that I will remain so for the rest of my life.

And what of just plain old truth?

Perhaps talk of absolute truth lead philosophers astray, so that they threw out good old plain ordinary truth along with absolute truth.

So folk like Apo get stuck not being able to say that it is true that Paris is the capital of France and so on. — Banno

Sure, plain old truth is attainable and there is nothing wrong with saying that it is true that Paris is the capital of France.

Seeing as how you are so fond of Popper, there's always his approach, a metaphor using a castle being built in a bog. We need drive the foundations down only so far as is needed to keep the castle stable. When we add a new level, we can push the foundations down a bit further. — Banno

Why do you think I am so fond of Popper? Popper wanted to pursue truth for its own sake. He had a problem with the idea that some of us, not daring to suggest most of us, pursue truth in order to better secure the attainment of our goals (whatever they are.) He was also a staunch opponent of verification which I think was excessive. What we have common, if there is anything we have in common, is the idea that absolute truth is unattainable; that truth can only be approached or approximated. But then, that's what other philosophers, such as Nietzsche and Mach, thought as well, and that long before he was even born. And what about Hume? We are not going to mention him at all.

All in all, I agree with the stance that our foundations need only to be strong enough so that whatever is built on top of them can be stable. However, Sam's exposition sounds far more complicated than that and that suggests to me that he has something else on the menu.

His idea is that there are some propositions that we are caused to believe. — Banno

What does it mean that we are caused to believe some propositions? I very much notice the emphasis on the word "caused". What's so special about it?

Is it related to the following passage?

Third, the basis for beliefs in prelinguistic man is causal in nature, not based on reasoning, reasoning is a linguistic endeavor, at least as how it is defined here. How are beliefs causally formed? It seems to be the case that beliefs arise causally within the mind based on the interactions between our sensory experiences and the world around us. The interaction between our sensory experiences and the world do not necessitate the belief, but are simply sufficient to cause the belief. One acts upon the information given through sensory impressions, which in turn has a causal relationship with the belief. — Sam26

I don't understand the distinction he's making between "causal basis of beliefs" and "rational basis of beliefs [beliefs based on reasoning]".

He also says that reasoning is a linguistic endeavor and I disagree with that. Language merely represents the process of reasoning in a manner that is useful for the purpose of communication. But then he says "at least as how it is defined here" which makes me wonder what he really means by reasoning.

Yes! That's what both Sam and I are saying! — Banno

But you are saying there are bedrock propositions that are not subject to skeptical scrutiny. I am not saying say so. It appears that you believe there is such a thing as "down". So you really want to go "all the way down". You are merely claiming that there is a point beyond which it no longer makes sense to go "down". I say that the process of going down is infinite, it has no end, so you can't go all the way down. You can go more and more down but not all the way down.

Right, the infinite regress is about justifications. For example, how do you know X is true, because of A, B, and C. How do you know A, B, and C are true, because of D, E, and F, and so on; but my theory ends with statements or propositions that are outside of any epistemic considerations. I don't think this would solve all infinite regress problems, but some, or many. — Sam26

I have yet to understand your position fully but my current impression is that this isn't the right solution. The right solution is to understand that you do not need to justify yourself "all the way down".

The problem is solved in realising that there is a way of understanding a rule that is not given by another rule, but in actually following the rule in what one does. — Banno

People want to know why you choose X instead of Y. For example, they want to know why you believe the Sun will rise tomorrow instead of believing the Sun will not rise tomorrow. They want to know what causes you to choose X instead of choosing Y. Really, what they are looking for is a correlation between some event or some set of events in the past and your choice of X. If there is no such a correlation then that means that your choice is arbitrary; it means it's irrational.

Now, when you say there are rules that are not given by other rules, what you are saying is that there are choices that are arbitrary or irrational i.e. that there are choices that are not caused by some other events (such as some other choices.) Does this make sense? To make things worse, you can never be absolutely sure that a choice is irrational. It might be the case that you are simply unaware of the causes of your beliefs.

