What is Logic?: Philosophy Forums

Philosophy Forums » Logic and Philosophy of Math » What is Logic? » What is Logic?

What is Logic?

Ryzor
Initiate

Usergroup: Members
Joined: Jan 14, 2008
Location: Winchester UK
Total Topics: 1
Total Posts: 16

Posted 01/15/08 - 01:36 PM: Subject: What is Logic?	#1
Much of my personal philosophy and world view is based around the use of logic (as is most peoples), but recently (last year or so) I have come to see the flaws with logic, and removed it, or reduced it's presence in some of/from some of my thinking (for example I see no logical reason for the formation of values, or even for the use of logic in personal thought besides communication) and I find myself enamoured with Nietzsche's thoughts on the matter (possibly not only his, but he is what I have read/am reading). But all my (ironically logical) dissasembly of logic in my head has not allowed me to answer one question: What is Logic? This strikes me as the great unasked question in philosophy, and I cannot think of any philosopher who has yet asked it (although my reading is far from comprehensive). How can we even start to rely on something when we dont even know what it is. That in itself is illogical. As far as I can tell, logic exists purely as a form of common communication for allowing others to understand your own views, and since we often want other people to understand our view(s) then we are forced to think logically - what Nietzsche calls the "Tyranny of Logic" - our views will not be respected or heard unless they are logical. I also see logic as the basis for the structure (possibly). From the way I see it, language is a way of communicating logic, and the structure is based on logic, not (as many philosophers have contended) that logic is a product of language. Have I missed something? Is there something more to it?
My views: Agnostic, Moral Nihilist, I ignore God if he exists. A right is only a right if it is in the law.

Incision
Graduate

Usergroup: Members
Joined: Jan 04, 2008
Location: Utah
Total Topics: 6
Total Posts: 116

Posted 01/15/08 - 02:26 PM:	#2
As a matter of fact, there is dispute over exactly what the definition of "logic" should be. Logic is just like over things this way: mathematicians can agree that 4 x 3 = 12, but the meaning of the word "mathematics" itself is more difficult. However, logicians generally agree that "logic" has two main meanings: first, something like "the study of what makes a good argument," second, roughly, "a theory or system that says what arguments are good or bad." Notice that according to these definitions, logic isn't an ability or something you can do. The first one says that logic is a field of study, like biology or economics. The second says that logic is a particular theory in that study; so in this sense there can be different "logics," such as classical logic, first-order predicate logic, fuzzy logic, and so forth. If someone says they do not believe in logic, then assuming they've got a basically correct understanding of how logicians use the word, I suppose they could mean two different things: first, they might be saying that there is no real standard whatever for reasoning. This is a strange idea and I'm not sure what I can say about it. Second, they might disagree with a particular system of logic. Dialetheists are people who deny the famous law of noncontradiction; they obviously disagree with standard logic, but many of them have alternative systems of logic, so they obviously haven't given up on the study of logic altogether. Beyond this, you might see the pinned threads in the logic forum, or look on Wikipedia.

Ryzor
Initiate

Usergroup: Members
Joined: Jan 14, 2008
Location: Winchester UK
Total Topics: 1
Total Posts: 16

Posted 01/15/08 - 02:57 PM:	#3
Thanks for the reccomendations. Further than that I am not really interested in exactly how logic works, I know enough to string together a coherent arguement (on a good day), but I would also question the VALUE of logic. Why do we value it and take it to the heart of mainstream philosophy. After all, why not illogic? Logically, it is possible to criticise logic itself. How is this possible?
My views: Agnostic, Moral Nihilist, I ignore God if he exists. A right is only a right if it is in the law.

Reformed Nihilist
Oblong

Usergroup: Administrators
Joined: Jul 15, 2004
Location: The mighty fortress of the north
Total Topics: 8
Total Posts: 7871

