Understanding Logic: A Beginner's Guide to Philosophy

[Kerrie]

For those of us who are still learning and understanding philosophy, can we differentiate logic in the most simple terms?

 

[Mentat]

Originally posted by Kerrie
For those of us who are still learning and understanding philosophy, can we differentiate logic in the most simple terms?

Differentiate logic from what?

 

[jammieg]

The most practical and simplistic definition I've so far heard is, "logic makes things better"- Marylin Savant

 

[Mentat]

Kerrie, did you mean to "define" logic?

 

[FZ+]

Formalised reasoning?

 

[quantumdude]

A good working definition of logic is that it is the set of prescriptive (as opposed to descriptive) laws of reasoning.

If I may do a little cut-and-paste job from my Logic Notes:

[?] Is logic the study of the laws of thought?
That’s too broad. There is plenty of thought that logic is not concerned with. For example, imagining two-headed goats is thought, but the logician does not care about that. We are interested in that particular subset of thought called reasoning

[?]Ah, so logic is the study of the laws of reasoning then, right?
Still too broad, and the root of the problem lies in the two uses of the word “law”. Laws can be either descriptive or prescriptive. A descriptive law is a statement of how something is done, as in the laws of nature. They cannot be broken or repealed. On the other hand, a prescriptive law is a statement of how something should be done, as in the laws set forth by a legislature. They can be broken and changed. The study of the descriptive laws of reason (how people do, in fact, reason) is not logic, but psychology. But the study of the prescriptive laws of reason (how people ought to reason) is logic.

[?]So, we are interested in the latter—the prescriptive laws of reasoning.
Correct. That will be our definition of logic throughout this study

 

[Kerrie]

Originally posted by Tom
On the other hand, a prescriptive law is a statement of how something should be done, as in the laws set forth by a legislature. They can be broken and changed. The study of the descriptive laws of reason (how people do, in fact, reason) is not logic, but psychology. But the study of the prescriptive laws of reason (how people ought to reason) is logic.

[?]So, we are interested in the latter—the prescriptive laws of reasoning.
Correct. That will be our definition of logic throughout this study[/I] [/B]

so who or what determines "should" be done? or how it should be done?

 

[quantumdude]

Originally posted by Kerrie
so who or what determines "should" be done? or how it should be done?

Keeping to the simple example of a 2-valued logic (T and F), we have a variety of logical inferences that can always be trusted, as well as some that cannot be trusted. Logical forms can be shown to be either valid or invalid by Venn diagrams (in syllogistic logic) or truth tables (in propositional logic). That is, we can determine with certainty whether a logical form always leads from true premises to a true conclusion. If it does then it is valid, and if not then it is invalid.

Note that establishing validity does not tell us whether or not the premises are actually true, it merely tells us that if the premises are true, then the conclusion is also true.

From the Stanford Encyclopedia of Philosophy, in an article called Logical Form, we find the following discussion (color emphasis mine):

Some inferences are impeccable[/color].

Consider:

(1) John danced if Mary sang, and Mary sang; so John danced.
(2) Every politician is deceitful, and every senator is a politician; so every senator is deceitful.
(3) The tallest man is in the garden; so someone is in the garden.

Such reasoning cannot lead from true premises to false conclusions.[/color] The premises may be false. But a thinker takes no epistemic risk by endorsing the conditional claim: if the premises are true, then the conclusion is true.[/color] Given the premises, the conclusion follows immediately--without any further assumptions that might turn out to be false. By contrast, it would be very risky to infer that John danced, given only the assumption that Mary sang. More interesting examples include:

(4) John danced if Mary sang, and John danced; so Mary sang.
(5) Every hairless biped is a bird, Tweety is a hairless biped; so Tweety can fly.
(6) Every human born before 1850 has died; so every human will die.

Inference (4) is not secure. Suppose John dances whenever Mary sings, and he sometimes dances when Mary doesn't sing. Similarly, (5) relies on unstated assumptions--e.g., that Tweety is not a penguin. Even (6) falls short of the demonstrative character exhibited by (1-3). While laws of nature may preclude immortality, it is conceivable that someone will escape the grim reaper; and the conclusion of (6) goes beyond its premise, even if it is (in some sense) foolish to resist the inference.