You can say "the rook can't move diagonally". I can ask "why?" and you can answer "because that's the rule of the game" I can then ask "why is that the rule of the game? why not something else?" and then what do you answer? because you chose so? you chose that the rook can't move diagonally? I ask "why did you choose so?" and you say "I chose it randomly". "Well, then", I can say, "I can choose equally randomly that the rock can move diagonally". And you're fucked.

↪Banno Yes, we can choose to violate the rules, I can move the bishop like the castle, but then who will understand what you're doing? Your talk and actions will be meaningless. — Sam26

Not meaningless but simply difficult to understand. If I am not speaking in a language that is familiar to you, does that mean that what I am saying is meaningless? Not necessarily.

As I said early on it solves the problem of circular reasoning and it solves the infinite regress problem. — Sam26

The infinite regress problem arises when people start asking for an infinite number of explanations on how you know what you know. The problem arises as a conflict between your desire to answer every single one of their questions and your other desires (such as the desire to do something else in your life other than to justify yourself.) The problem is solved by simply ignoring their questions and objections.

The problem also arises when you think that your beliefs must be "beyond any kind of doubt" in order to accept them. In such a case, the problem is solved by understanding that your beliefs do not have to be "beyond any kind of doubt". The problem is NOT solved by deceiving yourself into thinking that there are beliefs that are beyond doubt (classical dogmatism) or that there are beliefs that are neither true nor false and thus not subject to skeptical scrutiny (Wittgenstein's position.)

It would be agreeable to think of language games as a group of actions and their associated set of rules. It's more than just the rules. — Banno

It's what is known as "ontology" in AI, isn't it? I don't like that term either. Very strange. But I understand that it's basically just a bounded possibility space. When I say "rules" I mean the limits of what is possible such as "the chess board is made up of 64 positions aligned in a 8x8 grid" instead of "there is an infinite number of positions on a chess board". Also things such as "the rook can only move to an adjacent position in one of the four directions: left, right, up and down" instead of "the rook can move to any position on the chess board". Boundaries narrow the possibility space. They make it simple. And yes, when you limit the possibility space, certain things become impossible and thus immune to doubt. If we say that the chess board is made up of squares aligned in a 8x8 grid it is impossible for a chess piece to be on a position outside of this 8x8 grid (such as i9 square.) But it is better to say that it is illegal for a piece to be on a position outside of this 8x8 grid because it is nonetheless possible for a piece to occupy i9 square. Yes, that would no longer be the game of chess, but it is nonetheless possible.

So no normative constraints should apply to intellectual discourse; we can all just assert whatever we want? Sounds like a recipe for fun (if you like that kind of senseless chaos) and/or disaster (like it or not). — Janus

That's not what I said. We can discuss all sorts of imaginary scenarios if you want to. We can talk about the life of a psychopath and the kind of decisions he should make if he wants to fully express his way of life. Or we can talk about us, our own ways of life, if that's what you prefer. The problem is I have no interest in these things. Alright? What I am attacking here in this thread is this idea that there are propositions (or more precisely, assumptions) that are beyond doubt. Wittgenstein's claim is that there are propositions that lie beyond questions of knowledge and doubt. That's my interest. You can discuss all the different patterns of doubting and you can discuss whether it is a good or a bad decision to doubt within a specific situation within some framework, you can do any of these things if you want, but that's not what I want to do. All I am saying in this thread is that the universe does not necessarily follow some set of rules that we came up with or any rules at all.

Gravity and such, perhaps; but otherwise, no. — Banno

Gravity isn't a universal rule. There is no such a thing as a universal rule. There are temporary rules and among them there are rules that exist for a long period of time and rules that exist for a short period of time.

Anyone can do whatever they want.
— Magnus Anderson

But that's not right. There are all sorts of things that we can't do - walk through walls, Fly like superman, play guitar well without practicing... It's a long list. — Banno

Anyone can do whatever they want provided that they can do it. Do I have to say that? I think it's a given.

We ask "should" questions precisely because we have a degree of freedom in deciding how we're going to act. That does not mean we can do anything we want. Freedom has limits. When I say "one can do anything one wants" I am saying "anyone can do anything one wants within the limits of their freedom".

