Logic is Empty

1. Philosophy Forum
2. » Logic
3. » Logic is Empty

Fri 4 Jun, 2010 11:39 pm
Ok, that's a playful title, because I want to lure folks in. The logic I am calling empty is formal logic. I call it empty because the more formal it is, the emptier it is. I feel that Wittgenstein went out of his way to point out how little formal logic tells us. (to wit, nothing.)

Quote:

5.551 Our fundamental principle is that whenever a question can be
decided by logic at all it must be possible to decide it without more
ado. (And if we get into a position where we have to look at the world
for an answer to such a problem, that shows that we are on a completely
wrong track.)

Quote:

6.1 The propositions of logic are tautologies.
6.11 Therefore the propositions of logic say nothing. (They are the
analytic propositions.)

TuringEquivalent

Sat 5 Jun, 2010 04:20 am
@Reconstructo,
Logic is not empty. You have all these axioms, and they are surely something, thus, logic is not empty .:shifty:

xris

Sat 5 Jun, 2010 04:50 am
@TuringEquivalent,
As I don't understand formal logic , it appears incapable of giving actual examples and lives in world all of its own, I cant comment. Formal education on the subject appears essential to give a valid reply. To me the statement is contradictory, if it has no value , logic, then it has been based on ill informed information.

jgweed

Sat 5 Jun, 2010 07:07 am
@Reconstructo,
Formal logic only concerns the validity of an argument or chain of arguments; a logical argument is so because it obeys the laws of correct thinking.
Truth comes into play only when the X,Y,Zs used to exhibit logical structure are filled by reality. All X is Y only takes on existential truthfulness, importance, and meaning when it becomes the tautology but nevertheless an expanding statement "All human beings are mortal beings."

If one were to take very simple arguments, Wittgenstein has a point when he says they are tautological in nature, since we immediately "know" in a sense, the conclusion when we glance at the premises. "All that just to prove JGW is mortal." And one could also say that about even very long and complicated arguments except that we often need to be able to follow the argument's steps to really understand it. It is only then that we can look back at it and say the conclusion is "clear as day now" and "I knew it all the time" and so on. It's tautological nature is understood in hindsight.

Sometimes people will take a tool of philosophical thinking for the thinking itself, for philosophy itself because of the powerful ways it aids the activity; but at the same time, philosophy must concern itself with the truth of each of the propositions or components in a logical argument or exposition.

Owen phil

Sat 5 Jun, 2010 07:13 am
@xris,
xris;173320 wrote:
As I don't understand formal logic , it appears incapable of giving actual examples and lives in world all of its own, I cant comment. Formal education on the subject appears essential to give a valid reply. To me the statement is contradictory, if it has no value , logic, then it has been based on ill informed information.

I agree that "Logic is Empty" is an incorrect conclusion, even if 'Logic' only consists of tautologies.
That tautologies are senseless is granted by Wittgenstein because of his interpretation (understanding) that only empirical propositions have sense.

For an 'actual' example, the tautology (2+2=4) is not without sense, in virtue of its generalized application to the world of sense.

eg. (2x +2x = 4x) for all objects x, means that two of anything in the world added to two of anything in the world is equal to four of anything in the world.

If logical/mathematical tautologies were meaningless then there would be no application to logic/math at all.
Because we do know that logic/math has application, we can deny that tautologies are without sense, that is, we can deny that Logic is Empty.

I don't agree that formal education on the subject is needed to give an opinion on this subject.

xris: "To me the statement is contradictory, if it has no value , logic, then it has been based on ill informed information."

This remark seems to me as valid as any other remark on the issue.
Logical tautologies are indeed useful to explain and verify/validate such remarks.

xris

Sat 5 Jun, 2010 07:17 am
@jgweed,
Can you tell me, when X is never the same, why it should represent anything in fact. Mathematical logic could only apply if everything was scrutinised with the same mathematical logic. I can never find an exact relationship in formal logic to reality. X could be Y but X is never Y and X is not always X . Sorry for my ignorance on this subject but my logic is not sufficient.