Appeals to logical form arose in the context of attempts to say more about this intuitive distinction between impeccable inferences, which invite metaphors of security and immediacy, and inferences that involve a risk of slipping from truth to falsity.[/color]

There's a lot more there, but I think the question is answered with what I presented here. The validity of some reasoning and the invalidity of others is determined by philosophers and mathematicians (this is where philosophy and math overlap) who find such "impeccable inferrences".

 

[scott_sieger]

Philisophically speaking (ha I love the length of that word)

Some one once said to me

"There is a logic for everything and everything has a logic"

"There is a science for everything and everything has a science"

The logic I love the most is the logic of music, it is so infinite in it's application, the logic of a performer giving it all, the logic of the audience with tears in their eyes, the logic of rhythm and melodies, counterpoint, harmony, harmonics and discord.

The logic of what is it? hmmm 72 notes ,just add humanity and wow what a outcome.

I am sailing...I am sailing...home again ...cross the sea. I am sailing stormy waters to be near you to be free...(Rod Stewart)

Ha ...i'm going to cry... and i can tell you if you look hard enough you'll find that response quite logical to.

 

[Mentat]

Originally posted by scott_sieger
Philisophically speaking (ha I love the length of that word)

Are you one given to sesquipedalian extravagance?

 

[scott_sieger]

actuallymydictionaryhasbeencensoredhavingallwordsinexcessofonefootinlengthdeletedandsotomakeupforitijustaddafewlettersandalittleextrameaningandwellificanunderstanditthenIassumethatyoucantoo. And if you can't I would suggest you get a dictionary like mine that has been censored, having all words in excess of one foot deleted, and so to make up for it i...

 

[phoenixthoth]

Such reasoning cannot lead from true premises to false conclusions. The premises may be false. But a thinker takes no epistemic risk by endorsing the conditional claim: if the premises are true, then the conclusion is true. Given the premises, the conclusion follows immediately--without any further assumptions that might turn out to be false. By contrast, it would be very risky to infer that John danced, given only the assumption that Mary sang. More interesting examples include:

in particular:

Given the premises, the conclusion follows immediately--without any further assumptions that might turn out to be false.

this is correct as long as one realizes that one of the premises is that ((A-->B)&A)-->B is true for all statements A and B. or you could say by definition of -->.

 

[Jeebus]

Originally posted by Kerrie
For those of us who are still learning and understanding philosophy, can we differentiate logic in the most simple terms?

I would say that it is deductive and inductive arguments from previously stated points that theorize the wrong of a system/design, which is not supposed to be based on emotion or whim but is often substituted for those purposes and principles.

 

[phoenixthoth]

I would say that it is deductive and inductive arguments from previously stated points that theorize the wrong of a system/design, which is not supposed to be based on emotion or whim but is often substituted for those purposes and principles.

check out http://mathworld.wolfram.com/PropositionalCalculus.html. it gives some axiom schemata for formal logic. i guess most people would say that (11), modus ponens, is the most important one.

these all seem like whims to me though they don't seem to be based on emotion. however, once you accept those axiom schemata which i could call whims, the theorems that follow from them are not of the whim variety.

 

[Jeebus]

Originally posted by phoenixthoth
check out http://mathworld.wolfram.com/PropositionalCalculus.html. it gives some axiom schemata for formal logic. i guess most people would say that (11), modus ponens, is the most important one.

these all seem like whims to me though they don't seem to be based on emotion. however, once you accept those axiom schemata which i could call whims, the theorems that follow from them are not of the whim variety.

Ok, I see what you mean by the whims of Modus Ponens, but all formal logic has to deal with some level of truth from that given someone. All logic has to be supplied and attributed to axiom schemata's, and axioms help provide information for theories, which in turn could form into laws.

So in conclusion all logic, could be a form of mental projection of whim and and absolute immplicit reason without a(n) of option of a doubt in their mind? And for that matter wouldn't logic have to have a basis of rule or law with propositional statistics to support that idea?

You could make a connection and say that logic is extremely parallel to faith, couldn't you in some cases?

