Do you only know that you exist?

I dispute that mathematics or logic can be argued not to exist - they exist by definition. By which I mean, by the time you’ve got done defining the terms of the statement “2 + 2 = 5”, you then know what “2” is, what “+” is, what “=” is, and what “5” is, and based on the definitions you have applied to those terms/symbols themselves, you know that “2+2=5” is false. Similarly, logic also stands on its own definitions.

Now, of course you could argue that perhaps you define “5” to mean what normal people mean when they say “4” - but in that case, you’re doing the same math as everyone, just with different symbols. It’ll make communicating with anybody on the subject crazy-difficult, but it doesn’t actually mean that your math is any different. “II + II = IV” is “2+2=4”, mathematically speaking; what symbols you are actually using is irrelevent.

As for everything else in your senses, memory, or imagination - that’s all of doubtable veracity. Your memories and sensory inputs could be being faked, or could (in theory) actually be completely random; in fact, you may have no past or senses at all, but merely be existing for a fractional moment, with the memory of all your past and current senses and experiences having just fallen into place for this instant, ceasing to exist an instant later. Or you could be more permanently existing, but frozen in time with artificial memories and senses; characters in a book or movie are this way on any given page or in any given still image.

The only reason we believe anything we remember or sense is because it’s really darn consistent. I don’t know if the door is actually real, but I do know that experience tells me that if I try to impell the action of walking into the door with the body I appear to have, that apparently-real body is likely to give me something realistically approximating an unpleasant sensation where it whams into the apparently-existing obstacle. I trust the past experience as consistently predicting the future results of my intended actions, so I don’t walk into the door.

I don’t agree with Russell, however, when he claims, “…Thus no fact about any particular existing thing can be self-evident to more than one person.” He would dismiss Gabba Gabba Hey’s question “If you know more than one thing, what it it?” I think it is a very intriquing and innocent philosophical question.

Well, according to objectivism, you know three things - Existence, Identity and Consciousness.

Existence - we exist ie we are actually here right now.

Identity - you are a different thing to me. I am a different thing to you. We are both different to all the other things around us. The only alternative is solipsism which has been downgraded in philosophical circles. The argument being summed up by Samuel Johnson while on a walk with Boswell.

Boswell asked Johnson what he thought of solipsism. Johnson replied “I refute it thus” and he kicked a heavy rock lying on the ground. His point was that he could feel the rock “kick back” when he kicked it. Anything that “kicks back” exists.

Consciousness - we’re aware we exist

No – even without external sensations, you’d experience your self. The ability to form the thought ‘I think, therefore I am’ is not dependent on any external stimuli. If you were blind, you could think that thought; if you were deaf, you could as well; and similarly if you couldn’t taste, feel, or smell anything. There wouldn’t be many things for you to think about, perhaps, but you could nevertheless think – well, provided it is possible to have conscious thoughts if you don’t know language, something I think I’ve heard disputed by Dennett. But I think solipsism already rests on the assumption that it is, since it views all external input as being ultimately fabrication of one’s self in some way, including language and its rules (there might be an argument against solipsism here – can a singular being come up with language? Perhaps, if it were able to form conscious thoughts, but doesn’t that presuppose some sort of language?).

Besides, the rules of language are another thing that you know.

That’s all very well, but could they actually come from you? That’s what I’m disputing – that if there’s an entity creating all those illusions, there’s no meaningful way to identify it with you; thus, there must at least something else exist besides you.

Simulated objects in computer games “kick back” - and I’ve had things “kick back” in dreams.

Just sayin’.

This might be the point where we differ, but here goes. Arithmetic doesn’t say 2+2=4. Arithmetic states rules which, if applied, will presumably lead you to 2+2=4. Pop Quiz: Is the statement 24-17x(57/113)=78 true? You’ll probably have to bust out the calculator, or at least write it out to solve it. There are steps in the problem and, as you solve it, each step you complete could conceivably contain an error (I got a D in high school algebra, so I know what I’m talking about). Granted 2+2=4 is a lot simpler, but isn’t it possible to still get it wrong? With a definition there are no steps for possible errors to sneak into. You could argue that you know the rules of arithmetic (the definitions) but since no one else can verify them (because you don’t know that anyone else exists), you can’t prove that you didn’t just make them up.

It’s my personal opinion that we can’t even be sure we exist, so that may very well colour my responses.

As far as I can tell, if my reading of Chesterton’s summary is correct, Aquinas offers no refutation at all for that particular premise. Aquinas points out that if we cannot be sure that our recognition of reality is correct, then we can make no further premises or guesses; that it’s a philosophical dead end, and if we accept it, we can’t then say anything else at all about reality. And I would agree. But that’s not a refutation; it’s not saying that it isn’t the case, it’s saying that should it be the case, here are the results of that - not pleasant results if we care about philosophical inquiry, certainly, but they are results, of a possibility.

