Is philosophy a waste of time?
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J-E-N-O-V-A
wtf
1+1=2 is not a law - it's a definition. We've defined 1+1 as 2 for shorthand - why (and how) would it be possible to contradict this?
1+1=2 is not a law - it's a definition. We've defined 1+1 as 2 for shorthand - why (and how) would it be possible to contradict this?
The principia, although seminal, is deeply flawed. Russell's 'logic' in it is anything but so, for the principia to succeed we need to adopt non-logical axioms - which clearly prevents russell from showing that 2 is the logical consequence of 1 plus 1.
Also, it is susceptible to both of Godel's incompleteness theorems.
It's not possible to contradict it, within the system you have used to define 1+1 as equalling 2. But just because we just all so happened to define this doesn't make it a 'truth of the universe'
I took Philosophy at AS, and respect anyone that can handle it. It's very interesting, but just not the subject for me. I don't think it's a waste of time though, as some people have said, it teaches you how to think, and to explore how we know the things we think we know.
Oddjob39A
This is indeed a problem, as someone else pointed out.
Although Wittgensteinian conventionalism can make sense of large number sums like 1736464 + 5554478 = 7290951, it seems on shakier grounds with basic things like 1 item plus 1 item equals 2 items.
I guess all Wittgenstein could say to respond is that we need to differentiate between numbers and numerals. when we say 1 item plus 1 item equals 2 items, we are reffering to numbers. When we say 1+1=2 we are reffering to numerals and it is the numerals that are fixed by the mathematical games we play. So 500 items plus 500 items will always equal 1000 items, but that doesn't make 500+500=1000, because 500+500 could just as equally equate 54031 in a different mathematical game.
But even then, when we say 500 items, we are using 'items' as a numeral which we already hold to refer to the numeral 500! So for Wittgenstein, even 500 items plus 500 items doesn't always have to equal 1000 items, it just so happens that this 'convention' happily coincides with what we 'think' is the analytical truth of 500+500=1000....
confusing? you bet your arse it is, Wittgenstein has never been known for being easy to understand
Although Wittgensteinian conventionalism can make sense of large number sums like 1736464 + 5554478 = 7290951, it seems on shakier grounds with basic things like 1 item plus 1 item equals 2 items.
I guess all Wittgenstein could say to respond is that we need to differentiate between numbers and numerals. when we say 1 item plus 1 item equals 2 items, we are reffering to numbers. When we say 1+1=2 we are reffering to numerals and it is the numerals that are fixed by the mathematical games we play. So 500 items plus 500 items will always equal 1000 items, but that doesn't make 500+500=1000, because 500+500 could just as equally equate 54031 in a different mathematical game.
But even then, when we say 500 items, we are using 'items' as a numeral which we already hold to refer to the numeral 500! So for Wittgenstein, even 500 items plus 500 items doesn't always have to equal 1000 items, it just so happens that this 'convention' happily coincides with what we 'think' is the analytical truth of 500+500=1000....
confusing? you bet your arse it is, Wittgenstein has never been known for being easy to understand
Are you essentially referring to Formalism here? It's the view that mathematics is no more than a human invention, a closed and empty system of deductions produced from an intial set of self evident axioms.
According to the formalists maths is like a game of chess - a self regulating and consistent game. This means that mathematics can produce elegant and complex 'models' of truth, but can never be the truth itself.
So, words like 'true' or 'false' just don't apply.
Was Wittgenstein a formalist? I've yet to study him in great detail but I always thought that he came to the conclusion that there is no such thing as 'truth' except in the field of mathematics . . . but your posts seem to contradict that.
Please enlighten me!
Nude
In Mathematics, the assumptions (Axioms) do not extend much farther than 1+1 = 2 . Axioms are things considered to be blatantly obvious. You are welcome to disprove those assumptions (although, mathematics is rigourus to the extent whereby it is aknowledged that no set of axioms can be proven correct from within).
The ZF-set theory actually underpins all of modern day mathematics, although 1 + 1 = 2 can be "proved" with a few axioms.
i.e. {{}} = {{}}
Obvious or not, you need to set down rules and things which you are allowed to assume, before you can delve into complicated Maths. Of course the axioms themselves cannot be proved... that's the whole point. You assume that they're true in order to prove further things true. Might I also add that you only think they're obvious because you've been taught them from a very very young age. They're certainly not "obvious".
oldrafiki
Even 'cogito ergo sum' assumes that there is an 'I' to think and to be. It assumes a definable 'self'.