---------- Post added 06-05-2010 at 08:18 AM ----------

Owen;173345 wrote:
I agree that "Logic is Empty" is an incorrect conclusion, even if 'Logic' only consists of tautologies.
That tautologies are senseless is granted by Wittgenstein because of his interpretation (understanding) that only empirical propositions have sense.

For an 'actual' example, the tautology (2+2=4) is not without sense, in virtue of its generalized application to the world of sense.

eg. (2x +2x = 4x) for all objects x, means that two of anything in the world added to two of anything in the world is equal to four of anything in the world.

If logical/mathematical tautologies were meaningless then there would be no application to logic/math at all.
Because we do know that logic/math has application, we can deny that tautologies are without sense, that is, we can deny that Logic is Empty.

I don't agree that formal education on the subject is needed to give an opinion on this subject.

xris: "To me the statement is contradictory, if it has no value , logic, then it has been based on ill informed information."

This remark seems to me as valid as any other remark on the issue.
Logical tautologies are indeed useful to explain and verify/validate such remarks.
Sorry but I was writing the last post and then saw yours..I am about to read it.

---------- Post added 06-05-2010 at 08:32 AM ----------

Owen;173345 wrote:
I agree that "Logic is Empty" is an incorrect conclusion, even if 'Logic' only consists of tautologies.
That tautologies are senseless is granted by Wittgenstein because of his interpretation (understanding) that only empirical propositions have sense.

For an 'actual' example, the tautology (2+2=4) is not without sense, in virtue of its generalized application to the world of sense.

eg. (2x +2x = 4x) for all objects x, means that two of anything in the world added to two of anything in the world is equal to four of anything in the world.

If logical/mathematical tautologies were meaningless then there would be no application to logic/math at all.
Because we do know that logic/math has application, we can deny that tautologies are without sense, that is, we can deny that Logic is Empty.

I don't agree that formal education on the subject is needed to give an opinion on this subject.

xris: "To me the statement is contradictory, if it has no value , logic, then it has been based on ill informed information."

This remark seems to me as valid as any other remark on the issue.
Logical tautologies are indeed useful to explain and verify/validate such remarks.
I can understand the logic of pure maths, it can not be denied but the relationship to its understanding with reality always bemuses me. It appears an exercise rather than have any real value. Thanks xris

Owen phil

Sat 5 Jun, 2010 07:56 am
@xris,
xris;173346 wrote:
Can you tell me, when X is never the same, why it should represent anything in fact. Mathematical logic could only apply if everything was scrutinised with the same mathematical logic. I can never find an exact relationship in formal logic to reality. X could be Y but X is never Y and X is not always X . Sorry for my ignorance on this subject but my logic is not sufficient.

---------- Post added 06-05-2010 at 08:18 AM ----------

Sorry but I was writing the last post and then saw yours..I am about to read it.

---------- Post added 06-05-2010 at 08:32 AM ----------

I can understand the logic of pure maths, it can not be denied but the relationship to its understanding with reality always bemuses me. It appears an exercise rather than have any real value. Thanks xris

I think that there is 'real' value in logic and mathematics as to application.

We can understand the world better and easier, if we can sort out the not so obvious errors of our reasoning with the aid of logic and mathematics.

eg. (p or ~p) is true and applies to any proposition whatever, empirical or not.
It's that kind of generality that makes the pursuit of logic worthwhile, imo.

Reconstructo

Sat 5 Jun, 2010 10:07 am
@Owen phil,
Owen;173356 wrote:
I think that there is 'real' value in logic and mathematics as to application.

We can understand the world better and easier, if we can sort out the not so obvious errors of our reasoning with the aid of logic and mathematics.

I agree. I gave this thread a playfully aggressive title just to get a good discussion of the nature of logic going.

