Logic - User contributions [en]

Rhetoric and Propaganda

Admin — Sun, 11 Mar 2012 07:27:25 GMT

Admin: /* Emotional words */

=Sophistry and the fine art of rhetoric emotionalism? - bah!=

I usually leave such nonsense to this robotic roustabout Ever since I began the logic page, I have naturally considered sources that only deal with the subject of logic. Recently, I have decided this was a mistake.

My feeling now is that in order to really delineate logic from other modes of persuasion, I would need to specifically point out the other methods. This has led to my addition of a Sophistry section - on the art of rhetoric.

==A little history on the Sophists - the first advocates of rhetoric==

The ancient Greek Sophists were the first organized group of philosophers to point out the fallacy of naive empiricism - the natural assumption that what we take in with our senses represents the totality of reality, without error. The Sophists argued that in a rapidly changing and evolving world, no one could get a true reading on reality. As Heraclitus said: How can we know anything in a world that never is, but instead is always becoming something else? While many Sophists, such as Gorgias took this to the extreme of nihilism, denying that anyone could ever know anything (so, how did he know that?), all sophists agreed that our view of reality was at best subjective, prone to error, and not capable of creating certain premises for logical arguments. Today we tend to agree with the Sophists on this point.

Since empirical evidence was flawed at its root, the Sophists claimed that the only valid means of persuasion was rhetoric - an appeal to our emotions. Rhetorical appeals clearly had benifits over empiricism - we could be more certain of our own emotions, and they could be counted on to motivate us to action.

The Sophists took this view to "heart' and became experts in the use of rhetoric, to the point that it irritated their enemies - who then became desparate to find something that could be certain - i.e.: clear, unchanging and perfect, that would be suitable for a premise.

Soon, Socrates would come up with the idea of reals, a mental construct of reality, that suited this need. Eventually, the concept of reals would be used in Aristotles art of logic. Since the school of the rationalists and the empiricists won out over the Sophists, and, as history is written by the victors, the Sophists would come to be seen in disparaging terms, to the point that the words sophistry and rhetoric now have negative connotations, even amongst the common man.

However, to be fair, it should be stated that rhetoric does have a value - and in fact, this is recognized by its still popular use today - mostly in the hands of (not, surprisingly) lawyers and politicians. While the extreme skepticism of the sophists is in disfavor, (Betrand Russell makes the point that I inferred above, that extreme skepticism is merely a dogmatic belief system, and as such prone to error itself) it would do us good to know the methods of the sophists today.

So, in order to better explain the value of logic, and to explain how politicians work, I have listed the basics of what I consider to be the inferior tool of rhetoric here:

==Rhetoric - The use of persuasive words to win an argument==

There are two general ways to argue, although both forms are not necessarily mutually exclusive. The first is through logical argument, the second, through rhetorical persuasuion. In logic, we attempt to convince through logical necessity - if one accepts our premises, they must accept our conclusions. While emotions of course play a part, they are not directly appealed to. When one attempts to persuade as opposed to convince, they rely more on emotion than on logic.

Therefore, in rhetoric, we refers to "premises" as appeals. When one wants to appeal to another's emotions, they call upon different strategies - they attempt to personalize the argument, appeal to our own vanities. Here are some of the most common methods:

===Anecdotes, Stories, Metaphors===

These cast an issue in a favorable or unfavorable light, or can highlight or suppress certain aspects. They work by suggesting a likeness between a character and the listener, or a situation and the listener's. In logic we see that this appeal often commits the logical errors of the small sample bias, weak comparison, and excluded middle.

===Double-bind===

One way of getting a child to eat her vegetables is to offer a "choice" "Would you like peas or spinach?" Regardless of the alternative chosen, your desired objective is met. "Which kind of environmental bureaucracy do you want -- one that stifles business and innovation, or one that burdens American industry with impossible extra costs?" In logic we see that this appeal often commits the false dichotomy error.

===Contingency===

This works by getting you to accept both parts of a statement because of how they are linked; one part might be reasonable enough by itself, but. . .

"Unless you want the earth to turn to a barren crust, you must oppose corporate capitalist pigs, tooth and nail." In logic we see that this appeal often commits the logical error of false dichotomy or hasty generalization.

===Rapport===

How does the author go about building a sense of friendliness and receptivity on the part of the audience? Some methods are friendly introductions ("my friends"), complimenting, showing respect, speaking the speakers 'language,' and conveying optimism. These are important communicative techniques! Rapport is important. We just have to be aware of its use in persuasive contexts. Used car salesmen use rapport. In logic we see that this appeal often commits the Red Herring Fallacy.

===Authority===

A speaker may claim in many ways to be an authority; sometimes external checking of this is called for. Sometimes the "authority" is specious, or openly fallicious. In logic we refer to phoney cases of authority as an "appeal to authority", A perfect example would be "Dr. Laura" who, in fact, does not have a doctorate in psychology, but physiology. (If she attempted to do this in professional practice, she would be sanctioned by the APA)

===Humor===

Humor has a great way of defusing our critical faculties. Whenever Ronald Reagen couldn't deal with facts, he'd make a joke. The most famous case was his uttering "There you go again!" to Walter Mondale during a debate. The fact that Reagen was saying this because Mondale nailed him on a fact he couldn't escape from, was lost to the audience. They prefered the humor of Reagen to the reality of Mondale. In logic we refer to Reagen's use of humor as "missing the point"

===Emotional words===

Advertisers are especially keen about the emotional qualities of certain words, and the sway they can give a speaker, just by their associations. Consider the possible power of: winner, loser, infantile, powerful, lovely, courage, freedom, radical. How are these kinds of words employed to generate a certain response in the listener? What purposes are served? A fine example would be Newt Gingrich's "GOPAC" an organization that existed to postively define conservative values and negatively define liberal values. One should ask: If conservative values are clearly superior to liberal values, why would a conservative need to create an organization that purposely tried to redfine liberal values with negative words? Is this not a implicit admission from conservatives that both liberal and conservative values are in many way, on an equal par, and that that one must purposely attempt to create a distinction in order to devalue one of them? In logic we see that this appeal often commits the false "emotional reasoning".

===Pacing===

How do you move a listener along to your conclusion? Certain phrases help a speaker move us from one idea to another, regardless of whether strong connection or evidence has been established. Don't let phrases like these lull your assessment of the argument: "Naturally..."; "Certainly then..."; "Surely..."; "Without question..." But we must question any of these terms, particularly when we have no proof of the validity of their appeals. In logic we see that this appeal often commits various fallacies of presumption, as well as circular logic and begging the question.