 

[phoenixthoth]

dictionary.com provides definitions of the word faith, of which, here are two:
1. Confident belief in the truth, value, or trustworthiness of a person, idea, or thing.
2. Belief that does not rest on logical proof or material evidence. See Synonyms at belief. See Synonyms at trust.

axioms do not rest on logical proof but one could say they do rest on material evidence. one who would say they rest on material evidence wouldn't be having faith in those axioms as in the second sense of faith. the first sense of faith makes it seem as though whenever one is confident in the truth of something that faith is involved.

just for fun, i was wondering what would happen if instead of adopting a definition of if/then, symbolized by A→B, and a definition of and, symbolized by A∧B, and then proving that modus ponens is a tautology, what would happen if we assume the definition of ∧ and that modus ponens is a tautology? would that force the definition of A→B?

ok, one usually says that A→B is defined by this truth table:
A B A→B
T T T
T F F
F T T
F F T.

but let's leave it open:
A B A→B
T T ?
T F ?
F T ?
F F ?

two assumptions:
A B A∧B
T T T
T F F
F T F
F F F

and that modus ponens is a tautology:
A B ((A→B)∧A)→B
T T T
T F T
F T T
F F T.

using these assumptions, can we solve for the ?'s?

let's put it together and keep track of the different ?'s with subscripts denoted ?_n:
A B A→B (A→B)∧A ((A→B)∧A)→B
T T ?_1 ?_5 T
T F ?_2 ?_6 T
F T ?_3 ?_7 T
F F ?_4 ?_8 T

by definition of ∧, we already know that ?_7=?_8=F since A is F in those two cases.

from this truth table, we can derive this, substituting F for ?_7 and ?_8:
C B C→B
?_5 T T
?_6 F T
F T T
F F T

we also have this:
A B A→B
T T ?_1
T F ?_2
F T ?_3
F F ?_4

from the table before this, we get ?_3=?_4=T. (thus we can say that vacuous truth must be in place in order for modus ponens to operate, which is nice.)

from the first table with subscripted question marks, we can turn to the 4th column for info. let me write down some statements:
?_5=T iff ?_1=T and
?_6=T iff ?_2=T.

hence ?_5=?_1 and ?_6=?_2. let's repeat the original table including what we know and leaving ?_1 and ?_2 as they are for now:
A B A→B (A→B)∧A ((A→B)∧A)→B
T T ?_1 ?_1 T
T F ?_2 ?_2 T
F T T F T
F F T F T.

there are four possibilities now (a reduction from 2⁸ possibilities):
?_1 ?_2
T T
T F
F T
F F

i don't see anything wrong with any of these possibilities. I'm not seeing how ?_1 is forced to be T and ?_2 forced to be F... perhaps if we add the assumption that (A→B)→(¬B→¬A) is a tautology then that will force ?_1 to be T and ?_2 to be F...

 

[cassiopeiae]

The best way I have found to describe logic -

Think well and live in harmony with your thoughts.
Think logically and live consistently. -MP Hall

 

[Loren Booda]

Logic attempts reduction of representation for given information.

 

[diverz]

Logic cannot be defined.

Logic to me may be utter rubbish to the insane man in the asylum. What the cheetah sees as logic may be foolish to what we humans believe.

Hence, I'll say logic is relative. It varies from individual to individual. Why then do you want to define logic?

But if you insist on defining logic, its simply a set of reasoning which we believe holds true in our context. Thats my opinion.

 

[benzun_1999]

Originally posted by Kerrie
For those of us who are still learning and understanding philosophy, can we differentiate logic in the most simple terms?

I believe logic is something that you gain by daily experience.

 

[Iacchus32]

Is logic really anything other than applying basic common sense? Afterall, what are we trying to define then, if not that which is basic and makes sense?

 

[laserblue]

what's logic?