However, a statement such as 2 + 2 = 4 is not a thing based upon the senses, it is not an impression. It is a fact of logic. Even if nobody had ever taught you that 2 + 2 = 4, 2 apples and 2 more apples would still make 4 apples, you just wouldn't have named the entities of 2 and 4. Even if there were no apples, the abstract notion of 2 things plus 2 more things equalling 4 things is constant.
However, a statement such as 2 + 2 = 4 is not a thing based upon the senses, it is not an impression. It is a fact of logic. Even if nobody had ever taught you that 2 + 2 = 4, 2 apples and 2 more apples would still make 4 apples, you just wouldn't have named the entities of 2 and 4. Even if there were no apples, the abstract notion of 2 things plus 2 more things equalling 4 things is constant.
The mere fact that you think proves that there is an "I" to do the thinking, proving existence. The "self" is certainly not definable, but it exists beyond all reasonable doubt.
2 + 2 = 4 is not a fact of logic. It is only true because we assume the 10 axioms are true. Only then can we say that 2 + 2 = 4. You merely take it for granted that 2 + 2 = 4 because you were taught the basic rules of maths from a very early age.
J-E-N-O-V-A
You can't just make a statement like that without proof. 
Whilst "you" cannot be defined, you yourself can prove that you, or your conscience or whatever it is that allows you to think, exists.
Toiletpaper8
The mere fact that you think proves that there is an "I" to do the thinking, proving existence. The "self" is certainly not definable, but it exists beyond all reasonable doubt.
2 + 2 = 4 is not a fact of logic. It is only true because we assume the 10 axioms are true. Only then can we say that 2 + 2 = 4. You merely take it for granted that 2 + 2 = 4 because you were taught the basic rules of maths from a very early age.
2 + 2 = 4 is not a fact of logic. It is only true because we assume the 10 axioms are true. Only then can we say that 2 + 2 = 4. You merely take it for granted that 2 + 2 = 4 because you were taught the basic rules of maths from a very early age.
Descartes cogito makes the assumption that thoughts require a thinker. If we rigidly follow Descartes' method of doubt we have no right to assume this at all. Although it may sound absurd, we must accept the possibility that thoughts simple are - they exist in their own right without necessarily having a cause. After all, if Descartes claims that an evil demon could destroy the logic of mathematics, then he must carry this through and admit that there may not be an 'I' doing the thinking.
We can take this to less extreme level however. Have you ever had a dream in which you inhabit the mind of another person? I sure have and so therefore the conclusion ought to be:
'I think, therefore someone/something is.'
Toiletpaper8
The mere fact that you think proves that there is an "I" to do the thinking, proving existence. The "self" is certainly not definable, but it exists beyond all reasonable doubt.
2 + 2 = 4 is not a fact of logic. It is only true because we assume the 10 axioms are true. Only then can we say that 2 + 2 = 4. You merely take it for granted that 2 + 2 = 4 because you were taught the basic rules of maths from a very early age.
2 + 2 = 4 is not a fact of logic. It is only true because we assume the 10 axioms are true. Only then can we say that 2 + 2 = 4. You merely take it for granted that 2 + 2 = 4 because you were taught the basic rules of maths from a very early age.
What HappinessHappening said.
I can't remember where I read it, but there was something about how the 'I think' of the cogito should really be 'there is a thought'. Thoughts just appear - how do you know that there is a 'you' that created them? They are perceived from without, just like anything else.
You can say 'but it exists beyond all reasonable doubt', but what does that really mean? What is 'reasonable doubt'? Surely if there is any room for doubt, that doubt cannot be unreasonable? You might assume the self, we might say that although it's possible that the self does not exist it's not at all probable, but the element of uncertainty that remains, however small, prevents the cogito from being a universal or absolute truth.
As for the 2 + 2 = 4 thing, the point you made has been discussed over the past couple of pages of the thread.