===Questions===

Jacobs points out 3 ways posing questions helps a persuader do her work.
1. A question can substitute for a request (recall the peas and spinach).
2. While a listener is searching for an answer, the speaker can give his own answer to the question. The listener is more likely to accept it than if it were given as an assertion.
3. A question can have a suggestion embedded in it. Sales people skillfully use questions to lead the listener and control the discussion. In logic we recognize that true questions are not logical arguments at all - making them the perfect tool for a rhetorician.

===Absolutes===

We've all heard "never say never"; any totalizing statement is likely to result in a fallacy. But words like "don't" and "must" creep in and can give a writer's statements and indisputable air. In logic we see that this appeal often commits the false dichotomy error or fallacies of presumption.

==An overview of the technical aspects of Rhetoric - Grounds, Warrants and Conclusions==

Much of this work is culled from Enviromental Sociology - by J. A. Hannigan

Rhetoric, according to Hannigan, involves the deliberate use of language in order to persuade, without providing logical proofs.

Rhetoric can be said to be based on two methods: One of Emotionalism, or appealing to strong subjective emotional states (during which people usualy don't make the best decisions, wouldn't you agree?) and the second on Aesthetics, or the concept that whatever best appeals to you is what is true. A fine proponent of this is any politician, who usually makes the claim that whatever you yourself desire is what is best for the country. Sounds ridiculous? Well, why do Republicans claim that Tax cuts are the solution to every problem while liberals believe a losening of restrictions is always what is needed? Because they are playing to the aesthetic desires of their constituents! (For more, see philos, dictionary section.)

Now, these emotional and aethetic rhetorical statements contain 3 principal components: grounds, warrants and conclusions. Let's go over them.

===Grounds===

Grounds are the data furnished by the speaker to support his cause. This includes:

Persuasive definitions: (Slanted definitions i.e. a person against abortion can be called either a "pro lifer" OR "anti choice" depending upon which side is referring to him or her.)

Unscientific statistics, (often biased, if not wholesale falsified - i.e. Ronald Reagan's use of statistics), and/or

Case study examples - Easily identifiable victims, usually of a rare and extreme nature - i.e. Rodney King beating by L.A. police is held to be indicative of normal police/black populace interaction, or , on the other side, Ronald Reagan's use of a fictitious welfare queen (a complete lie) is held to be proof of the misuse of welfare.

Again, case study examples are shown by psychological study to be extremely convincing, since one personal example bears more weight than a bookload of negating statistics. For proof, try telling a person afraid of air travel that jets are safer than cars. (Also, see my Social Psychology page for more...)

One should note from this open definition, that it is entirely possible for rhetoric to include valid, logical data. Usually, however, even when this is the case, it is often used in emotional or unscientific ways, or along with a conclusion that goes much further than the valid evidence supports.

===Warrants===

Warrants are justifications for the speaker to demand action.

Usually, a claim that basic rights have been violated or impinged upon. Two main modes are used:

====Rhetoric of rationality====

Our sense of logic must compel us to agree. It makes sense for others to agree with the speaker, since they will benefit by agreeing. This is the most valid of rhetoric, because, again, it comes closest to apeing the art of logic. However, while appearing like logic, often rhetoric is tinged with emotionalism, slanted views or unobjective judgements.

====Rhetoric of Rectitude====

Our values or morality should drive us to agree. No pretense of logic is made - instead, other, more important drives should motivate us, that go beyond logic. Hmmmm...

Within these two basic modes, stereotypes are called upon, called rhetorical idioms:

====Rhetorical Idioms====

These are schemas or groups of cognitions that one stereotypically has about certain areas of moral significance:

Rhetoric of loss: We are losing our innocence, our ability to enjoy nature
Rhetoric of unreason: we are being manipulated by a conspiracy - that somehow avoids are detection - but this is just further proof of its insidiousness! (Hey, if we could detect it, then it wouldn't be a conspiracy, right?)
Rhetoric of calamity: Favorite of religion - Deteriorism - the world is falling to pieces and judgement is at hand, therefore, we should change this (but, if it is preordained, can you change it? Or, even, should you??)
Rhetoric of entitlement: We have the RIGHT to kick the foreigners out of our country, etc. I haven't made a nazi reference in a few paragraphs, so I will note that our favorite Fuhrer, Adolf Hitler, used this technique, to justify his actions towards the Jews.
Rhetoric of endangerment: We must build 50,000 nuclear bombs, or the soviets will be feeding us borsch by June. And borsch sucks!

====Rhetorical motifs====

These methods all use recurrent metaphors - with an unbelievable persuasive power to change others minds, regardless of the reality of the situation. Examples include the claim that aids is a plague, or that the hole in the ozone is a ticking time bomb, or that we are suffering under a worldwide population explosion. They appeal to all facets of rhetoric, from emotional appeal, to moral to logic. The sad truth is that all of us have swallowed more than a few of them whole, without any critical examination!

(Example: - There is no ozone hole - a recolored infrared reading of ozone leaves the THINNING LAYER of ozone clear, making it look to non professionals that no ozone exists over the arctic circle. Aids is not a plague, its a sexually transmitted disease (also, through blood transfusions) and it has hardly killed off 1/2 of the worlds population like the true plagues did, and lastly, the population in Europe is decreasing, and leveling off in America - its only in 3rd world nations where the growth is still quite high (and even there, the population increase comes from longer longevity, not increasing birthrate.) None of this is intended to say these are not problems, its only intended to show that rhetoric causes overstated misperceptions in the cause of rectifying what the speakers honestly feel are horrible problems.

===Conclusions===

What action is needed to solve this problem. Usually this is simply stated as just agree/vote with/for us, and we will do the job...

==How to further delineate Rhetoric from logic - look for "Intent signals"==

I've certainly provided you with much already that stresses the differences between logic and rhetoric, but there is yet another indicator. There are things to look for in persuasive language that reveal putative self-serving motivations. Self-interest is fine, but too much of it, especially in the apparent pursuit of helping others, should cause us to question the integrity of the speaker. We call statements that reveal an abundance of self interest "intent signals" - i.e. what someone's real intent may be. Whether the presence of any of these in writing is cause for rejection requires analysis; their presence should call up further examination.

Look for the following themes...

===Us vs. Them===

Does the speaker see two "sides," with the other side being in some way inferior or denigrated? This happens all the time in environmental discourse, and often tends to cloud the real issues, and impede useful analysis. Many techniques of propaganda employ this technique: name calling, touting how great it is to "belong," using one-sided testimonials of famous people, simplifying issues for slogans, emphasizing being on the right side of the competition.

