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1. (Original post by wanderer)
What do you mean by arbitrary here? Just because my use of a rule is arbitrary doesn't mean that it isn't a rule. I don't define a rule based on previous cases, I have an abstract conceptualisation of it. I know how to count without referring to previous cases of counting, and there is no question as to whether in previous cases I was counting because I remember counting, not doing something else.
Arbitrary in the sense that your actions are not governed by rules. You don't answer 265 because the rule for addition tells you to and that's the rule you have been following. Rather you just answer 265.

I know 265,003,041,971 comes after 265,003,041,970. But I've certainly never counted those numbers before. The common reponse would be to say that the rule for number says that 1 is larger than 0, units, tens, hundreds, etc run from right to left and that numbers are ordered sequentially by size.
In this sense I am pretty sure I define this rule by looking at previous cases- how I was taught to count, and then infering rules like this from that- or from statements of these rules when I was taught to count.
If you really want an abstract conceptualisation I don't really know what to say except to ask you to flesh that out into something I can understand. that would certainly offer a fact of the matter and answer the paradox but I can't find that in myself (difficulties of introspection) and can't honestly make much sense of the idea either. Hmmm... Does abstract conceptualisation of counting really mean something to you without including the concept of following a rule?

I'm tempted to quote Wittgenstein here "Don't think, Look!"
2. I'm feeling quite out of my depth here, but I'll write down what I'm thinking anyway.
Surely it doesn't matter? Both addition and quuaddition are just words which describe a set of rules about how arithmetic works. You can define "quuaddition" into existence, but does that alter the fact that addition exists as well? If not, then all the additions you have done previously are both quuaddition and addition... by coincidence the two functions have the same results in all the examples you have used.

Basically: I don't even get what the problem is. Maybe I SHOULD be a scientist.
3. No your making sense. The problem essentially is this:

When you say "how arithmatic works" the claim is that there are rules for it. That, given such and such a maths question you should give such and such an answer. The right answer being the one that accords with the rule we follow in arithmetic.

1. But what is that rule that we follow- not what is the name, but what is the function, what does it tell us to do? (and you have to make sure you avoid appealing to other rules like "counting" or "joining" etc because then we can repeat the same problem on those rules instead.)

2. What fact about the world makes it the case that you have been following this rule rather than some similar rule (like Quuaddition)?

3. If there is no fact then you can't have been using one rule rather than another, so then what now justifies you saying 265 is the "right answer" (instead of '5', or '@&\$') if you haven't been following a rule which tells you what to answer? What makes 265 the right answer?
4. (Original post by Calvin)
Arbitrary in the sense that your actions are not governed by rules. You don't answer 265 because the rule for addition tells you to and that's the rule you have been following. Rather you just answer 265.

I know 265,003,041,971 comes after 265,003,041,970. But I've certainly never counted those numbers before. The common reponse would be to say that the rule for number says that 1 is larger than 0, units, tens, hundreds, etc run from right to left and that numbers are ordered sequentially by size.
In this sense I am pretty sure I define this rule by looking at previous cases- how I was taught to count, and then infering rules like this from that- or from statements of these rules when I was taught to count.
If you really want an abstract conceptualisation I don't really know what to say except to ask you to flesh that out into something I can understand. that would certainly offer a fact of the matter and answer the paradox but I can't find that in myself (difficulties of introspection) and can't honestly make much sense of the idea either. Hmmm... Does abstract conceptualisation of counting really mean something to you without including the concept of following a rule?

I'm tempted to quote Wittgenstein here "Don't think, Look!"
Lets look at learning to count. When you learn, you do it with particular instances, counting certain groups of objects. But then you move from that into knowing how to count in general - as an abstract. I know how to count any number of things you put in front of me, but beyond that, I know how to count any possible number of things. I know I was counting in the past and not doing something else because I remember counting. I'm not explaining this too well. Analogy is always dangerous, but here goes - think about intentions. If you look at an action or series of actions I have performed, you can propose an infinite number of increasingly esoteric possible intentions that I had when performing those actions. However, i know what my intentions were through memory.
5. And in that sense I want to agree with you. Damn Philosophers, making me give obvious answers to the simplest things... What was I doing? "I was counting, I remember counting". Duh!

...So I certainly want to call what I was doing 'counting'. (This is beginning to make me feel a little like a freudian psychiatrist)

But though I wish to call my action counting, what was I actually doing? What rule was I following? I don't remember the rule. I remember giving answers and calling that counting. The paradox isn't challenging the name you give it. It's challenging the rule behind it. I would agree with you. I was counting. But what is that?

I think that's the difference. Your intention is a fully formed thing. "I intend to do X" completely states what you will do.

