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Defining Unity

 
 
Reply Thu 27 May, 2010 12:34 am
Frege mentions the difficulty of defining unity in his book on arithmetic. I agree. I think it's an intuition, something hard-wired. But that's just my opinion. I invite you to define unity, or oneness, etc. You can use synonyms, but that's not ideal, for obvious reasons. What is it for something to be singular, or one?
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Reconstructo
 
  1  
Reply Thu 27 May, 2010 02:21 pm
@Reconstructo,
100101011101110100100100111010100101 Is there a simpler code?
Fil Albuquerque
 
  1  
Reply Thu 27 May, 2010 03:01 pm
@Reconstructo,
Reconstructo;169686 wrote:
100101011101110100100100111010100101 Is there a simpler code?

...1, -1, 1, -1, 1, -1, 1...
Reconstructo
 
  1  
Reply Thu 27 May, 2010 03:32 pm
@Fil Albuquerque,
Fil. Albuquerque;169697 wrote:
...1, -1, 1, -1, 1, -1, 1...


Same difference! This is still just two symbols. Smile

One could also use spaces, but the spaces are the presence of an absence. Zeroes or negative ones are just convenient ways to represent what a space represents.
1 111 1 1 1 111 1 1 111 1 1 1 1 1 1
Fil Albuquerque
 
  1  
Reply Fri 28 May, 2010 06:50 am
@Reconstructo,
Reconstructo;169709 wrote:
Same difference! This is still just two symbols. Smile

One could also use spaces, but the spaces are the presence of an absence. Zeroes or negative ones are just convenient ways to represent what a space represents.
1 111 1 1 1 111 1 1 111 1 1 1 1 1 1


I am sorry, the spaces are just for the purpose of not reading eleven...the point was about not changing to mutch from One to anything else...something like, one, and not one has the shadow of one....Smile

So, for the purpose in here, not one, (-1), represents zero...(I am pointing to a false absence...)
Reconstructo
 
  1  
Reply Fri 28 May, 2010 01:30 pm
@Fil Albuquerque,
Fil. Albuquerque;169903 wrote:
I am sorry, the spaces are just for the purpose of not reading eleven...the point was about not changing to mutch from One to anything else...something like, one, and not one has the shadow of one....Smile

So, for the purpose in here, not one, (-1), represents zero...(I am pointing to a false absence...)


The spaces could be seen as unwritten numbers. It doesn't matter what visual representation we use. Of course "0" and "-1" are better. I just used spaces to argue that any two glyphs will do.

Of course this is off the main topic of unity. What do you think about unity? Are we born with an intuition of it? Is nature in itself, apart from man, if such a thing can be, already unified?

Does the concept of unity found arithmetic and our concept of number? Or concepts like being and nothingness? Or the self?
0 Replies
 
Twirlip
 
  1  
Reply Sun 30 May, 2010 10:20 am
@Reconstructo,
I'm afraid my answer would have to be the rather dry one (at least at first sight) that Frege was right about this, in sections 54 and 55 of his The Foundations of Arithmetic.

However, I find at least one crucial passage in section 54 obscure. In the second, long paragraph, after the main thesis of this section, which is that it would be a good idea to "call a concept the unit relative to the Number which belongs to it", he immediately goes on to try to make some sort of distinction between what might be called (although he does not use the terms) discrete and continuous concepts. Although I appreciate the need for some such distinction, I find his version of it unintelligible. (This admission may prompt me to have another go at understanding it.)

Section 55, defining (among other things) what it means for the number 1 to belong to a concept - he later goes on to explain that this does not yet define the number 1 as an object - raises (as does Russell's theory of definite descriptions) the question of what it means for two things to be "the same" or "equal" or "identical" - but let's leave that question for the thread with the title "The same"!
Night Ripper
 
  1  
Reply Sun 30 May, 2010 10:26 am
@Reconstructo,
Reconstructo;169438 wrote:
Frege mentions the difficulty of defining unity in his book on arithmetic. I agree. I think it's an intuition, something hard-wired. But that's just my opinion. I invite you to define unity, or oneness, etc. You can use synonyms, but that's not ideal, for obvious reasons. What is it for something to be singular, or one?


The smallest whole unit.

It's fairly easy to see the differences between half a pig, a whole pig and two pigs.
Twirlip
 
  1  
Reply Sun 30 May, 2010 10:40 am
@Night Ripper,
Night Ripper;170856 wrote:
The smallest whole unit.

It's fairly easy to see the differences between half a pig, a whole pig and two pigs.

What about one pair of pigs?
Night Ripper
 
  1  
Reply Sun 30 May, 2010 10:42 am
@Twirlip,
Twirlip;170861 wrote:
What about one pair of pigs?
0 Replies
 
Reconstructo
 
  1  
Reply Sun 30 May, 2010 03:30 pm
@Twirlip,
Twirlip;170852 wrote:
I'm afraid my answer would have to be the rather dry one (at least at first sight) that Frege was right about this, in sections 54 and 55 of his The Foundations of Arithmetic.

However, I find at least one crucial passage in section 54 obscure. In the second, long paragraph, after the main thesis of this section, which is that it would be a good idea to "call a concept the unit relative to the Number which belongs to it", he immediately goes on to try to make some sort of distinction between what might be called (although he does not use the terms) discrete and continuous concepts. Although I appreciate the need for some such distinction, I find his version of it unintelligible. (This admission may prompt me to have another go at understanding it.)

Section 55, defining (among other things) what it means for the number 1 to belong to a concept - he later goes on to explain that this does not yet define the number 1 as an object - raises (as does Russell's theory of definite descriptions) the question of what it means for two things to be "the same" or "equal" or "identical" - but let's leave that question for the thread with the title "The same"!


Yes, I was reading this book lately. He is better at showing the faults of other explanations than really driving his own point home. I felt in the end that I vaguely agreed with him, but I was surprised (and am repeatedly surprised) that no one hammers the ESSENCE home. The ONE! How can we neglect the ultimate atom of number? It deserves an entire book, this cornerstone. But Frege was good all and all. Smile

---------- Post added 05-30-2010 at 04:32 PM ----------

Night Ripper;170856 wrote:
The smallest whole unit.

It's fairly easy to see the differences between half a pig, a whole pig and two pigs.



Yes, but that is not adding anything. I say this respectfully. I understand in the usual sense the concept of unity. In fact, I probably have put more thought into it than most, for whom it is just a given. I'm saying given by what? And I'm saying it's a Platonic Form of sorts, and fundamental to the structure of human thought. All of our abstractions and not just mathematics. Can we define unity non-redundantly? Or is it something we just understand. Without being able to further reduce this intuition/understanding?
0 Replies
 
 

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