Posted 01/15/08 - 03:29 PM:	#4
Ryzor wrote: Thanks for the reccomendations. Further than that I am not really interested in exactly how logic works, I know enough to string together a coherent arguement (on a good day), but I would also question the VALUE of logic. Why do we value it and take it to the heart of mainstream philosophy. After all, why not illogic? Logically, it is possible to criticise logic itself. How is this possible? Typically, logic deals with just the relationship between different claims. It is usually a set of rules that says things like "A=A" is valid and "A=~A" is invallid (where "A" represents some sort of claim). Socially, in order to be understood, and in order to get along to some degree, we do have to have some level of agreement about the way we structure our language. So the reason that the claim "I am 6'1" tall while being 5'4" tall" is a bad sort of claim is that it doesn't convey any useful information to others (except that you are a nutcase). The rules of a system of logic are formalizations of the practical rules of speaking, as well as having a normative implication among reasoning humans. The problem occurs when we believe that logic is somehow a certain access to some sort of truth that goes beyond hhuman values, desires, habits and goals.
Vivian Jaffe: Have you ever transcended space and time? Albert Markovski: Yes... No... Uh, time, not space... No, I don't know what you're talking about. I Heart Huckabees (2004)

jdrw
definitely ~d1

Usergroup: Moderators
Joined: Apr 11, 2004
Location: Pennsylvania
Total Topics: 11
Total Posts: 1532

Posted 01/15/08 - 03:46 PM:	#5
By applying the laws of logic in our reasoning about our engagement with the world we dramatically increase the predictive reliability of the conclusions we generate. Claims about the world that cannot be shown to be derived logically are far less likely to prove to be reliable than claims that can be shown to be logically derived. By rigorously applying logic (and empirical evidence) in our reasoning about the world we dramatically increase the likelihood that our conclusions will actually be the case. Cheers. jd
OTOH I might be exhaustively wrong about everything I've ever thought--with the possible exception of this sentence.

Ryzor
Initiate

Usergroup: Members
Joined: Jan 14, 2008
Location: Winchester UK
Total Topics: 1
Total Posts: 16

Posted 01/16/08 - 09:50 AM:	#6
Allight guys, thanks for those ideas/explanations. My question seems to be answered.
My views: Agnostic, Moral Nihilist, I ignore God if he exists. A right is only a right if it is in the law.

sqeecoo
Graduate

Usergroup: Members
Joined: Oct 05, 2007
Total Topics: 2
Total Posts: 136

Posted 01/17/08 - 04:50 PM:	#7
I'm not sure that I would say that using logic makes our claims "reliable", and the claim A=not A is not logically invalid. But the rules of logic are the rules of our language (although we might be wrong about some of them), so if you want to be right, you would do well to use logic. I recommend Popper's "Why are the calculi of Logic and arithmetic applicable to Reality?".

Ryzor
Initiate

Usergroup: Members
Joined: Jan 14, 2008
Location: Winchester UK
Total Topics: 1
Total Posts: 16

Posted 01/18/08 - 02:25 PM:	#8
Thanks once again! If anyone else has any other ideas for books/papers/essays etc that I could read then please post them here...it would be most helpful!
My views: Agnostic, Moral Nihilist, I ignore God if he exists. A right is only a right if it is in the law.

jdrw
definitely ~d1

Usergroup: Moderators
Joined: Apr 11, 2004
Location: Pennsylvania
Total Topics: 11
Total Posts: 1532

Posted 01/18/08 - 05:13 PM:	#9
sqeecoo wrote: I'm not sure that I would say that using logic makes our claims "reliable", and the claim A=not A is not logically invalid. But the rules of logic are the rules of our language (although we might be wrong about some of them), so if you want to be right, you would do well to use logic. I recommend Popper's "Why are the calculi of Logic and arithmetic applicable to Reality?". Indeed, using logic does not make our claims about the world reliable. It’s rather that claims that can be demonstrated to be logically coherent (and supported by empirical confirmation) are far more reliably predictive on the whole than claims that cannot be demonstrated to be logically coherent. There’s a very high correlation between claims that can be reliably demonstrated to be the case and their logical coherence with other claims that can be reliably demonstrated to be the case. After I wrote the above I read some of the Popper article. I’ll finish it when I have more time. Thanks for the reference. The rules of logic, as Popper points out, are the rules of inference. Which is to say, a description of the way we think, the way we form conceptions of the world. Our language also conforms to the way we think, the way we conceive of the world. I would think that our evolved cognitive processes precede both our language and our conceptions of "logic" (which are procedural descriptions of cognitive processes.) Popper wrote: And he finds the procedure [the rules of logic] useful because he finds that, whenever he observes the rules of logic, whether consciously or intuitively, the conclusion will be true, provided the premises were true. In other words, he will be able to obtain reliable (and possibly valuable) indirect information, provided his original information was reliable and valuable. Note that Popper, too, talks about reliability as a desirable consequence of our reasoning. Perhaps he’s where I first learned the idea, I don’t remember. I find that talking about validity and demonstrable reliability is far more meaningful than talking about “truth” of our claims and conclusions Cheers. jd
OTOH I might be exhaustively wrong about everything I've ever thought--with the possible exception of this sentence.