---------- Post added 06-05-2010 at 11:09 AM ----------

TuringEquivalent;173313 wrote:
Logic is not empty. You have all these axioms, and they are surely something, thus, logic is not empty .:shifty:

Actually I said it gets more empty as it gets more formal, not that it was empty. The thread title is an exaggeration to bring the troops in.

---------- Post added 06-05-2010 at 11:38 AM ----------

Owen;173345 wrote:

For an 'actual' example, the tautology (2+2=4) is not without sense, in virtue of its generalized application to the world of sense.

This is a great thing to mention, for I am really looking at the grounding intuition of math and logic. Is 2 + 2 = 4 a tautology? In a way, yes. From another angle it's more complicated. Because we have the numerals and the number "behind" the numerals. As you may know, logicism has its problems as far as grounding mathematics is concerned. What is the basic abstraction of number and how does it related to the basic abstraction that grounds formal logic? Propositions seem like bits to me. Bits are the simplest kinds of numbers. I am quite curious to find and contemplate the root(s) of mathematics and logic.

I should stress that I do think logic is useful, even at its emptiest. We can draw necessary conclusions from more complex situations, just as in math we can transform groups of symbols according to rules and discover useful information implicit in less immediately useful information.

One of the main points I want to emphasize is that logic has an intuitive foundation, or so it seems to me. And this would be the transcendental aspect of logic, which cannot (so far as I can tell) itself be logically justified. My goal is not to attack logic but to point at its grounds. What do you make of this?
Quote:

3.334 The rules of logical syntax must go without saying, once we know
how each individual sign signifies.
5.122 If p follows from q, the sense of 'p' is contained in the sense of
'q'.
I think as we move into the real world, we move away from the perfect digital (binary) clarity of abstract propositions (bits).
No doubt many users of logic recognize that P or not P is as plain as day if P is conceived of as a bit/abstract proposition. But I fear
there are some who have not really looked at what's going on here, have not considered that the rules of logic are not handed down by God but rather are formalizations of what is really quite obvious to us on a fundamental level.

xris

Sat 5 Jun, 2010 10:49 am
@Owen phil,
Owen;173356 wrote:
I think that there is 'real' value in logic and mathematics as to application.

We can understand the world better and easier, if we can sort out the not so obvious errors of our reasoning with the aid of logic and mathematics.

eg. (p or ~p) is true and applies to any proposition whatever, empirical or not.
It's that kind of generality that makes the pursuit of logic worthwhile, imo.

Sorry but can you give an example where this could be used in a realistic logical problem that would not be obvious without it. Thanks xris

Sat 5 Jun, 2010 12:56 pm
@xris,
Formal logic is empty. It is a black box, a tool, a method. Input Facts. Calculate using an axiom. Reject or accept output. Saying logic has inherent meaning (this is how I am interpreting Full vs. Empty) is like saying the processes inside my calculator has inherent meaning. Anything gained from logic is based on the axiomatic presuppositions,the motivation and predisposition of the 'thinker' and the very idea that one must use that particular calculatory black box to think correctly.

Reconstructo

Sat 5 Jun, 2010 01:04 pm
Saying logic has inherent meaning (this is how I am interpreting Full vs. Empty) is like saying the processes inside my calculator has inherent meaning.

I agree. Logic it its most abstract is a tautology calculator. It's just math with bits and truth tables. As soon as one hooks it up to language that means something to our lives, one runs into the slipperiness of this meaning.
To define truth, the self, justice, beauty, purpose, love, etc. is simply beyond the ability of logic, and yet these are essential theme in philosophy. There's just no dodging dialectic if one is serious about foolosophy.

xris

Sat 5 Jun, 2010 01:16 pm
@Reconstructo,
Reconstructo;173452 wrote:
I agree. Logic it its most abstract is a tautology calculator. It's just math with bits and truth tables. As soon as one hooks it up to language that means something to our lives, one runs into the slipperiness of this meaning.
To define truth, the self, justice, beauty, purpose, love, etc. is simply beyond the ability of logic, and yet these are essential theme in philosophy. There's just no dodging dialectic if one is serious about foolosophy.

logic is not a useless tool, its this mathematical reasoning that tries to tell me how to be logical that bewilders me, its a half empty bottle that cant really tell me if its half empty or half full. I can love but logic will give me the confidence to reject it. It aids my respect, it guides my morality.