Nonetheless, the point remains that everything can be doubted; if you decide to, which you don't have to.
— Magnus Anderson

So, what should one doubt? It's a question worth asking. — Banno

You appear to think that there is a universal set of rules that everyone must adhere to. There isn't such a thing. Anyone can do whatever they want. What I can do is I can explain to you how my type of organism functions. But I am not motivated to do so. Another thing we can do is we can explore all the different manners in which organisms that inhabit the environment within which we live operate e.g. we can observe how they behave and based on that develop various models of thinking. But I am not motivated to do so. Not at this point in time. Other than that, there is nothing we can do. We cannot ask questions such as "what one SHOULD do?" because all behavior is fundamentally irrational. It's a relative thing. You must first choose a goal in order for such a question to make sense and when you do so you are no longer asking a general question, but instead, you are asking a specific question that only applies to organisms that posit the goal we chose for our discussion.

Why is reason defined as deductive logic? Seems that animals and humans rely heavily on inductive reasoning. Deductive is something we came up with rather recently, but our ancestors didn't use it to survive, communicate and utilize tools, etc. — Marchesk

You can also say we came up with both inductive and deductive reasoning just recently. You think that induction isn't about "deducing" what's going to happen in the future? You think it's not about eliminating alternative possibilities in favor of a single possibility (or a narrow set of possibilities)? I was never much of a fan of this inductive/deductive division. I mean, sure, I understand the differences between the two, but I think that these differences are rather insignificant. The same with the claim that thinking (or reasoning) is necessarily a conscious activity. It's like saying that apples are necessarily conscious . . . it's sort of hilarious. Are apples necessarily conscious? Not really. There are apples out there whether we are aware of them or not. We don't make a distinction between "conscious apples" and "unconscious apples" based on whether we are aware of them or not.

Well, you don't have to doubt everything at once. In fact, you don't have to doubt at all. Nonetheless, the point remains that everything can be doubted; if you decide to, which you don't have to.

Some people think that "you can doubt X" is the same as or is necessarily followed by "you must immediately start doubting X". Apparently, these folks are absolutists. They think like this: if there is a possibility that your beliefs are wrong you must doubt them because you cannot accept a belief if you are aware that it can turn out to be wrong -- it must be absolutely true, in your mind at least if not in reality. Black-and-white thinking. From one extreme to another. There is nothing in between. Your beliefs are either absolutely true or they are absolutely false.

Perhaps it's worth noting that inductive arguments are invalid by definition. — Michael

Every single inductive argument can be presented as a deductive argument without any kind of significant loss.

Here's an example of an inductive argument:

1. All swans we have seen in the past are white.
2. Therefore, every single swan we will see in the future will also be white.

This argument can be presented as a deductive argument in the following manner:

1. All swans we have seen in the past are white.
2. The future mimics the past to the best of its ability.
3. Therefore, every single swan we will see in the future will also be white.

The reverse is also true. You can present any deductive argument as an inductive argument.

Here's the common example of a deductive argument:

1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.

Both premises can be presented as an inductive argument. In fact, that's how they are derived. "All men are mortal" simply means that every single man we have observed in the past eventually died. "Socrates is a man" simply means that what we know about Socrates is typically associated with traits that are characteristic of men. The conclusion is reached by joining these two inductive arguments.

Deduction and induction have far more in common than most people are willing to admit.

There are two types of thinking: on is focused on similarities (holism) and the other on differences (reductionism.) I prefer to focus on similarities.

Do you think it's more important to know the extent to which your interlocutors are grammatically correct than it is to know what they are trying to say?

There is an interesting insight in OC 402 where Wittgenstein seems to reject that Moorean propositions are empirical propositions. — Sam26

Sort of what I said? Why is this so? It's clear to me Moore's propositions are empirical. "Here's a hand" means "what I'm looking at right now is what is symbolized by the word 'hand'". This is either true or false.

Wittgenstein appears to be saying that Moore and skeptics are violating the rules of language. Who cares? The important thing is are they stating a belief, and if so, what is this belief and is it true?