With this though there is a difference. "I give the answer that accords with rule X" says completely what I do only if we know what Rule X requires me to do.
It's like saying "I shall carry out plan B" without knowing what Plan B is.
So although I call what I was doing 'counting' that isn't to say what the content of that is. What 'counting' involves. And then this sceptical problem jumps on top of you when you try to say what the rule you were following actually requires.
6. (Original post by Calvin)
And in that sense I want to agree with you. Damn Philosophers, making me give obvious answers to the simplest things... What was I doing? "I was counting, I remember counting". Duh!

...So I certainly want to call what I was doing 'counting'. (This is beginning to make me feel a little like a freudian psychiatrist)

But though I wish to call my action counting, what was I actually doing? What rule was I following? I don't remember the rule. I remember giving answers and calling that counting. The paradox isn't challenging the name you give it. It's challenging the rule behind it. I would agree with you. I was counting. But what is that?

I think that's the difference. Your intention is a fully formed thing. "I intend to do X" completely states what you will do.

With this though there is a difference. "I give the answer that accords with rule X" says completely what I do only if we know what Rule X requires me to do.
It's like saying "I shall carry out plan B" without knowing what Plan B is.
So although I call what I was doing 'counting' that isn't to say what the content of that is. What 'counting' involves. And then this sceptical problem jumps on top of you when you try to say what the rule you were following actually requires.
Ah, I get it now! You're not questioning the rule of counting as applied, you're questioning our move from what we do to a formalised rule, our attempt to define what rule we have been following - right? Thats something to think about, I'll decide whether I agree and get back to you.
7. (Original post by Calvin)
A rock is falling. There is no rule that says the rock is falling.
Unless, I'm missing something you have used four words there. Each word is capable of deconstructiion, So, for example, why do you say that it's a rock? What does 'falling' indicate?
What there is is a fact of the matter.
So you say, but it's far from clear that you've managed to establish why it's a fact or even what a fact is.
Take the grue paradox as a different familiar example. What fact shows that something has been green rather than grue?
The international colorimetry standard, perhaps?
But I think what you want to say is "what fact of the matter makes it the case that there must be a fact of the matter?"
No, that's not what I want to say. I deny your reductionist approach entirely. I'm continually pointing out that you want to use 'fact' for 'perception' and that you want to pretend that your own language is the bare minimum and that everyone else's ideas can be reduced to it. While I accept a realist approach, I believe that all our language and explanations rely upon a community, not upon some logical calculus.
A fact of the matter is something like "there is an X".
So you're committing the epistemic fallacy and assuming that ontology can be reduced to epistemology (or maybe its converse).
8. (Original post by wanderer)
Ah, I get it now! You're not questioning the rule of counting as applied, you're questioning our move from what we do to a formalised rule, our attempt to define what rule we have been following - right? Thats something to think about, I'll decide whether I agree and get back to you.
Yay! I've made sense to someone
9. (Original post by grumballcake)
Unless, I'm missing something you have used four words there. Each word is capable of deconstructiion, So, for example, why do you say that it's a rock? What does 'falling' indicate?
Well precisely...

(Original post by Grumballcake)
So you say, but it's far from clear that you've managed to establish why it's a fact or even what a fact is.
I see, I assumed we would agree on this point to the extent I wouldn't have to justify every point I made. We do agree on something right?

(Original post by Grumballcake)
The international colorimetry standard, perhaps?
In the case of Grue? How does that help?

(Original post by Grumballcake)
No, that's not what I want to say. I deny your reductionist approach entirely. I'm continually pointing out that you want to use 'fact' for 'perception' and that you want to pretend that your own language is the bare minimum and that everyone else's ideas can be reduced to it. While I accept a realist approach, I believe that all our language and explanations rely upon a community, not upon some logical calculus.
I fail to understand you completely. What do you think needs to be the case for somebody to be counting?

(Original post by Grumballcake)
So you're committing the epistemic fallacy and assuming that ontology can be reduced to epistemology (or maybe its converse).
What epistemic content there is in the statement "There is an X"
10. (Original post by Calvin)
In the case of Grue? How does that help?
You're arguing from silence. There are an infinite set of things that we could have called 'green'. For words (which could be infinitely long), it would be uncountably infinite. So what's the point? For any word you can ask "why say 'fat' rather than 'floobledogoob'?". The answer is that it's based on a community in which both the meaning and the word are in a state of dynamic equilibrium. So a word like 'gay' can gain a new meaning, just by usage alone. Words like 'quiz' can be invented and promulgated into a community too.

No word has a unique, unchangeable one-to-one correspondence with anything. Words are defined by usage and usage is defined by words.
What do you think needs to be the case for somebody to be counting?
That a community say that he is.
What epistemic content there is in the statement "There is an X"
What does 'is' indicate, for example? Isn't it a shorthand for a whole set of sensory perceptions here?
11. (Original post by grumballcake)
That a community say that he is.
Do you agree with the private language argument then?
12. (Original post by wanderer)
Do you agree with the private language argument then?
Not completely. I understand Wittengenstein's point that public langauge is always shared within a community. However, it's far from clear that we think in language as such. If I've lost my keys, I think of finding them by having a visual picture in my head of where they were. I also believe that thought preceeds langauge. For example, I think that dogs probably have thoughts (they certainly have dreams) but they have very little language (if any), of the type which Wittgenstein considers.