HappinessHappening
Are you essentially referring to Formalism here? It's the view that mathematics is no more than a human invention, a closed and empty system of deductions produced from an intial set of self evident axioms.
According to the formalists maths is like a game of chess - a self regulating and consistent game. This means that mathematics can produce elegant and complex 'models' of truth, but can never be the truth itself.
So, words like 'true' or 'false' just don't apply.
Was Wittgenstein a formalist? I've yet to study him in great detail but I always thought that he came to the conclusion that there is no such thing as 'truth' except in the field of mathematics . . . but your posts seem to contradict that.
Please enlighten me!
According to the formalists maths is like a game of chess - a self regulating and consistent game. This means that mathematics can produce elegant and complex 'models' of truth, but can never be the truth itself.
So, words like 'true' or 'false' just don't apply.
Was Wittgenstein a formalist? I've yet to study him in great detail but I always thought that he came to the conclusion that there is no such thing as 'truth' except in the field of mathematics . . . but your posts seem to contradict that.
Please enlighten me!
Plus it doesn't follow from 'there is thought going on' that 'the thoughts are mine'
I could be brain-dead and standing in a room with Einstein. Just because I may be aware that Einstein is having a thought doesn't mean that Einstein's thought is mine.
As such, Descartes' deduction as to the independence of the res cogitans is invalid.
As far as I'm aware Wittgenstein was a game formalist - conventionalist.
Check out Crispin Wright's Wittgenstein on the foundations of mathematics as Wittgenstein's views are often very obscure and hard to pin down.
The Wittgenstein of the Tractatus may have held that the only truths we can be sure of are mathematical but the Wittgenstein of the Investigations was heavily conventionalist and may have simply intended 'truth' to be the case within a conventional system you are using - he was extremely anti-platonic.
Oddjob39A
As far as I'm aware Wittgenstein was a game formalist - conventionalist.
Check out Wright's Wittgenstein on the foundations of mathematics
Check out Wright's Wittgenstein on the foundations of mathematics
By the way, was it Wittgenstein who threatened Karl Popper with a poker? An RE/philosophy teacher at my school told me the story when we were discussing Philosophy of Science but I've forgotten.
oldrafiki
By the way, was it Wittgenstein who threatened Karl Popper with a poker? An RE/philosophy teacher at my school told me the story when we were discussing Philosophy of Science but I've forgotten.
Yes, Popper was arguing with Wittgenstein over whether there were any objective moral truths, Wittgenstein held that they weren't (for him ethics didn't have a truth value) and Popper held that there was.
Wittgenstein got extremely irrate and pointed at Popper with the poker and asked for an example. Popper replied 'don't threaten visiting professors with pokers'
Wittgenstein stormed out.
Oddjob39A
Yes, Popper was arguing with Wittgenstein over whether there were any objective moral truths, Wittgenstein held that they weren't (for him ethics didn't have a truth value) and Popper held that there was.
Wittgenstein got extremely irrate and pointed at Popper with the poker and asked for an example. Popper replied 'don't threaten visiting professors with pokers'
Wittgenstein stormed out.
Wittgenstein got extremely irrate and pointed at Popper with the poker and asked for an example. Popper replied 'don't threaten visiting professors with pokers'
Wittgenstein stormed out.
Bloody hell . . .
Oddjob39A
Has anyone realised that the point I am trying to make is that even in the spheres of physics and maths EVERYTHING is contestable? There are no 'answers' or 'hard-fast rules' !
Again - you are mistakenly associating Physics and Mathematics. Physics makes use of Mathematics in describing and defining empirical laws of the physical world. Mathematical Axioms do not rely on any empirical evidence. You, and those making similar assumptions, have very likely not studied mathematics beyond A Level, and thus have very little idea of what Mathematics is - but to be in the belief that the fundamental "laws" of mathematics are as contestable as those of Physics are very much mistaken. The two areas are ultimately in stark contrast. There is nothing in any "science" which is "hard-fast", to use your terminology - however, in Mathematics there is nothing with proof which is not "hard fast". Sciences attribute earthly/humanly meaning to quantities and numbers. The numbers are never in doubt, but the meaning can always be.
To use a popular result;
18*27 = 486
That is Mathematics.
Mass*Acceleration = Force
That is Physics.