The author of a text I used in my first year philosophy class defined logic as 'the science that evaluates arguments'. However, both of the words 'logic' and 'argument' were used with strict technical definitions. Some think the use of the word science is pompous. In common usage, both of the words 'logic' and 'argument' are used in several different ways with different meanings that causes confusion.
I know of a writer who defined logic in terms of what makes things illogical. He made a list of about a dozen things like 'all related facts are known', 'correct time sequence', etc. Most of these are covered as informal fallacies in logic texts but the subject seems simpler in this writer's world where being logical is equated with being rational.
The definitions of logic in terms of reasoning seem too encompassing because the study of logic doesn't get into many of the reasoning skills people use like LATERAL THINKING as defined by Edward DeBono or the 13 creative thinking skills such as abstraction mentioned by Root-Bernstein in SPARKS OF GENIUS.
Many people seem to use the word 'logic' informally as a word to describe what seems like an evolutionary process. It is logical for an acorn to become an oak but it isn't logical for an acorn to become a dragon.
Defining logic in terms of common sense only makes me wonder what common sense is and where it comes from.What is reasoning for that matter? It's amazing how much disparity there is in people's statements regarding what subjective things are going on when they 'reason'.

 

[jammieg]

Logic is a verbally or symbolically aided form of a natural function of the animal brain.
Logic is the natural way of thinking that everyone uses, animals too. The function of logic is probably like basic conditioning or stimulus response learning, or in humans we might observe more cause and effect relations and a bit more complex conditioning type situations, for example, even though we known very well that the used car saler's nice suit shouldn't have anything to do with getting a good car it nevertheless helps to sell cars because of the subconscious reasonings going on based on past experience or whatever, and if they throw in a few compliments that car looks even better to me wether I'm aware of this or not. Using simple logic verbally is a human advantage that with the aid of words or symbols give people more control just as using words give people the ability to manipulate ideas. The syllogism demands certainty of thinking, and inductive reasoning seems like the application of imagination to reason.

 

[Loren Booda]

Have any of you heard John Archibald Wheeler's argument that the physical universe is reducible to binary logic?

 

[TampaUSA]

Originally posted by Loren Booda
Have any of you heard John Archibald Wheeler's argument that the physical universe is reducible to binary logic?

Yes but Binary logic is forever bounded by Human Logic so we are back where we started with the question. Even reduced to Binary logic the question of which switch to choose (0 or 1) still poses a choice of logic. Common sense is aslo bounded by the rules of loogic. I think one logical explanation are those outsite universal "influences" if you will: Nature and the Theories of spiritual momentum are influences that should be considered when discussing this topic.

 

[Loren Booda]

TampaUSA,

Is your avatar "mask" formed by two hands? More daunting that the usual puppetry.

 

[TampaUSA]

I dunno.. It was an avatar avialable within the profile settings.. I chose it cause it reminds me of what the fictional character XENU might have looked like..

 

[Elledan]

"Logic means the ability to see everything in its true shape. It is the essence of understanding. Where there is no logic, ignorance covers everything under a layer of pretence."

Logic arises from the interactions between the most basic elements out of which the universe is composed. These interactions are governed by causality, hence causality is the essence of logic.

Any reasoning which does not acknowledge causality as defined by the universe itself is very likely to be flawed, leading to wrong conclusions, or "pretence".

 

[jammieg]

My theory is that logic is the means of communication from the super ego to the ego, basically the ego understands actions and simplicity, the super ego or cerebral cortex is a lying machine, or imagination machine, or analyzing device, the reason using reason and being honest improves the mind is because it is the proper method of communication between the two.
I mean if you understood that the reason we make so many mistakes is partly because we need things to get irritated about, would you still be able to push yourself deliberately to new heights in order to get that medicinal daily requirement of irritation? If you never come to accept and understand your nature and actions then your actions will control you, one ought to take actions deliberately according to their true nature with an eventual constructive intent.
Or perhaps logic is sometimes fantasy that happens to make things better...in the hard reality but not fantasy...like the saying that the logical solution isn't always the right solution, so that all fantasy must be tested with logic for it's practicalness in reality...therefore one's imagination may be determined in part by their logical ability to wield it and make long term good use of it.

 

[CronoSpark]

dunno,

logic to me just represents an understanding of cause and effect of various aspects (which is pretty much similar to common sense), but more focused on mathematics

eg.
math - the result of 1 + 1 is 2
binary - if not 0, must be 1
fight - it hurts (effect) when you are hit with a bat (cause)
talking - verbal abuse may cause disputes
walking - move one leg at a time to walk
...