Again I answer these questions in my other thread on OC. — Sam26

I am looking into it. I have to say this is all very confusing. We have this weird guy who calls himself Moore and who wants to prove the existence of an external world and that by waiving his hands. And then we have these skeptics who question the existence of this same external world. What does that even mean? That's the first question we have to ask. But Moore skips this step and proceeds to counter the skepticism using a rather dull argument. And then Wittgenstein goes on to make a career out of this. Sorry if I can't take this stuff seriously. Fortunately for me, Banno isn't a moderator, so he can't ban me. The statement "there is an external world out there" must mean something specific so that we can test it and thus either verify or falsify it, and again, only to a degree. I can interpret it to mean "there is a world out there that is not under our control". This makes perfect sense. Lots of things that are not under our control. So it's pretty clear: there is an external world out there. But I am pretty sure these guys don't see it in this light, and in fact, I have a feeling they have no clue what they are talking about. Either that or we simply don't understand what they are talking about and we should first make an attempt to understand them before we proceed to dedicate an entire philosophy to them.

We can understand our world in simple terms like the bishop that moves on the diagonal simply because that is a convention of a language game. — apokrisis

I find the very term "language game" rather strange. It apparently means nothing other than "set of restrictions". Still, it bothers me that there are people who choose to call it "language game" instead of something simpler such as "set of rules". There must be some kind of strange process going on behind the scenes. I am not following what is popular, apparently. Certainly not Wittgenstein's train of thought.

Well, a synthetic version of "Here is a hand" appears to me to be a knowledge claim. This means it can either be true or false; or if you prefer to think in continuous rather than in discrete terms, it means it is true or false to a degree. Clearly, I am wrong when I say "this is a dragon" while looking at my hand. Would you agree? On the other hand, restricting yourself to the analytic version produces a more convincing but nonetheless incorrect argument.

I could be wrong but I think the central point of this thread is Wittgenstein's claim that Moore's propositions such as "Here is a hand" are neither true nor false. I don't agree with this regardless of how you interpret the statement. And there are two ways you can interpret it. One way to interpret it is as an analytic proposition where "Here is a hand" simply means "let this [the experience of a hand] be one of the things the word 'hand' symbolizes". It appears to me this is how Wittgenstein interprets it. Not sure why because you can also interpret it synthetically where it means "this thing that we experience matches our definition of the word 'hand'". It's a subtle distinction. In the first case, the experience is necessarily that of a hand (which isn't really true but let's ignore that for now.) It is not a question of whether what we're experiencing is a hand or not. We are simply declaring that it is (thereby creating a new concept.) In the second case, we are declaring that what we're experiencing is what is symbolized by an existing concept. This can be either true or false. If I say "this is a dragon" while looking at my hand I'd be wrong. It's not a freaking dragon. Unless, of course, I mean it in the first sense "here, let this be a dragon". I can call my hand "dragon" if I want to, right?

Exactly.

Can I doubt that "2" means what I think it does? Surely not, since I have decided what "2" means. What about this can I doubt then? — PossibleAaran

If you want to decide whether something is true or false, and you don't want this to be an arbitrary decision, there must be a standard. There must be something that is fixed.

Is 2 + 2 = 4 true or is it false? If it is an arbitrary decision, you can choose any of the two. But if it is not an arbitrary decision, then there must be something else, something other than your momentary will, that decides. It could be, for example, your earlier decision. For example, you might have said at some point in the past that 2 + 2 = 4 is true. This might have been an arbitrary decision. You could have said 2 + 2 = 4 is false but you didn't. You chose to say that 2 + 2 = 4 is true. It does not matter. You chose what you chose and now you want to remain consistent with that decision. You can't say 2 + 2 = 4 is false because that's not what you said in the past. And this is why doubt makes perfect sense: you want to verify that you are consistent. You want to make sure that what you say in the present corresponds to what you said in the past. You can never be sure that you are consistent due to the fact that memory is fallible. It's easy to forget. And that's how analytic propositions can be doubted. When people say that analytic propositions cannot be doubted what they mean is that they cannot be doubted in the same way that synthetic propositions can be doubted.

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.

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".

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.)

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

Because it's not important.

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".