===Supremacy===

Although there is nothing wrong with asserting superiority, it can suggest a need that is stronger than the desire to give a sound argument.

===Absolute Certainty===

Science doesn't provide it; scholarly research doesn't. Mathematics has it, but only within its self-defined deductive systems. When someone asserts they know something with absolute certainty, it can really only be based on self-evidence, faith, or mythology.

===Righteous indignation===

To quote Jacobs from his text On Rhetoric (1994, p. 74):

When someone is so full of guiltless virtue and vengeance because of "unjust treatment," his information is likely to be biased and inaccurate. Ultimately, this could hurt a worthy cause. Admittedly, what is truth and what is worthy are difficult things to know. But if this is not appreciated by a persuader, it could indicate he has taken an easy path to his position. It shows he may not have carefully analyzed his assertions. It is not likely he has open-mindedly compared his ideas to other viewpoints. The listener should thus question his information.

==Propaganda==

There are numerous rhetorical devices used in propaganda. Here are the most commonly employed propaganda tools used by Bill O'Reilly:

===The seven propaganda devices include:===

* Name calling -- giving something a bad label to make the audience reject it without examining the evidence;
* Glittering generalities -- the opposite of name calling;
* Card stacking -- the selective use of facts and half-truths;
* Bandwagon -- appeals to the desire, common to most of us, to follow the crowd;
* Plain folks -- an attempt to convince an audience that they, and their ideas, are "of the people";
* Transfer -- carries over the authority, sanction and prestige of something we respect or dispute to something the speaker would want us to accept; and
* Testimonials -- involving a respected (or disrespected) person endorsing or rejecting an idea or person.

How Does A Materialist Account for Logic?

Admin — Sun, 11 Mar 2012 07:20:29 GMT

Admin: /* Common Responses */

You probably already know how this complaint goes:

"How can you account for axioms in a materialistic universe? What part of your brain are axioms located in? Can you actually point to some neurons and say 'these are what the axioms really are'? Also, since the axioms of math are carried around in people's heads, are there really millions of little axioms of math running around? Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Let's take this apart, piece by piece:

==How do you account for the 'laws of logic' in a materialistic universe?==

This question contains a false presumption. And to reveal it, I ask the following: 'The' laws of logic? Which set of laws? For which logic? First-order logic, first-order predicate logic, second-order predicate logic, modal logic, fuzzy logic? Which one? Logic is not a monolithic entity, and there is no one set of 'laws' for all of logic. Some logical systems do not require axioms at all. The set of axioms for the sentential, or propositional, logic is {} - the empty set.

"The point is that there can be no axioms in propositional logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything in predicate logic is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally."- Gregory Lopez.

==The Basic Metaphysical Requirements for any Logical System==

Now that we have done away with the blunders attached to that misunderstanding, let's explain the basic metaphysics required for the creation of an a priori system - the existence of sentient brains. The basic axioms of existence, identity and consciousness - the so called laws of reason (which are prior to any logical system '''and''' NOT part of logic itself), are necessary elements of reason; to reason one must first exist, and exist as something. These axioms are therefore implicitly inescapable - an explicit awareness of these axioms is another matter.

We can express this truth thusly:

To exist is to exist as something. And to be aware of this, is to be conscious. To update Descartes, we might say:

"I exist, therefore I think"

These axioms of reason are necessary truths, given the existence of consciousness. They are defended through retortion. But they are '''not''' a part of logic, they exist prior to the formation (or learning) of any set of logical rules. Other rules, such as the other laws of classical logic, can also be gleaned a priori, all of them flow from the axiom of identity (i.e. classical logic, a system of tautologies, can be traced back to the axiom of identity). The specifics of which rules we create do not matter here; what matters is as long as we have sentient brains, we will have the basis for the creation of any a priori system.

To 'explain' the human invention of logical systems as somehow the work of God is to explain precisely nothing at all. No one who ever asserts this putative 'solution' ever defines this 'god' in a noncontradictory way, nor do they ever explain how this 'god' provides the foundation for logic. If they were to undertake an examination of their assertion they'd soon recognize that referencing the supernatural as foundation for a natural system leads to an infinitely greater problem than working out the metaphysics for logic, to whit: supernatural references are broken terms. Invoking "god" to explain anything is the very abdication of reason and insight.

== What part of your brain are axioms (or abstractions) located in?==

The cerebral cortex, frontal lobes. http://www.waiting.com/brainanatomy.html#anchor2587568

"Also, since the axioms of math are carried around in people's heads, are there really billions of little axioms of math running around?"

Billions of representations of the same axioms. Billions of sentient brains coming to the same, necessary, analytic, unavoidable, a priori conclusion, just as billions of different bits of falling matter all conform to the same phenomenon of nature that we can summarize in one law: the law of gravity.

If you fail to find it puzzling how 'different pieces of matter' can all conform to the same law of gravity, then you ought to re-examine your supposed puzzlement over axioms. The process is similar. Billions of sentient brains encountering the same, singular reality - the unavoidable basic metaphysics of our universe. If you are looking for a missing 'constant' for the materialistic account, it is this: the universe. You've misplaced the universe. One universe with a basic set of unavoidable, inescapable metaphysics. One universe imprinting itself onto phylogenetically similar sentient beings, who are able to draw the same abstractions from the same stimuli, based on the same rules...

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains is because the same idea can be gleaned, analytically, a priori, by similar brains in the same exact universe. The same idea can be represented in multiple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

==Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all...==

Ah, but you forget something else: Abstract entities written on a page have no meaning in and of themselves. They are interactive phenomena - a sentient brain is required to interpret them and provide them with 'meaning'. Thus, when we say that the number "eighteen" is written on a page, what materialists are really saying is that this sensory input'18' through some social convention (some rule), yields the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

A word written on a page and the same word spoken and traveling as a wave through the air are not 'the same matter'. However, when I read the word, and when I hear the word, my brain eventually interprets them the same way, producing similar electrochemical responses with enough fidelity that slightly different brains can reproduce the same abstraction, based on the same rules.

Of course, the mapping itself is completely arbitrary. Our written alphabet needn't be what it is, and we could choose totally different symbols to represent the same thing as the spoken word.

==Common Responses==

The Identity of Indiscernibles is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.

This formula can be used to demonstrate that if x shares the same properties of y, then x and y are the same entity.

The argument continues:

A material entity cannot be in more than one spatio-temporal location at the same time.