In other words, I think the flaw is that we don't just use public language in thought.
13. (Original post by grumballcake)
Not completely. I understand Wittengenstein's point that public langauge is always shared within a community. However, it's far from clear that we think in language as such. If I've lost my keys, I think of finding them by having a visual picture in my head of where they were. I also believe that thought preceeds langauge. For example, I think that dogs probably have thoughts (they certainly have dreams) but they have very little language (if any), of the type which Wittgenstein considers.

In other words, I think the flaw is that we don't just use public language in thought.
Have you encountered Stephen Pinker at all? Theres some idea about 'mentalese'...
14. (Original post by grumballcake)
Not completely. I understand Wittengenstein's point that public langauge is always shared within a community. However, it's far from clear that we think in language as such. If I've lost my keys, I think of finding them by having a visual picture in my head of where they were. I also believe that thought preceeds langauge. For example, I think that dogs probably have thoughts (they certainly have dreams) but they have very little language (if any), of the type which Wittgenstein considers.

In other words, I think the flaw is that we don't just use public language in thought.
Well we also have feelings and perceptions which are not language based. Need Wittgenstein deny (and does he in fact deny) mental imagery? He certianly denies its usefulness in certain cases. For example the whole 'how do we recognise red' case. (We can't compare an object to a mental image because we must first have recognised the mental image as red) but, and perhaps I'm just being dense, I don't see that he need deny mental images exist at all.
15. (Original post by Calvin)
I don't see that he need deny mental images exist at all.
The question is whether I think in language and, if we do, is it a private language? I'd contend that it is a language which is richer than verbal language, since it encompasses impressions, feelings and emoptions. It's also clearly private. While typing this, I could actually phrase my ideas in French, but type in English without any apparent translation phase. Which implies to me that my thought is in a higher language than either.
16. Yes I understand that. My question though is whether this really contradicts anything Wittgenstein is saying. He hardly denies emotions and feelings, he simply says that naming them is a public rather than a private endevour.
Similarly he isn't saying that all thinking must be public, quite the contrary. A private language is one that is logically impossible for another person to understand. If you wish to phrase all your thought in French that's fine. But he would say you can only do that because you either learnt French as a public language, or else you learnt something else like English as a public language and are using French words to stand in for English ones. He needn't deny that.
17. (Original post by Calvin)
A private language is one that is logically impossible for another person to understand.
Not necessarily - like any language, you can find points of similarity and establish a glossary between it and any public language. No-one else can speak that language, of course, because it exists only in your mind. So it's both private and a language. QED.
18. I still don't understand how any of this relates to solipsism.
19. (Original post by grumballcake)
Not necessarily - like any language, you can find points of similarity and establish a glossary between it and any public language. No-one else can speak that language, of course, because it exists only in your mind. So it's both private and a language. QED.
But I believe Wittgensteins understanding of private language was (by hypothesis) one that is logically impossible for anyone else to understand. (QED )

(Original post by Wanderer)
I still don't understand how any of this relates to solipsism.
Yeah I know it's weird... I'm gonna have to have a word with my logic supervisor because it's beginning to bug me. We must be missing something.

Though philosophers do tend to have a pretty short shrift when it comes to Solipsism. Russell gives a couple of arguments against it that are complete bull. You get the impression the only reason they accept such lax arguments is because they really want solipsism to be false. But in this case I can't believe it's that.
So essentially what is the argument? Private language is impossible. A Solipsist must by necessity use a private language. Thus solipsism is necessarily false.

But then either public language is still possible if we allow mindless zombies to count as using language.
Or if we require language use to have some kind of understanding behind it then private language isn't impossible because we can at least allow behaviourist support from zombies. That is, our use of words appears with the sort of use we can see from zombies...

I dunno... any ideas?
20. (Original post by Calvin)
But I believe Wittgensteins understanding of private language was (by hypothesis) one that is logically impossible for anyone else to understand.
Pfff. And in saying so he runs into the exact same problem as the epiphenomenalists; a private language which no one else could even in theory understand, is one which I shouldn't be able to understand. Epiphenomenal qualia which exist in some weird 'mental space', if it cannot be connected to anyone else by virtue of its non-physicality cannot be accessed by me either. There seems to be some kind of categorical overlap going on here, in both cases.

I... uh... demand to have... Kierkegaard's face adorn my name. In return I'm willing to help (or, as is more likely, hinder) any of the cambridge freshers with logic next year, if you catch me on a good day.

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