dvy001
Aspirant

Usergroup: Members
Joined: Jan 16, 2008
Total Topics: 2
Total Posts: 35

Posted 01/19/08 - 09:53 PM:	#10
Im not sure what you talk about. Logic is bred of the 10 mathematical axioms. Things so fundamantal they do not require proof. If it wasnt for math, philosophy wouldnt exist Edited by Postmodern Beatnik on 05/30/08 - 05:51 AM. Reason: apostrophes

dvy001
Aspirant

Usergroup: Members
Joined: Jan 16, 2008
Total Topics: 2
Total Posts: 35

Posted 01/19/08 - 10:10 PM:

#11

I give you the original 10 axioms:

A-1 Every two points lie on exactly one line.

A-2 Any line segment with given endpoints may be continued in either direction.
A-3 It is possible to construct a circle with any point as its center and with a radius of any length. (This implies that there is neither an upper nor lower limit to distance. In-other-words, any distance, no mater how large can always be increased, and any distance, no mater how small can always be divided.)
A-4 If two lines cross such that a pair of adjacent angles are congruent, then each of these angles is also congruent to any other angle formed in the same way.
A-5 (Parallel Axiom): Given a line l and a point not on l, there is one and only one line which contains the point, and is parallel to l.

In addition to its axiom, Euclidean geometry is based on a number of common notions that Euclid listed in "The Elements". Unlike the axioms which deal with objects of geometry, the common notions are general rules of logic:

CN-1 Things which are equal to the same thing are also equal to one another.
CN-2 If equals be added to equals, the wholes are equal.
CN-3 If equals be subtracted from equals, the remainders are equal.
CN-4 Things which coincide with one another are equal to one another.
CN-5 The whole is greater than the part.

Euclid's goal was for these axioms and common notions to be (1) few in number

All mathematics can be derived from this and the Axiom of Choice"

Edited by Postmodern Beatnik on 05/30/08 - 06:01 AM. Reason: punctuation.

dvy001
Aspirant

Usergroup: Members
Joined: Jan 16, 2008
Total Topics: 2
Total Posts: 35

Posted 01/19/08 - 10:17 PM:	#12
These 10 axioms and the Axiiom of Choice derive all logic. i dont see the issue. Edited by Postmodern Beatnik on 05/30/08 - 06:03 AM. Reason: apostrophes, capitalization.

dvy001
Aspirant

Usergroup: Members
Joined: Jan 16, 2008
Total Topics: 2
Total Posts: 35

Posted 01/19/08 - 10:22 PM:	#13
These 10 axioms derived all equations in geometry , astronomy, physics, chemistry and biology.

sqeecoo
Graduate

Usergroup: Members
Joined: Oct 05, 2007
Total Topics: 2
Total Posts: 136

Posted 01/20/08 - 03:27 AM:	#14
Hm, my post is blank. Don't know why. Too bad, I liked it Anyway, what I said was that I agree with you jdrw about that article and logic in general, and that I am glad you read it. However, I have to point out that Popper says we can never have reliability, and that we can never verify our claims in a meaningful way. Try reading more on induction and falsification in his "conjectures and refutations", the book where you probably found that article. Cheers mate!

sqeecoo
Graduate

Usergroup: Members
Joined: Oct 05, 2007
Total Topics: 2
Total Posts: 136

Posted 01/20/08 - 08:40 AM:	#15
Hey, here's another article about the rules of logic, and incidentally also about Popper: http://www2.warwick.ac.uk/fac/soc/philosophy/staf... A small quotation: D. Miller wrote: A more promising approach, more congenial to critical rationalism, is to volunteer the rules of deduction as conjectures, and to invite all comers to identify counterexamples to them. Critical rationalists will not be flustered by the platitude that, here as elsewhere, a failure to falsify a conjecture provides no shred of justification for it; a rule is not justified because no counterexample has been found.

muxol
yuletide

Usergroup: Members
Joined: Dec 07, 2003
Total Topics: 1
Total Posts: 1843

Posted 02/02/08 - 02:53 PM:	#16
Logic is an entity without identity. Good joke, huh?