Noone cares about Popper. Every test either verifies or falsifies that which is being tested. Popper had this weird obsession with falsification. Anyways, every analytical statement can be tested. One only has to understand that analytical statements are tested against some set of rules that determine what is allowed and what is forbidden. 2 + 2 = 4 can be tested against any set of definitions of concepts "2", "+", "=" and "4".

In order for a statement to be testable (verifiable/falsifiable) there must be something against which it can be compared. Mathematical equations must be compared against something; otherwise, 2 + 2 = 5 is just as good as 2 + 2 = 4. There must be some sort of standard. If I want to speak in English I can't use any kind of words I want. I must respect the rules of English language.

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?

It's like when someone says "truth is there is no truth" and then some moron comes along and objects with a statement such as "but that would be a truth, no? you said it yourself . . . it's a truth which states there are no truths . . . . so your statement is self-defeating" which indicates nothing but autism on their part.

So have I understood you correctly? You are saying that because one might doubt more complex equations, one might also doubt that twice two is four? — Banno

You verify that a mathematical equation is true by checking whether it belongs to some set of mathematical equations. You verify that "not T = F" is true by checking whether it belongs to some set of mathematical equations. If this set is {"not T = F", "not F = T"} then it is true; otherwise, it might be not. This set has a location. This means you have to properly locate it. If you don't then your conclusions might not be true. If instead of locating {"not T = F", "not F = T"} you locate a set such as {"not T = T", "not F = F"} then you will conclude, erroneously, that "not T = F" is not true. And it is possible that it is aliens who are responsible for your failure to properly locate the set you want to locate.

You can think of this set in more concrete terms. Think of a drawer that contains balls that are equal in all respects except in color. They can be equal in color but not necessarily. Say you're holding a red ball in your hand and you want to know whether there is such a ball in the drawer. What do you have to do in order to find your answer? You have to open the drawer and look for a ball that is of the same color. But you might end up opening the wrong drawer . . . and this could be because of the aliens. Through some action at a distance, each time you try to open the drawer, these evil aliens replace the original drawer with a different one.

Do you get my point?

There's a religious zeal associated with the mantra "Doubt Everything". Doubt is not a bad thing, provided it does not dissuade you from doing mathematics or playing chess or squeezing lemon onto your fish and chips. — Banno

I am not saying "doubt everything". What I am saying is that "everything can turn out to be wrong". There is no statement that is indubitable. Rather, there are simply statements that we choose not to doubt for one reason or another. A man who doubts everything cannot act for action requires that he settles on what's going to happen. If I can't decide whether it is raining outside or not I can neither take an umbrella and go outside nor go outside without taking an umbrella with me. Most of us don't want to be stuck in a limbo, so we are more than happy to put an end to doubt. But that does not mean we stop doubting when we reach absolute truth. If I decide that it is raining and that I should take an umbrella with me that does not mean it is raining outside. It simply means I got tired of doubting which forced me to go with my best guess. I am not a fan of extreme skepticism but at the same time I am not a fan of dogmatism according to which there are indubitable statements. There is no such a thing as indubitable statements. Everything can turn out to be wrong including 2 + 2 = 4. 2 + 2 = 4 will turn out to be wrong when we realize, if we ever realize, that the set of valid mathematical equations that is of interest to us does not contain this expression.

2+2=4 is not immune to doubt? But doubt here could only mean that the doubter did not know what "2", "+", "=" or "4" meant...

So what is it they are doubting? Not that 2+2=4, because they do not understand what that means, and so could not doubt it. — Banno

Mathematical equations such as 2+2=4 are not immune to doubt. They can turn out to be wrong. One only has to understand how.

How do we determine whether any given mathematical equation is true or false? This is the question we must answer.