They are two fundamentally differing siutuations - you may doubt whether F=ma will always hold true, but only a retard would doubt the mathematics. You amateur Philosophers, blindly quoting other mens work, would do well by first studying in depth any area which you care to ponder and comment upon.
Nude
Again - you are mistakenly associating Physics and Mathematics. Physics makes use of Mathematics in describing and defining empirical laws of the physical world. Mathematical Axioms do not rely on any empirical evidence. You, and those making similar assumptions, have very likely not studied mathematics beyond A Level, and thus have very little idea of what Mathematics is - but to be in the belief that the fundamental "laws" of mathematics are as contestable as those of Physics are very much mistaken. The two areas are ultimately in stark contrast. There is nothing in any "science" which is "hard-fast", to use your terminology - however, in Mathematics there is nothing with proof which is not "hard fast". Sciences attribute earthly/humanly meaning to quantities and numbers. The numbers are never in doubt, but the meaning can always be.
To use a popular result;
18*27 = 486
That is Mathematics.
Mass*Acceleration = Force
That is Physics.
They are two fundamentally differing siutuations - you may doubt whether F=ma will always hold true, but only a retard would doubt the mathematics. You amateur Philosophers, blindly quoting other mens work, would do well by first studying in depth any area which you care to ponder and comment upon.
To use a popular result;
18*27 = 486
That is Mathematics.
Mass*Acceleration = Force
That is Physics.
They are two fundamentally differing siutuations - you may doubt whether F=ma will always hold true, but only a retard would doubt the mathematics. You amateur Philosophers, blindly quoting other mens work, would do well by first studying in depth any area which you care to ponder and comment upon.
I note that you are not actually describing why you believe that mathematical proofs are hard-fast, only repeating that they are, which seems a bit dogmatic. I agree with you, as I have said, but that's not to say that that position cannot be argued against. You are classing people like John Stuart Mill and Wittgenstein as 'retards', without actually offering a response to their views. Every thing can be questioned, just as we can always attempt to find answers.
As I have stated, I know nearly nothing about maths, so according to you, I should go and lock myself away to study it before bothering to make any comment. But the truth is, in commenting on this thread and being responded to, I have learnt in a far more effective manner than I would do holeing myself up in a book which I wouldn't be able to understand.
I will openly admit that my knowledge of Philosophy and especially Mathematics is very limited. Any Philosophy I do know is self-taught and I have not studied maths since GCSE. Thus I am very ready to be proved wrong if I make any comment on these matters. But just because I nearly always can be proved wrong, does this mean I should not comment? I comment exactly in order to be proved wrong, so that I can learn. Otherwise, what would be the point? Why read books? So that they can prove assumptions you might have drawn wrong, or challenge your views. It would be fairly useless if everyone only ever read books that told them what they already knew.
I apologise if I have misinterpreted your tone, but there's really no need to be so snotty.
Nude
Again - you are mistakenly associating Physics and Mathematics. Physics makes use of Mathematics in describing and defining empirical laws of the physical world. Mathematical Axioms do not rely on any empirical evidence. You, and those making similar assumptions, have very likely not studied mathematics beyond A Level, and thus have very little idea of what Mathematics is - but to be in the belief that the fundamental "laws" of mathematics are as contestable as those of Physics are very much mistaken. The two areas are ultimately in stark contrast. There is nothing in any "science" which is "hard-fast", to use your terminology - however, in Mathematics there is nothing with proof which is not "hard fast". Sciences attribute earthly/humanly meaning to quantities and numbers. The numbers are never in doubt, but the meaning can always be.
To use a popular result;
18*27 = 486
That is Mathematics.
Mass*Acceleration = Force
That is Physics.
They are two fundamentally differing siutuations - you may doubt whether F=ma will always hold true, but only a retard would doubt the mathematics. You amateur Philosophers, blindly quoting other mens work, would do well by first studying in depth any area which you care to ponder and comment upon.
To use a popular result;
18*27 = 486
That is Mathematics.
Mass*Acceleration = Force
That is Physics.
They are two fundamentally differing siutuations - you may doubt whether F=ma will always hold true, but only a retard would doubt the mathematics. You amateur Philosophers, blindly quoting other mens work, would do well by first studying in depth any area which you care to ponder and comment upon.