When he goes on to point out why exactly Aquinas believes this view to be false, he suggests it is because Aquinas is one for selecting the “obvious” answer, the result of common sense, and of simplicity. Reality is as we percieve it because that’s the more clear way of thinking - to drag in Occam, it’s not multiplying entities unnecessarily. The problem with using that in this particular line of theory of course is that we are postulating the existence of the intial (and every other) entity in the first place. If Chesterton’s analysis is correct (and my reading of it is, also), then Aquinas is using the conclusions to support his premise.

Read this, if you haven’t already. I think it answers your point.

If I suddenly went deaf, dumb, blind, etc… and had absolutely no sensory input, you’re right, I could still think. But I would be thinking about past sensations, from before I fell into this state. On the other hand, if I was born without senses, I would be in a vegetative state. My autonomic system might keep my body running, but I would never notice it. I am capable of thought, but, since I never receive any stimuli, I have nothing to think about.

As far as knowing the rules of language, I disagree. They are “rules” because everyone agrees with them. Since I’m not sure other people exist, I might have invented the rules. If I invented them, I can change them at will and if rules can change, they’re no longer rules.

You have a point about that. If I have a split personality, the “other” me is external of my existence, though not necessarily of my body. But maybe my existence has the natural side-effect of causing hallucinations?

I understand where you’re coming from, but I would say that you are similarly following some sequence of rules (the rules of logic) in crafting the argument which establishes “I exist”. [After all, you didn’t just say “Well, duh, this is true by definition.” You instead spun out a nontrivial explanation for how you knew it to be true (“Well, even if I was making all kinds of mistakes and being deceived all over the place, there’d still be some existent me there making the mistakes and being deceived; ergo,…”).] So is not equally as possible that you may have made an error in following these rules (i.e., that you accidentally constructed an argument which contained some slip-up somewhere, and was thus not actually valid)?

This appears contradictory – if there truly is nothing to think about without receiving any input, then you can’t hallucinate your own world in a solipsistic manner, since there exists nothing else to give you any input; if, on the other hand, you are able to create the hallucination of the world from nothing, then you get something to think about without ever having received sensory input. So either there must exist something besides you, or you must be able to think without ever receiving any stimuli; and in both cases, it seems to me, you know the appearance of other things.

Regarding language, I don’t see how its arbitrariness prevents you from knowing it; even if there’s never a consistent set of rules from one moment to another, and all expressions of language (written documents, your memory etc.) change constantly and instantly in such a fashion as to present an apparently coherent picture, you must still know the rules in any given instant, simply because they come from you – if you create a reality in which a sentence in the English language needs to contain a verb to be proper, then you must know this requirement first.

I think a distinction must be drawn between ‘accessible’ and ‘inaccessible’ knowledge (going, for the moment, with the assumption that a singular entity capable of simulating the world to itself in a believable way can exist); in some way, since you are the creator of everything and must keep track of every entity’s path in space and time within your hallucination, you must know everything, but you aren’t aware of everything, obviously. From that point of view, I can see why you’re saying that the experience of everything seemingly external is merely an experience of your self; but from the point of view of your own conscious part, there clearly is a variation in the amount of things known to you – there are new experiences, and every new experience adds the knowledge of having experienced it. You can also forget things, implying that what you forgot once was known to you. Which point of view one wishes to adapt, may be largely due to taste, I guess. To me, there seems a slight tension between on the one hand saying that you can’t be sure of anything other than your conscious experience, and on the other hand postulating that you’re simply the self-experiencing part of some entity that contains the knowledge of everything there is (or seems to be). But that’s maybe more a conceptual than a logical problem, I guess.

Yet, even if one adapts the position that the experience of the external world doesn’t constitute gaining new knowledge, but merely the actualization of pre-existing, subconscious knowledge, I think there is one way for you to gain genuinely new knowledge, namely if the underlying fundamental you is genuinely capable of innovation – if it can come up with a genuinely new idea, then you can gain knowledge of that idea, and that knowledge would extend beyond simply knowing of your own existence.

When Cantor proposed Set Theory in 1874, many thought that he had discovered the Philosopher’s Stone that could unify all of mathematics. Then Russell (among others) discovered that Cantorian Set Theory led inevitably – and very simply – to self-contradiction. By 1910 or so Zermelo (and others) discovered that this was because Cantor tried to define his basic terms using his basic terms; or, in other words, Cantor tried to use his primary language to construct his primary language.

This can’t be done, ever. It always leads to self-contradiction. This means that any attempt to nail down a definition of your most basic terms will lead either to (1) a provably wrong system (because it leads to self-contradiction), or else (2) an infinite regress (because you will need to invent a higher language to define your most basic terms, which in turn will need a yet higher language to define its most basic terms).

If I understand this correctly, this means that Aquinas is not using his conclusions to support his statements. He is, instead, cutting off the infinite regress at the point where further regression becomes useless.

I’m afraid you’re going to need to dumb the first part down for me, because i’m afraid I can’t follow you. My point was that Chesterton’s claim is that Aquinas bases his selection of what is true on the comparitively more “simple” explanation; the problem is that, in this case, it is the “simple” explanation which is being questioned, as well as everything else. It’s like supporting a statement that a potential liar is telling the truth by pointing out the liar claims to be telling the truth - the supporting statement requires the premise to be true before we accept it.