Any given mathematical equation is true if it belongs to the set of all valid mathematical equations. We can narrow this down by saying: any given mathematical equation of the form a + b = c is true if it belongs to the set of all valid mathematical equations of the form a + b = c. This is still complex. We need something simpler. Let's focus on the logical operation of negation. Any logical expression of the form not p = q is true if it belongs to the set of all valid logical expression of the form not p = q. Still, this is somewhat complex. To make it simpler, I'll generalize it. Instead of speaking of a specific logical expression that is negation I'll speak of a unary operation on a set of bits. Thus, any given unary operation on a set of bits, op x = y, is true if it belongs to the set of all valid unary operations a on set of bits. This will allow me to escape social conventions and use language any way I want. It will allow me to demonstrate that 2 + 2 = 4 is true not because of social conventions but because of what the individual decides to be the set of all valid mathematical equations.

So what is the set of all valid unary operations on a set of two bits? You choose. It's a personal choice. It can be anything you want. For example, it can be {(1,0), (0,1)}. This would be what most call negation. But you don't have to call it that. You can call it anything you want. You can call it "fuck your mother bastard" if you are badass enough. What is important is that the individual himself chooses the set against which he's going to be comparing mathematical expressions for their validity.

My orientation is extensional rather than intensional. I focus on actions first and words second. I have a negative opinion of philosophies that put way too much emphasis on language and other social conventions.

The set of all unary operations on the set of bits {0, 1} is {(0,0), (0,1), (1,0), (1,1)}. Now we have to choose the set of all valid unary operations on a set of bits. Let this be {(0,1), (1,0)}. This means that unary operations such as (0,0) and (1,1) are invalid (a.k.a. false) and unary operations such as (0,1) and (1,0) are valid (a.k.a. true.)

The only thing left to do right now is to explain how it is possible to be wrong about these sorts of statements. How is it possible to be wrong that 2 + 2 = 4?

There are three things we must focus on:

1. the set of all valid mathematical equations
2. the mathematical equation under consideration
3. our judgment as to whether the mathematical equation under our consideration (2) belongs to the set of all valid mathematical equations (1) expressed as either true or false

It looks sort of like a deductive argument, doesn't it? Let's give an example.

1. the set of all valid ordered pairs of bits is {(1,0), (0,1)}
2. the order pair of bits under our consideration is (0,0)
3. the statement that the order pair of bits under our consideration (2) belongs to the set of all valid ordered pairs of bits (1) is true

But this is wrong, isn't it? It is not true that (0,0) belongs to the set {(1,0), (0,1)}. We made a mistake and this mistake has nothing to with language i.e. we did not make it because we failed to understand the concepts.

That was a simple example. In reality, we rarely make mistakes with simple calculations such as "not F = q". But when a calculation is sufficiently complex, mistakes of this kind are very common.

For example, a mathematical equation such as (235110 * 2 - 65261 + 81) * 163 - 1684 = 66019836 is more difficult to verify. If an average person was asked to calculate the result of (235110 * 2 - 65261 + 81) * 163 - 1684 it wouldn't be surprising if they made a mistake. And such a mistake, you will agree, has nothing to do with an inability to understand concepts. Most people who make such mistakes understand the concepts very well. More often than not, the cause of such mistakes is a weak concentration.

So is it reasonable to suppose that there are aliens interfering with our taste buds? — Banno

You have this problem of not being able to respond to what I am saying with something that is in some way relevant.

My point is that there is nothing that is immune to doubt. That's my point. And in order to demonstrate this, I had to show that there is always a possibility that we are wrong no matter how certain of our beliefs we are. Beliefs such as "lemons are bitter" are not necessarily true. There is always a possibility that they are wrong. I gave you an example of how such a belief can turn out to be wrong. I am not saying that such a belief is necessarily wrong. I am not saying that "lemons are bitter" is wrong. I am simply saying that such a belief MIGHT be wrong.

You preoccupy yourself with REASONS for questioning our beliefs. There can be any set of reasons for why we choose to question our beliefs. In fact, there might be no reasons at all -- we might question our beliefs for no reason at all. None of that is relevant. You give me the impression that you feel that you are under attack for the manner in which you maintain your beliefs. Again, I am not giving any instructions on how others should live their lives. What I am doing is I am simply saying that any belief can turn out to be wrong and that questioning your beliefs can turn out to be useful in one important sense: it can help you discover weaknesses in your position which can then motivate you to change your position in such a way so that it becomes a stronger position.