Response: This claim is built on intellectual dishonesty, for it fails to consider that abstractions are tokens or representations - formed in neurons by the same set of rules. However, leaving this aside, the claim fails even if we accept this bit of dishonest, as quantum physics tells us that there is no contradiction in having the same material entity in more than one spatio-temporal location:

http://www.fizyka.umk.pl/~jkob/physnews/node30.html

For more in the principle of Identity of indiscernibles and Liebnitz' transposition of the principle, the law of Indiscernability of Identicals, see here:

http://plato.stanford.edu/entries/identity-indiscernible/#Rec

How Does A Materialist Account for Logic?

Admin — Sun, 11 Mar 2012 07:16:42 GMT

Admin: /* What part of your brain are axioms (or abstractions) located in? */

You probably already know how this complaint goes:

"How can you account for axioms in a materialistic universe? What part of your brain are axioms located in? Can you actually point to some neurons and say 'these are what the axioms really are'? Also, since the axioms of math are carried around in people's heads, are there really millions of little axioms of math running around? Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Let's take this apart, piece by piece:

==How do you account for the 'laws of logic' in a materialistic universe?==

This question contains a false presumption. And to reveal it, I ask the following: 'The' laws of logic? Which set of laws? For which logic? First-order logic, first-order predicate logic, second-order predicate logic, modal logic, fuzzy logic? Which one? Logic is not a monolithic entity, and there is no one set of 'laws' for all of logic. Some logical systems do not require axioms at all. The set of axioms for the sentential, or propositional, logic is {} - the empty set.

"The point is that there can be no axioms in propositional logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything in predicate logic is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally."- Gregory Lopez.

==The Basic Metaphysical Requirements for any Logical System==

Now that we have done away with the blunders attached to that misunderstanding, let's explain the basic metaphysics required for the creation of an a priori system - the existence of sentient brains. The basic axioms of existence, identity and consciousness - the so called laws of reason (which are prior to any logical system '''and''' NOT part of logic itself), are necessary elements of reason; to reason one must first exist, and exist as something. These axioms are therefore implicitly inescapable - an explicit awareness of these axioms is another matter.

We can express this truth thusly:

To exist is to exist as something. And to be aware of this, is to be conscious. To update Descartes, we might say:

"I exist, therefore I think"

These axioms of reason are necessary truths, given the existence of consciousness. They are defended through retortion. But they are '''not''' a part of logic, they exist prior to the formation (or learning) of any set of logical rules. Other rules, such as the other laws of classical logic, can also be gleaned a priori, all of them flow from the axiom of identity (i.e. classical logic, a system of tautologies, can be traced back to the axiom of identity). The specifics of which rules we create do not matter here; what matters is as long as we have sentient brains, we will have the basis for the creation of any a priori system.

To 'explain' the human invention of logical systems as somehow the work of God is to explain precisely nothing at all. No one who ever asserts this putative 'solution' ever defines this 'god' in a noncontradictory way, nor do they ever explain how this 'god' provides the foundation for logic. If they were to undertake an examination of their assertion they'd soon recognize that referencing the supernatural as foundation for a natural system leads to an infinitely greater problem than working out the metaphysics for logic, to whit: supernatural references are broken terms. Invoking "god" to explain anything is the very abdication of reason and insight.

== What part of your brain are axioms (or abstractions) located in?==

The cerebral cortex, frontal lobes. http://www.waiting.com/brainanatomy.html#anchor2587568

"Also, since the axioms of math are carried around in people's heads, are there really billions of little axioms of math running around?"

Billions of representations of the same axioms. Billions of sentient brains coming to the same, necessary, analytic, unavoidable, a priori conclusion, just as billions of different bits of falling matter all conform to the same phenomenon of nature that we can summarize in one law: the law of gravity.

If you fail to find it puzzling how 'different pieces of matter' can all conform to the same law of gravity, then you ought to re-examine your supposed puzzlement over axioms. The process is similar. Billions of sentient brains encountering the same, singular reality - the unavoidable basic metaphysics of our universe. If you are looking for a missing 'constant' for the materialistic account, it is this: the universe. You've misplaced the universe. One universe with a basic set of unavoidable, inescapable metaphysics. One universe imprinting itself onto phylogenetically similar sentient beings, who are able to draw the same abstractions from the same stimuli, based on the same rules...

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains is because the same idea can be gleaned, analytically, a priori, by similar brains in the same exact universe. The same idea can be represented in multiple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

==Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all...==

Ah, but you forget something else: Abstract entities written on a page have no meaning in and of themselves. They are interactive phenomena - a sentient brain is required to interpret them and provide them with 'meaning'. Thus, when we say that the number "eighteen" is written on a page, what materialists are really saying is that this sensory input'18' through some social convention (some rule), yields the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

A word written on a page and the same word spoken and traveling as a wave through the air are not 'the same matter'. However, when I read the word, and when I hear the word, my brain eventually interprets them the same way, producing similar electrochemical responses with enough fidelity that slightly different brains can reproduce the same abstraction, based on the same rules.

Of course, the mapping itself is completely arbitrary. Our written alphabet needn't be what it is, and we could choose totally different symbols to represent the same thing as the spoken word.

==Common Responses==

The Identity of Indiscernibles is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.

This formula can be used to demonstrate that if x shares the same properties of y, then x and y are the same entity.

The argument continues:

A material entity cannot be in more than one spatio-temporal location at the same time.

Response: This claim confuses fails to consider that abstractions are tokens or representations - formed in neurons by the same set of rules. However, the claim is doubly false, for even if we presume that abstractions are in fact the same identical entity, quantum physics tells us that there is no contradiction in having the same material entity in more than one spatio-temporal location:

http://www.fizyka.umk.pl/~jkob/physnews/node30.html

For more in the principle of Identity of indiscernibles and Liebnitz' transposition of the principle, the law of Indiscernability of Identicals, see here:

http://plato.stanford.edu/entries/identity-indiscernible/#Rec

How Does A Materialist Account for Logic?

Admin — Sun, 11 Mar 2012 07:16:04 GMT

Admin: /* The Basic Metaphysical Requirements for any Logical System */

You probably already know how this complaint goes:

"How can you account for axioms in a materialistic universe? What part of your brain are axioms located in? Can you actually point to some neurons and say 'these are what the axioms really are'? Also, since the axioms of math are carried around in people's heads, are there really millions of little axioms of math running around? Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Let's take this apart, piece by piece:

==How do you account for the 'laws of logic' in a materialistic universe?==

This question contains a false presumption. And to reveal it, I ask the following: 'The' laws of logic? Which set of laws? For which logic? First-order logic, first-order predicate logic, second-order predicate logic, modal logic, fuzzy logic? Which one? Logic is not a monolithic entity, and there is no one set of 'laws' for all of logic. Some logical systems do not require axioms at all. The set of axioms for the sentential, or propositional, logic is {} - the empty set.