Stinky Malinky
Student

Usergroup: Members
Joined: Apr 17, 2006
Total Topics: 2
Total Posts: 77

Posted 02/02/08 - 04:33 PM:	#17
Reformed Nihilist wrote: Typically, logic deals with just the relationship between different claims. It is usually a set of rules that says things like "A=A" is valid and "A=~A" is invallid (where "A" represents some sort of claim). Socially, in order to be understood, and in order to get along to some degree, we do have to have some level of agreement about the way we structure our language. So the reason that the claim "I am 6'1" tall while being 5'4" tall" is a bad sort of claim is that it doesn't convey any useful information to others (except that you are a nutcase). The rules of a system of logic are formalizations of the practical rules of speaking, as well as having a normative implication among reasoning humans. The problem occurs when we believe that logic is somehow a certain access to some sort of truth that goes beyond hhuman values, desires, habits and goals. Are you claiming that logic is subjective, a social construct? If everybody were suddenly struck with complete aphasia, would it become possible for me to be 6'1" while being 5'4"?

diotimajsh
Kinda twitchy these days

Usergroup: Members
Joined: Jun 06, 2007
Total Topics: 0
Total Posts: 39

Posted 02/04/08 - 12:29 AM:	#18
dvy001 wrote: All mathematics can be derived from this and the Axiom of Choice" This isn't actually true. Non-Euclidean geometry, as the name indicates, studies what results from rejecting or tweaking Euclid's original axioms. In hyperbolic geometry, for example, there are an infinite number of lines which pass through one point without intersecting the line in question (contrary to A5). Furthermore, it is not an established truth that "logic is bred from mathematics"--on the contrary, Bertrand Russell and Alfred North Whitehead actually tried to show that mathematics is derivable from logic, although they didn't necessarily succeed.
http://doubt-rests.blogspot.com/

Gort
Initiate

Usergroup: Members
Joined: Apr 17, 2008
Total Topics: 0
Total Posts: 11

Posted 04/17/08 - 05:01 PM:	#19
Reply to post #12 Euclid's Axioms are not sufficient to ground the geometry of the plane. Hilbert remedied this defect in -Grundlagen der Geometrie- in 1899. Euclid invoked assumptions that he did not list explicitly. For example, in establishing congruence he assumed a triangle could be moved from one place to another. This is not included in any of the axioms/postulates of -The Elements- Gort ( I really wanted to be Klaatu, but someone beat me to it)

Reformed Nihilist
Oblong

Usergroup: Administrators
Joined: Jul 15, 2004
Location: The mighty fortress of the north
Total Topics: 8
Total Posts: 7871

Posted 04/18/08 - 07:19 AM:	#20
Stinky Malinky wrote: Are you claiming that logic is subjective, a social construct? If everybody were suddenly struck with complete aphasia, would it become possible for me to be 6Æ‡" while being 5ÆŠ"? 1- Social constructs are not subjective. 2- Yes, logic is clearly and observably a social construct. 3- You height isn't a matter of logic, it is a matter of empirical fact. 4- If everybody were struck by aphasia either meaningfull language would be impossible or ther current meanings (and truth value, by extention) of claims would be altered.
Vivian Jaffe: Have you ever transcended space and time? Albert Markovski: Yes... No... Uh, time, not space... No, I don't know what you're talking about. I Heart Huckabees (2004)

ManiacJack
Dictator

Usergroup: Members
Joined: May 29, 2008
Location: austin tx
Total Topics: 19
Total Posts: 274

Posted 05/29/08 - 08:49 PM:	#21
Logic, in essence, is causality. If, then. language is an emotional construct. Logic is a construct around that. Ethics encompasses both. For more linear thought, language is a foundation for the rules of logic. Like Reformed Nihilist said: The problem occurs when we believe that logic is somehow a certain access to some sort of truth that goes beyond human values, desires, habits and goals. Geometry rocks! Edited by Postmodern Beatnik on 05/30/08 - 05:49 AM. Reason: capitalization
Why make Sense When You Can Make Dollars? "Although I am a typical loner in daily life, my consciousness of belonging to the invisible community of those who strive for truth, beauty, and justice has preserved me from feeling isolated." -Spacetime Bustin' Albert Muther F*cking Einstein

You don't have permission to post.

Please login or register.