This is different from Aquinas’s point that accepting that reality is not as we percieve it leads to a philosophical dead end, which isn’t a refutation either, but a pointing out of unfortunate implications.

It doesn’t, at all, because math and logic are made up. Seriously. How many ‘fours’ do you see wandering the earth? Not collections of four items - not symbols that represent “four” - but the abstract concept ‘four’ itself? Whoops, I said it: it’s abstract. It’s nothing but an idea, which has the mind as its native environment.

So it doesn’t matter if you just made them up. All that matters is that you know their definitions, which are just ideas. From the definitions, the entire systems based on them follow.

Which is not to say you can’t make errors and be wrong about your conclusions, but errors like that can be determined and ousted by sheer mental examination, which is possible form a solipsistic perspecive, so I don’t see how it’s a significant problem. (Assuming time is actually passing, anyway, but even if it’s not, the fact that you don’t know something doesn’t mean it’s not knowable.)

Okay, lets set up a system in which every term is defined. Now consider the definitions of our most primitive terms. These definitions contain words – how are these words defined? These definitions become circular. If we ignore this circularity, we can generate self-contradictions. For instance, we can define a set of all sets that don’t contain themselves. Does it contain itself? If it does, it doesn’t; if it doesn’t, it does. Because the system in which every word is defined can generate a self-contradiction, we know that it can’t exist.

But wait! Let’s get around it by defining a “higher” language, that we can use to create definitions of our primitive terms. Unfortunately this “metalanguage” has its own primitive terms, which in turn requires a meta-metalanguage, and so on. An infinite regress.

So the only way to create a complete system, in which everything is defined, is to simultaneously create an infinte regress. And remember, you have to actually make the infinite regress, not just sketch in the first two stages and put an et cetera at the end.

How does this affect our discussion of solipsism? Well, solipsists insist that we show them a system of reality in which everything is defined. Including reality. To do this, we need a super-reality, and to get the super-reality, we need a super-duper-reality.

Et cetera.

Solipsism assumes that something exists. It also (so far as I know) assumes that that something is somehow aware that it exists. From that, it is natural to develop the concept “one”.

Presumably this ‘something’ is probably also aware enough to form the concept of ‘none’.

From there, all math follows…without infinite regression.

And seriously speaking, your typical solipsist (if there is such a thing) doesn’t think he’s operating with nothing. He thinks that he’s being bombarded with a tremendous pile of data. Certainly including either static memory or a continuous influx of sensory data (and possibly both). Sure, the solipsist doesn’t trust that this data is an accurate reflection of objective reality, but it doesn’t mean the data isn’t there.

Which kind of kicks the knees out of the idea that infininite regress is necessary - even if all our memory data and sensory data is made-up crap, it still includes more than enough raw information to construct abstract concepts and systems from.

(Assuming time is passing and active thought is occuring, anyway - but I don’t know that many (or any!) solipsists actually entertain the notion that they are not actually progressing through time or actually thinking. (Of course, I don’t actually know any actual solipsists, so I could be wrong about that.))

Sorry. The most you can get from the existance of a single entitiy is Cantorian Set Theory, which contains well-known self-contradictions. To remove these contradictions you need to define its primitive terms. And this leads to a regression of definitional systems.

My point: you, Revenant Threshold, and others are requiring that a system exist in which reality is defined, and not merely stipulated. But if such a system exists it must be real, so you must use reality to define reality. This leads to self-contradiction.

To accomplish this feat (of a real system that defines reality), you need a super-reality in which to define the primitive concept, “reality”. To define the super-reality, you need a hyper-reality. Aquinas, via Chesterton, was asserting that this was pointless.

Okay. You also need to be able to imagine the existence of anything that isn’t yourself. (You don’t have to believe it; you just have to imagine it.) This gives you the number two, and by imagining the ‘other’ of that ‘other’, three, and so on - which gives you succession, and from there you have all of mathematics. (Directly, not via an intermediary such as set theory.)

So tough.

Um, nonsense. As I noted in the half of my post you didn’t quote, no solipsist starts from nothing. So, no infinite regress is necessary, and thus, no self-contradiction.

You seem to be tripping over the problem that solipisists merely believe all that data isn’t real. That doesn’t mean that it’s not there. And real conclusions can certainly be built upon false data - if nothing else, conclusions about the data.

I’m not requiring that a system exists at all, as far as I can tell. And I don’t believe your logic follows through, since it’s technically possible for the appearance of reality to define reality - it just won’t be “us” doing it.

While what you’re saying is right, I’m not sure if it’s actually that relevant – I don’t know that there’s, for instance, a requirement for the solipsistic system to be consistent, and if we don’t require an excluded middle, we don’t even get an explosion from that. After all, we can’t formulate a complete and consistent system of axioms in a non-solipsistic world, either, and most people don’t seem terribly bothered by that; the solipsist needs only to make stuff up and give it the appearance of consistency, and he’ll be fine for all practical purposes.