"The point is that there can be no axioms in propositional logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything in predicate logic is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally."- Gregory Lopez.

==The Basic Metaphysical Requirements for any Logical System==

Now that we have done away with the blunders attached to that misunderstanding, let's explain the basic metaphysics required for the creation of an a priori system - the existence of sentient brains. The basic axioms of existence, identity and consciousness - the so called laws of reason (which are prior to any logical system '''and''' NOT part of logic itself), are necessary elements of reason; to reason one must first exist, and exist as something. These axioms are therefore implicitly inescapable - an explicit awareness of these axioms is another matter.

We can express this truth thusly:

To exist is to exist as something. And to be aware of this, is to be conscious. To update Descartes, we might say:

"I exist, therefore I think"

These axioms of reason are necessary truths, given the existence of consciousness. They are defended through retortion. But they are '''not''' a part of logic, they exist prior to the formation (or learning) of any set of logical rules. Other rules, such as the other laws of classical logic, can also be gleaned a priori, all of them flow from the axiom of identity (i.e. classical logic, a system of tautologies, can be traced back to the axiom of identity). The specifics of which rules we create do not matter here; what matters is as long as we have sentient brains, we will have the basis for the creation of any a priori system.

To 'explain' the human invention of logical systems as somehow the work of God is to explain precisely nothing at all. No one who ever asserts this putative 'solution' ever defines this 'god' in a noncontradictory way, nor do they ever explain how this 'god' provides the foundation for logic. If they were to undertake an examination of their assertion they'd soon recognize that referencing the supernatural as foundation for a natural system leads to an infinitely greater problem than working out the metaphysics for logic, to whit: supernatural references are broken terms. Invoking "god" to explain anything is the very abdication of reason and insight.

== What part of your brain are axioms (or abstractions) located in?==

The cerebral cortex, frontal lobes. http://www.waiting.com/brainanatomy.html#anchor2587568

"Also, since the axioms of math are carried around in people's heads, are there really billions of little axioms of math running around?"

Billions of representations of the same axioms. Billions of sentient brains coming to the same, necessary, analytic, unavoidable, a priori conclusion, just as billions of different bits of falling matter all conform to the same phenomenon of nature that we can summarize in one law: the law of gravity.

If you fail to find it puzzling how 'different pieces of matter' can all conform to the same law of gravity, then you ought to re-examine your supposed puzzlement over axioms. The process is similar. Billions of sentient brains encountering the same, singular reality - the unavoidable basic metaphysics of our universe. If you are looking for a missing 'constant' for the materialistic account, it is this: the universe. You've misplaced the universe. One universe with a basic set of unavoidable, inescapable metaphysics. One universe imprinting itself onto phylogenetically similar sentient beings, who are able to draw the same abstractions from the same stimuli, based on the same rules...

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains is because the same idea can be gleaned, analytically, a priori, by similar brains in the same exact universe. The same idea can be represented in multiple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

==Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all...==

Ah, but you forget something else: Abstract entities written on a page have no meaning in and of themselves. They are interactive phenomena - a sentient brain is required to interpret them and provide them with 'meaning'. Thus, when we say that the number "eighteen" is written on a page, what materialists are really saying is that this sensory input'18' through some social convention (some rule), yields the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

A word written on a page and the same word spoken and traveling as a wave through the air are not 'the same matter'. However, when I read the word, and when I hear the word, my brain eventually interprets them the same way, producing similar electrochemical responses with enough fidelity that slightly different brains can reproduce the same abstraction, based on the same rules.

Of course, the mapping itself is completely arbitrary. Our written alphabet needn't be what it is, and we could choose totally different symbols to represent the same thing as the spoken word.

==Common Responses==

The Identity of Indiscernibles is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.

This formula can be used to demonstrate that if x shares the same properties of y, then x and y are the same entity.

The argument continues:

A material entity cannot be in more than one spatio-temporal location at the same time.

Response: This claim confuses fails to consider that abstractions are tokens or representations - formed in neurons by the same set of rules. However, the claim is doubly false, for even if we presume that abstractions are in fact the same identical entity, quantum physics tells us that there is no contradiction in having the same material entity in more than one spatio-temporal location:

http://www.fizyka.umk.pl/~jkob/physnews/node30.html

For more in the principle of Identity of indiscernibles and Liebnitz' transposition of the principle, the law of Indiscernability of Identicals, see here:

http://plato.stanford.edu/entries/identity-indiscernible/#Rec

How Does A Materialist Account for Logic?

Admin — Sun, 11 Mar 2012 07:00:36 GMT

Admin: /* How do you account for the 'laws of logic' in a materialistic universe? */

You probably already know how this complaint goes:

"How can you account for axioms in a materialistic universe? What part of your brain are axioms located in? Can you actually point to some neurons and say 'these are what the axioms really are'? Also, since the axioms of math are carried around in people's heads, are there really millions of little axioms of math running around? Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Let's take this apart, piece by piece:

==How do you account for the 'laws of logic' in a materialistic universe?==

This question contains a false presumption. And to reveal it, I ask the following: 'The' laws of logic? Which set of laws? For which logic? First-order logic, first-order predicate logic, second-order predicate logic, modal logic, fuzzy logic? Which one? Logic is not a monolithic entity, and there is no one set of 'laws' for all of logic. Some logical systems do not require axioms at all. The set of axioms for the sentential, or propositional, logic is {} - the empty set.

"The point is that there can be no axioms in propositional logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything in predicate logic is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally."- Gregory Lopez.

==The Basic Metaphysical Requirements for any Logical System==

Now that we have done away with the blunders attached to that misunderstanding, let's explain the basic metaphysics requires for the creation of an a priori system. The only metaphysic required for the creation of an a priori system is the existence of sentient brains. The basic axioms of existence, identity and consciousness - the so called laws of reason (prior to any logical system and not part of logic itself), are necessary elements of reason; to reason one must first exist, and exist as something. These axioms are therefore implicitly inescapable - an explicit awareness of these axioms is another matter.

We can express this truth thusly:

To exist is to exist as something. And to be aware of this is to be conscious.

