a Friend

Anything goes, but keep it seemly...
any logical reasoning can be studied mathematically. I think some branch of stats covers your snake example. If you come up with some form of logic that mathematicians haven't studied, then I'm sure they will undertake a mathematical analysis of it.

Anyway getting back to the original question, the type of logic required to solve sudoku puzzles is definately mathematical, whether or not you agree that logic is a subset of mathematics.
ab

Posts: 451
Joined: 06 September 2005

Firstly Luna, thank you for the definition.
Quoting that definition certainly made my original point much clearer to understand, that is, that not all logic or reasoning is necessarily mathematical in origin.

Ab, your original statement was "All logic is actually mathematical logic, therefore sudoku logic is mathematical".
You are now saying that "Logical reasoning can be studied mathematically, and Sudoku logic is a part of this mathematical logic, therefore sudoku logic is definitely mathematical".

I am saying that "Sudoku solving is achieved using logic. This logic could be expressed verbally without the use of mathematics or could also be expressed using the symbols of mathematical logic." The application of mathematics is a convenience rather than a necessity.

Ab, would you agree or disagree with my reasoning? How about anyone else?

Yours verbally
Michael
Heuresement

Posts: 54
Joined: 19 August 2005

you say 'this logic could be expressed verbally', but the thinking is mathematical. If you did a brainscan while you were solving sudoku, the verbal parts of the brain would not light up, but the parts that would light up would be the same as the ones that light up when you do maths.

I don't think there is some area of logic that lies outside that covered by mathematics. In my opinion solving a sudoku puzzle is a mathematical activity.

I certainly disapprove of the tagline 'no maths required'. people really enjoy doing sudoku, many of whom say things like, 'I'm usually no good with numbers', what they don't realise is they are doing some maths when they solve a sudoku. It's not arithmetic, granted, but it is mathematics.
ab

Posts: 451
Joined: 06 September 2005

Ab, ignoring your proposition about how brains work, your argument is almost tautological. Your opinion is that all logic is mathematical, and therefore Sudoku solving is mathematical. If the first assertion is true, then the second assertion is always true, and can never be false.

I dispute that all logic is mathematical. As I said above, we may use some of the symbols of mathematics to describe logic, but logic is logic, as per the definition provided by Luna. Thus, I am able to say that it is my opinion that no maths is required in the logic, but solvers can apply mathematical logic if they wish.

I am however happy that you acknowledge that it is your opinion rather than a statement of fact. Without any new input, I believe that we have developed this discussion as far as we can take it, as the disagreement comes down to a matter of opinion.
Heuresement

Posts: 54
Joined: 19 August 2005

ab wrote:If you come up with some form of logic that mathematicians haven't studied, then I'm sure they will undertake a mathematical analysis of it.

ab wrote:I don't think there is some area of logic that lies outside that covered by mathematics.

Which is it?

MCC
MCC

Posts: 1275
Joined: 08 June 2005

ab wrote:I don't think there is some area of logic that lies outside that covered by mathematics.

because

ab wrote:If you come up with some form of logic that mathematicians haven't studied, then I'm sure they will undertake a mathematical analysis of it.
ab

Posts: 451
Joined: 06 September 2005

This has all the hallmarks of the old T&E / logic argument that has occupied so many lines and so few ideas in total. Not to be disparaging, it’s just that I’m getting that goldfish feeling again.

I need to know what you actually mean by mathematics. Sounds obvious - but is it? Do you mean ‘sums’ – like the maths we used to do in school – or do you mean something more than that? If you have a big wide definition of maths you could possibly argue that logic is mathematical. This is from Wikipedia – ‘Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning.’ That sounds pretty much like Luna’s definition of logic. If your definition is wide enough then you’re likely to be able to drag almost everything in under the maths umbrella.