Reconstructo

Sat 5 Jun, 2010 02:35 pm
@xris,
xris;173455 wrote:
logic is not a useless tool, its this mathematical reasoning that tries to tell me how to be logical that bewilders me, its a half empty bottle that cant really tell me if its half empty or half full. I can love but logic will give me the confidence to reject it. It aids my respect, it guides my morality.

Yes, the real or more important logic is dialectic or reason. Formal logic is must less useful, because it's just too empty. And formal logic is the creation of dialectic/reason in the first place. Formal logic is just intuition in an efficient symbolic form.

Dr Seuss

Sun 6 Jun, 2010 07:21 pm
Logic is the illusion we come up with to try to explain that which was unexplainable. Since its based on language and its symbols, we are governed by language and its symbols. And if we were to remove that from you then you will be faced with the Real of logic. If we were to remove and cut off the signified's i.e. the concepts from the signifier i.e. the acoustic image (the word) all you will be left with is the Real (that which you cannot put to words or symbolize). Logic therefore is nothing masked as something. Because the Real of words are meaningless symbols, sounds, and images.

Reconstructo

Sun 6 Jun, 2010 07:24 pm
@Dr Seuss,
Dr. Seuss;174001 wrote:
Logic is the illusion we come up with to try to explain that which was unexplainable. Since its based on language and its symbols, we are governed by language and its symbols. And if we were to remove that from you then you will be faced with the Real of logic. If we were to remove and cut off the signified's i.e. the concepts from the signifier i.e. the acoustic image (the word) all you will be left with is the Real (that which you cannot put to words or symbolize). Logic therefore is nothing masked as something. Because words alone are just symbols, sounds, and images.

I am quite interested in the Real. I have some exposure to Lacan, and I find him fascinating. But besides Lacan I have been quite fascinated by the irreducibility of sensation and emotion, which presumably connects w/ Lacan's Real. Perhaps this isn't the thread to go into it, but it's a great subject. If you feel like it, start a thread on the Real. Or I have already started a thread called the Ineffable about the same sort of thing.

ughaibu

Sun 6 Jun, 2010 07:32 pm
@Owen phil,
Owen;173356 wrote:
(p or ~p) is true and applies to any proposition whatever, empirical or not.
It's that kind of generality that makes the pursuit of logic worthwhile, imo.
But it's not true in intuitionistic logics.

Reconstructo

Sun 6 Jun, 2010 07:43 pm
@ughaibu,
ughaibu;174006 wrote:
But it's not true in intuitionistic logics.

Terse as ever! I would love to hear whatever information you have on this sort of thing.

ughaibu

Sun 6 Jun, 2010 07:52 pm
@Reconstructo,
Reconstructo;174015 wrote:
I would love to hear whatever information you have on this sort of thing.
Stanford is usually a good place to start: Intuitionistic Logic (Stanford Encyclopedia of Philosophy)

Reconstructo

Sun 6 Jun, 2010 07:56 pm
@Reconstructo,
I like the LEM. It gives us the bit. The bit is the ultimate reduction of information, it seems. And this is large part of the beauty in logic, I think. Absolute form. Yes or no. P or ~P.

LEM helps keep logic empty?

ughaibu

Sun 6 Jun, 2010 08:10 pm
@Reconstructo,
Reconstructo;174020 wrote:
I like the LEM.
An equivalent is a implies b, or, b implies a, do you think this principle is true?

1. Philosophy Forum
2. » Logic
3. » Logic is Empty