The axioms are necessary truths, given the existence of consciousness. They are defended through retortion. But they are not a part of logic, per se. Other rules, such as the other laws of classical logic, can also be gleaned a priori, all of them flow from the axiom of identity (i.e. classical logic, a system of tautologies, can be traced back to the axiom of identity). The specifics of which rules we create do not matter here; what matters is as long as we have sentient brains, we will have the basis for the creation of any a priori system.

To explain the human invention of logical systems as somehow the indirect work of God is to explain precisely nothing at all. It is as good of an explanation as saying "it just happened." No one who ever asserts it ever defines this 'god' in a noncontradictory way, nor do they ever explain how this 'god' provides the foundation. Invoking God to explain anything is the very abdication of reason and insight. It is giving up the investigation and search for truth and filling it with some supernatural nonsense (literally). Instead, I think that people like Paul Feyerabend, Karl Popper, and Thomas Kuhn give us a good idea about how science and human knowledge progresses.

== What part of your brain are axioms (or abstractions) located in?==

The cerebral cortex, frontal lobes. http://www.waiting.com/brainanatomy.html#anchor2587568

"Also, since the axioms of math are carried around in people's heads, are there really billions of little axioms of math running around?"

Billions of representations of the same axioms. Billions of sentient brains coming to the same, necessary, analytic, unavoidable, a priori conclusion, just as billions of different bits of falling matter all conform to the same phenomenon of nature that we can summarize in one law: the law of gravity.

If you fail to find it puzzling how 'different pieces of matter' can all conform to the same law of gravity, then you ought to re-examine your supposed puzzlement over axioms. The process is similar. Billions of sentient brains encountering the same, singular reality - the unavoidable basic metaphysics of our universe. If you are looking for a missing 'constant' for the materialistic account, it is this: the universe. You've misplaced the universe. One universe with a basic set of unavoidable, inescapable metaphysics. One universe imprinting itself onto phylogenetically similar sentient beings, who are able to draw the same abstractions from the same stimuli, based on the same rules...

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains is because the same idea can be gleaned, analytically, a priori, by similar brains in the same exact universe. The same idea can be represented in multiple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

==Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all...==

Ah, but you forget something else: Abstract entities written on a page have no meaning in and of themselves. They are interactive phenomena - a sentient brain is required to interpret them and provide them with 'meaning'. Thus, when we say that the number "eighteen" is written on a page, what materialists are really saying is that this sensory input'18' through some social convention (some rule), yields the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

A word written on a page and the same word spoken and traveling as a wave through the air are not 'the same matter'. However, when I read the word, and when I hear the word, my brain eventually interprets them the same way, producing similar electrochemical responses with enough fidelity that slightly different brains can reproduce the same abstraction, based on the same rules.

Of course, the mapping itself is completely arbitrary. Our written alphabet needn't be what it is, and we could choose totally different symbols to represent the same thing as the spoken word.

==Common Responses==

The Identity of Indiscernibles is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.

This formula can be used to demonstrate that if x shares the same properties of y, then x and y are the same entity.

The argument continues:

A material entity cannot be in more than one spatio-temporal location at the same time.

Response: This claim confuses fails to consider that abstractions are tokens or representations - formed in neurons by the same set of rules. However, the claim is doubly false, for even if we presume that abstractions are in fact the same identical entity, quantum physics tells us that there is no contradiction in having the same material entity in more than one spatio-temporal location:

http://www.fizyka.umk.pl/~jkob/physnews/node30.html

For more in the principle of Identity of indiscernibles and Liebnitz' transposition of the principle, the law of Indiscernability of Identicals, see here:

http://plato.stanford.edu/entries/identity-indiscernible/#Rec

How Does A Materialist Account for Logic?

Admin — Sun, 11 Mar 2012 07:00:09 GMT

Admin: /* How do you account for the 'laws of logic' in a materialistic universe? */

You probably already know how this complaint goes:

"How can you account for axioms in a materialistic universe? What part of your brain are axioms located in? Can you actually point to some neurons and say 'these are what the axioms really are'? Also, since the axioms of math are carried around in people's heads, are there really millions of little axioms of math running around? Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Let's take this apart, piece by piece:

==How do you account for the 'laws of logic' in a materialistic universe?==

This question contains a false presumption. And to reveal it, I ask the following: 'The' laws of logic? Which set of laws? For which logic? First-order logic, first-order predicate logic, second-order predicate logic, modal logic, fuzzy logic? Which one? Logic is not a monolithic entity, and there is no one set of 'laws' for all of logic. Some logical systems do not require axioms at all. The set of axioms for the sentential, or propositional, logic is {} - the empty set.
''
"The point is that there can be no axioms in propositional logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything in predicate logic is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally."'' - Gregory Lopez.

==The Basic Metaphysical Requirements for any Logical System==

Now that we have done away with the blunders attached to that misunderstanding, let's explain the basic metaphysics requires for the creation of an a priori system. The only metaphysic required for the creation of an a priori system is the existence of sentient brains. The basic axioms of existence, identity and consciousness - the so called laws of reason (prior to any logical system and not part of logic itself), are necessary elements of reason; to reason one must first exist, and exist as something. These axioms are therefore implicitly inescapable - an explicit awareness of these axioms is another matter.

We can express this truth thusly:

To exist is to exist as something. And to be aware of this is to be conscious.

The axioms are necessary truths, given the existence of consciousness. They are defended through retortion. But they are not a part of logic, per se. Other rules, such as the other laws of classical logic, can also be gleaned a priori, all of them flow from the axiom of identity (i.e. classical logic, a system of tautologies, can be traced back to the axiom of identity). The specifics of which rules we create do not matter here; what matters is as long as we have sentient brains, we will have the basis for the creation of any a priori system.

To explain the human invention of logical systems as somehow the indirect work of God is to explain precisely nothing at all. It is as good of an explanation as saying "it just happened." No one who ever asserts it ever defines this 'god' in a noncontradictory way, nor do they ever explain how this 'god' provides the foundation. Invoking God to explain anything is the very abdication of reason and insight. It is giving up the investigation and search for truth and filling it with some supernatural nonsense (literally). Instead, I think that people like Paul Feyerabend, Karl Popper, and Thomas Kuhn give us a good idea about how science and human knowledge progresses.

== What part of your brain are axioms (or abstractions) located in?==

The cerebral cortex, frontal lobes. http://www.waiting.com/brainanatomy.html#anchor2587568

"Also, since the axioms of math are carried around in people's heads, are there really billions of little axioms of math running around?"