However if you define mathematics as the ‘study’ of mathematical things and logic as a ‘process’ of valid reasoning then there are not the same – they have two different ambits, although they are obviously interrelated. The process is used in the study. Maths is logical. Is logic mathematical? It’s getting a bit Alice-in-Wonderlandy but doesn't it depend on what you mean by ‘maths’.
emm

Posts: 987
Joined: 02 July 2005

That's my point em. A lot of people think of maths as ''sums'-like the maths we used to do in school', but it is so much more than that. That's why I entered into this thread. I am not really qualified to answer the philosophical point of whether all logic is maths. Probably none of us are, which is why we can't reach a consensus.

I think quoting dictionary definitions does not necessarily help, because language is a strange thing. Some parts of the definitions quoted have little to do with this discussion. Like Heuresement I think we should beg to differ on whether sudoku requires maths.
ab

Posts: 451
Joined: 06 September 2005

Nowadays mathematics can be applied to every subject you can think of, it's ubiquitous in that respect.

A 'Subject' can stand on it's own but it can have 'Math' applied to it, the apposite word here is 'applied'.

George Boole(1815-64) wrote, what is considered to be the first work on mathematical logic 'The Mathematical Analysis of Logic' in 1847.
The title implies that there was a subject called Logic that was in existence before Maths was applied to it.

The fact that we cannot come up with a non-mathematical form of logic at this time, shows how ubiquitous 'Math' has become.

MCC
MCC

Posts: 1275
Joined: 08 June 2005

Logic is deductive reasoning and does not necessarily involve maths.

I was taught deductive reasoning as a child (although it was never given that or any other name) insofaras 'if you walk into a room that contains your mother and your father then it must be your brother who is in the toilet' (given that there were only 4 of us in the house at any one time). Simplistic I'll grant you but that's where you start. There are plenty more. For example, 'if you don't want the cat to scratch you then don't pull it's tail'.

With reference to Sudoku : if there are two yellow splodges in a chute, one to the left and one to the right, then the third yellow splodge must be in the middle.

If the triangle is in r1 and r2 then the third triangle must be in r3.

We do it all the time. Another example: 'the mere fact that my best friend chose to 'phone at 1 a.m. means that it must be important because she wouldn't phone up just for a chat at that time'

There are more complicated examples, I'm sure, but that's the best that I can come up with at the moment.

Luna
lunababy_moonchild

Posts: 659
Joined: 23 March 2005

While I'm on my soap-box as it were :
ab wrote:I think quoting dictionary definitions does not necessarily help, because language is a strange thing.

Fair enough, but you should consider that mathematics is a form of language too, and not all of us have the capability to fully understand the most complex parts of mathematics any more than all us are capable of understanding the most complex aspects of the spoken (or in this case written) language. Also, it's open to interpretation. As someone has already said - think it was em - it comes back to how the individual defines logic, and that definition is dependent upon individual interpretation as well as being in the form of spoken/written language.

Not that it matters a tosspot in the grand scheme of things. It's only a game after all.

Luna
lunababy_moonchild

Posts: 659
Joined: 23 March 2005

CathyW wrote:But you certainly don't need to add, subtract, multiply, divide ... unless you're doing a "Killer Sudoku" when addition and subtraction skills are certainly necessary I haven't tried those yet. The ones I usually do are the basic sudokus, where you just have to know what the numbers look like. ;) I did buy one book in which some of the puzzles seemed to have more than one solution--THEN later I realized that you have to have all the #'s 1 thru 9 in the long diagonals as well as in each line, column, and box! I haven't done any yet that really require math skills.
LauraU

Posts: 4
Joined: 24 March 2006

Re: a Friend

Chessmaster wrote:i told him no. he does not belive me. what should i tell him to set him right

Code: Select all
`Mathematics can be defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions`

Tell him: sorry, you're right, it needs mathematics
foxglove

Posts: 12
Joined: 04 February 2006

in a democracy majortiy rules. more people say it does not need math.
Chessmaster

Posts: 191
Joined: 21 December 2005

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