Well put.
Although most philosophers are not questioning mathematics' validity - it's just in this thread. I would question F=ma's validity though, since it is wrong (when m is tiny).
Nude
Again - you are mistakenly associating Physics and Mathematics. Physics makes use of Mathematics in describing and defining empirical laws of the physical world. Mathematical Axioms do not rely on any empirical evidence. You, and those making similar assumptions, have very likely not studied mathematics beyond A Level, and thus have very little idea of what Mathematics is - but to be in the belief that the fundamental "laws" of mathematics are as contestable as those of Physics are very much mistaken. The two areas are ultimately in stark contrast. There is nothing in any "science" which is "hard-fast", to use your terminology - however, in Mathematics there is nothing with proof which is not "hard fast". Sciences attribute earthly/humanly meaning to quantities and numbers. The numbers are never in doubt, but the meaning can always be.
To use a popular result;
18*27 = 486
That is Mathematics.
Mass*Acceleration = Force
That is Physics.
They are two fundamentally differing siutuations - you may doubt whether F=ma will always hold true, but only a retard would doubt the mathematics. You amateur Philosophers, blindly quoting other mens work, would do well by first studying in depth any area which you care to ponder and comment upon.
To use a popular result;
18*27 = 486
That is Mathematics.
Mass*Acceleration = Force
That is Physics.
They are two fundamentally differing siutuations - you may doubt whether F=ma will always hold true, but only a retard would doubt the mathematics. You amateur Philosophers, blindly quoting other mens work, would do well by first studying in depth any area which you care to ponder and comment upon.
Ok, say Kant, Mill, Wittgenstein, Russell, Carnap, Wright, Frege etc are all retards are they?
Mill even went so far as to argue that mathematics is synthetic AND a posteriori but on your account, that's clearly only a thought a retard would have, which is why I can buy your work from any good bookshop whereas I can't get hold of a copy of Mill for love nor money. No, wait, somethings gone wrong here hasn't it?
On your account Quine wouldn't even be a retard, he'd be some sort of degenerate in-bred moronical potato.
Oddjob39A
Ok, say Kant, Mill, Wittgenstein, Russell, Carnap, Wright, Frege etc are all retards are they?
Mill even went so far as to argue that mathematics is synthetic AND a posteriori but on your account, that's clearly only a thought a retard would have, which is why I can buy your work from any good bookshop whereas I can't get hold of a copy of Mill for love nor money. No, wait, somethings gone wrong here hasn't it?
On your account Quine wouldn't even be a retard, he'd be some sort of degenerate in-bred moronical potato.
Mill even went so far as to argue that mathematics is synthetic AND a posteriori but on your account, that's clearly only a thought a retard would have, which is why I can buy your work from any good bookshop whereas I can't get hold of a copy of Mill for love nor money. No, wait, somethings gone wrong here hasn't it?
On your account Quine wouldn't even be a retard, he'd be some sort of degenerate in-bred moronical potato.
they could be. or could not. its all relative to..stuff.
I don't get why people talk about philosophy being useless in terms of employment. Obviously it's not like law or medicine (both of which lead to obvious career paths), but it's no worse than History or English!
I've looked into careers as I'm in my third year (philosopher) and there doesn't seem to be many things I'm ruled out of doing. Most graduate schemes require a 2.i in any degree discipline.
Aside from employability, as many others have said, I fail to see how it's a waste of time. Philosophy graduates are able to write coherently but at the same time are often mathematically (or at least logically) minded. I can't see how it is a waste of time. As with all arts subjects, a degree in philosophy also involves reading a variety of material, understanding it, and writing your own thoughts about it. I can't see why anyone would frown upon those skills.
I've looked into careers as I'm in my third year (philosopher) and there doesn't seem to be many things I'm ruled out of doing. Most graduate schemes require a 2.i in any degree discipline.
Aside from employability, as many others have said, I fail to see how it's a waste of time. Philosophy graduates are able to write coherently but at the same time are often mathematically (or at least logically) minded. I can't see how it is a waste of time. As with all arts subjects, a degree in philosophy also involves reading a variety of material, understanding it, and writing your own thoughts about it. I can't see why anyone would frown upon those skills.
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