Billions of representations of the same axioms. Billions of sentient brains coming to the same, necessary, analytic, unavoidable, a priori conclusion, just as billions of different bits of falling matter all conform to the same phenomenon of nature that we can summarize in one law: the law of gravity.

If you fail to find it puzzling how 'different pieces of matter' can all conform to the same law of gravity, then you ought to re-examine your supposed puzzlement over axioms. The process is similar. Billions of sentient brains encountering the same, singular reality - the unavoidable basic metaphysics of our universe. If you are looking for a missing 'constant' for the materialistic account, it is this: the universe. You've misplaced the universe. One universe with a basic set of unavoidable, inescapable metaphysics. One universe imprinting itself onto phylogenetically similar sentient beings, who are able to draw the same abstractions from the same stimuli, based on the same rules...

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains is because the same idea can be gleaned, analytically, a priori, by similar brains in the same exact universe. The same idea can be represented in multiple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

==Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all...==

Ah, but you forget something else: Abstract entities written on a page have no meaning in and of themselves. They are interactive phenomena - a sentient brain is required to interpret them and provide them with 'meaning'. Thus, when we say that the number "eighteen" is written on a page, what materialists are really saying is that this sensory input'18' through some social convention (some rule), yields the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

A word written on a page and the same word spoken and traveling as a wave through the air are not 'the same matter'. However, when I read the word, and when I hear the word, my brain eventually interprets them the same way, producing similar electrochemical responses with enough fidelity that slightly different brains can reproduce the same abstraction, based on the same rules.

Of course, the mapping itself is completely arbitrary. Our written alphabet needn't be what it is, and we could choose totally different symbols to represent the same thing as the spoken word.

==Common Responses==

The Identity of Indiscernibles is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.

This formula can be used to demonstrate that if x shares the same properties of y, then x and y are the same entity.

The argument continues:

A material entity cannot be in more than one spatio-temporal location at the same time.

Response: This claim confuses fails to consider that abstractions are tokens or representations - formed in neurons by the same set of rules. However, the claim is doubly false, for even if we presume that abstractions are in fact the same identical entity, quantum physics tells us that there is no contradiction in having the same material entity in more than one spatio-temporal location:

http://www.fizyka.umk.pl/~jkob/physnews/node30.html

For more in the principle of Identity of indiscernibles and Liebnitz' transposition of the principle, the law of Indiscernability of Identicals, see here:

http://plato.stanford.edu/entries/identity-indiscernible/#Rec

How Does A Materialist Account for Logic?

Admin — Sun, 11 Mar 2012 06:59:28 GMT

Admin:

You probably already know how this complaint goes:

"How can you account for axioms in a materialistic universe? What part of your brain are axioms located in? Can you actually point to some neurons and say 'these are what the axioms really are'? Also, since the axioms of math are carried around in people's heads, are there really millions of little axioms of math running around? Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Let's take this apart, piece by piece:

==How do you account for the 'laws of logic' in a materialistic universe?==

This question contains a false presumption. And to reveal it, I ask the following: 'The' laws of logic? Which set of laws? For which logic? First-order logic, first-order predicate logic, second-order predicate logic, modal logic, fuzzy logic? Which one? Logic is not a monolithic entity, and there is no one set of 'laws' for all of logic. Some logical systems do not require axioms at all. The set of axioms for the sentential, or propositional, logic is {} - the empty set.

[quote]"The point is that there can be no axioms in propositional logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything in predicate logic is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally." - Gregory Lopez.[/quote]

==The Basic Metaphysical Requirements for any Logical System==

Now that we have done away with the blunders attached to that misunderstanding, let's explain the basic metaphysics requires for the creation of an a priori system. The only metaphysic required for the creation of an a priori system is the existence of sentient brains. The basic axioms of existence, identity and consciousness - the so called laws of reason (prior to any logical system and not part of logic itself), are necessary elements of reason; to reason one must first exist, and exist as something. These axioms are therefore implicitly inescapable - an explicit awareness of these axioms is another matter.

We can express this truth thusly:

To exist is to exist as something. And to be aware of this is to be conscious.

The axioms are necessary truths, given the existence of consciousness. They are defended through retortion. But they are not a part of logic, per se. Other rules, such as the other laws of classical logic, can also be gleaned a priori, all of them flow from the axiom of identity (i.e. classical logic, a system of tautologies, can be traced back to the axiom of identity). The specifics of which rules we create do not matter here; what matters is as long as we have sentient brains, we will have the basis for the creation of any a priori system.

To explain the human invention of logical systems as somehow the indirect work of God is to explain precisely nothing at all. It is as good of an explanation as saying "it just happened." No one who ever asserts it ever defines this 'god' in a noncontradictory way, nor do they ever explain how this 'god' provides the foundation. Invoking God to explain anything is the very abdication of reason and insight. It is giving up the investigation and search for truth and filling it with some supernatural nonsense (literally). Instead, I think that people like Paul Feyerabend, Karl Popper, and Thomas Kuhn give us a good idea about how science and human knowledge progresses.

== What part of your brain are axioms (or abstractions) located in?==

The cerebral cortex, frontal lobes. http://www.waiting.com/brainanatomy.html#anchor2587568

"Also, since the axioms of math are carried around in people's heads, are there really billions of little axioms of math running around?"

Billions of representations of the same axioms. Billions of sentient brains coming to the same, necessary, analytic, unavoidable, a priori conclusion, just as billions of different bits of falling matter all conform to the same phenomenon of nature that we can summarize in one law: the law of gravity.

If you fail to find it puzzling how 'different pieces of matter' can all conform to the same law of gravity, then you ought to re-examine your supposed puzzlement over axioms. The process is similar. Billions of sentient brains encountering the same, singular reality - the unavoidable basic metaphysics of our universe. If you are looking for a missing 'constant' for the materialistic account, it is this: the universe. You've misplaced the universe. One universe with a basic set of unavoidable, inescapable metaphysics. One universe imprinting itself onto phylogenetically similar sentient beings, who are able to draw the same abstractions from the same stimuli, based on the same rules...

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains is because the same idea can be gleaned, analytically, a priori, by similar brains in the same exact universe. The same idea can be represented in multiple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

==Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all...==

Ah, but you forget something else: Abstract entities written on a page have no meaning in and of themselves. They are interactive phenomena - a sentient brain is required to interpret them and provide them with 'meaning'. Thus, when we say that the number "eighteen" is written on a page, what materialists are really saying is that this sensory input'18' through some social convention (some rule), yields the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

A word written on a page and the same word spoken and traveling as a wave through the air are not 'the same matter'. However, when I read the word, and when I hear the word, my brain eventually interprets them the same way, producing similar electrochemical responses with enough fidelity that slightly different brains can reproduce the same abstraction, based on the same rules.

Of course, the mapping itself is completely arbitrary. Our written alphabet needn't be what it is, and we could choose totally different symbols to represent the same thing as the spoken word.

==Common Responses==

The Identity of Indiscernibles is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.

This formula can be used to demonstrate that if x shares the same properties of y, then x and y are the same entity.

The argument continues:

A material entity cannot be in more than one spatio-temporal location at the same time.

Response: This claim confuses fails to consider that abstractions are tokens or representations - formed in neurons by the same set of rules. However, the claim is doubly false, for even if we presume that abstractions are in fact the same identical entity, quantum physics tells us that there is no contradiction in having the same material entity in more than one spatio-temporal location:

http://www.fizyka.umk.pl/~jkob/physnews/node30.html

For more in the principle of Identity of indiscernibles and Liebnitz' transposition of the principle, the law of Indiscernability of Identicals, see here:

http://plato.stanford.edu/entries/identity-indiscernible/#Rec

Admin — Mon, 18 Jun 2007 23:19:59 GMT

Admin: Law of the Excluded Middle moved to The Law of the Excluded Middle: Correct a fuckup

#redirect [[The Law of the Excluded Middle]]

The Law of the Excluded Middle

Admin — Mon, 18 Jun 2007 23:19:59 GMT

Admin: Law of the Excluded Middle moved to The Law of the Excluded Middle

The Laws of Classical Logic

Admin — Mon, 18 Jun 2007 23:18:52 GMT

Admin:

Classical logic rests upon a foundation of axioms. The axioms of classical logic, are a set of [[a priori]] abstractions that humans create, in order to make [[Classical Logic|categorical syllogisms]]; their existence is contingent upon sentient brains. Some may argue, like myself, that these laws have correlates to basic laws of metaphysics1 and that this accounts for the 'utility' of logic, but it does not follow that logical rules are rules for the universe - they are rules for arguments. Because of the relationship between the metaphysical status of these concepts and their application to logic, I will address both concepts in my definitions.

===The Axioms of Classical Logic===

* [[The Law of Identity]]: Metaphysically, this law asserts that "A is A" or "anything is itself." For propositions: "If a proposition is true, then it is true."

*[[The Law of Excluded Middle]]: Metaphysically, this law asserts "anything is either A or not A." For propositions: "A proposition, such as P, is either true or false." We also refer to such statements as "tautologies"

*[[The Law of Noncontradiction]]: Metaphysically, this law asserts:: "Nothing can be both A and not-A." For propositions: "A proposition, P, can not be both true and false."

All of our syllogisms rely on these laws - that any thing is equal to itself, that tautologies must be true, and that contradictions must be false. Classical logic holds that everything has a definite, non-contradictory nature. A [[metaphysical law of identity]] would hold that to be perceived or even exist at all it must have a definite, non-contradictory nature, but for our purposes, it is enough to say that If A, then A.

==Self Evident Nature of Axioms==

Seeing as axioms are the foundation to logic, it is not possible to use classical logic to justify them. However, Aristotle found this is unnecessary: the axioms of classical logic are held to be [[self evident]]. We hold that they are are [[self evident]] because all syllogisms rely on them, and because they can be defended through [[retortion]].

A defense through [[retortion]] occurs whenever an argument must rely opon the very principle it seeks to overturn. Any attempt to form a syllogism to refute the axioms of classical logic will have to rely on them ,leading to a self refutation (we call this type of self refutation the [[Stolen concept fallacy]].

==Necessity and Contingency==

An understanding of [[axiom]]s can be further advanced if the concepts of [[necessity]] and [[contingency]] are introduced. A [[proposition]] is said to be a [[necessary]] [[proposition]] if it's negation necessarily entails a contradiction. [[Axiom]]s are considered to be [[necessary]] [[proposition|propositions]].

A [[proposition]] is said to be a [[contingent]] [[proposition]] if it can be either true or false. As we will learn later, [[Categorical Propositions]] are one type of statement that can be either true or false.

==Controversy==

While some logicians refer to these axioms as the "Three laws of thought", implying that '''all''' cognition relies on them, it is important to realize that this presumption is false: not all logical systems rely on these axioms, and some logical systems do not rely on axioms at all. Other forms of logic, such as [[Propostional Logic]] instead rely on rules or definitions defined within the system, such as [[Well Formed Formular]].

===What these axioms are NOT===

It is also important to avoid conflating or confusing the so called "laws of thought" with set of nomological (Physical) laws for the universe. Logic is not cosmology. It is not descriptive of how the
universe works'. It is prescriptive: it sets forth a method of examining arguments.

The universe is not 'logical', it merely '''is'''.

It is also important not to confuse classical logic with psychology. The so called laws of thought are not rules for human behavior, they don't even cover all human thought: in our dreams, we are able to imagine contradictions, like being both the victim and the attacker, or being both young and old at the same time - human thought contains rational, irrational and non rational thought - both logic and emotions, impulses and instincts.

Finally, there is no reason to hold that these axioms are "immaterial", or transcendental. Such claims are usually based on arguments from ignorance. An incomplete physical account for abstractions is not a positive argument for an immaterial account for abstractions. Second, 'immateriality' is a negative concept, and a negative definition devoid of a universe of discourse, is meaningless. Unless someone can show how something immaterial can exist, how something immaterial can interact with physical brains, and how something immaterial can act - at all without violating basic physics (the principle of conservation of energy) then the claim that these logical laws that people create are transcendent or immaterial remains incoherent - because the term "immaterial" is meaningless.

==For Advanced Students==

The following section delves into the matter of axioms more deeply, and requires knowledge of symbolic logic. Those following the [[Course in Logic 101]] will learn everything required to grasp this section in later lessons, and can skip this section for now, if desired.

As stated above, some logical systems to not require any axioms at all. For example, the set of axioms for the sentential, or propositional, logic is {} - the empty set!

So how does such a system "get off the ground"?

It creates a set of rules, defined within the system:
<pre>
Let the set of English capital letters be well-formed formular (WFFs), which may be appended
by zero to an infinite amount of primes to indicate different WFFs
If A and B are WFFs, then (A v B) is a WFF
If A and B are WFFs, then (A & B) is a WFF
If A is a WFF, then (~A) is a WFF
If A and B are WFFs, then define (A -> B) to be ((~A) v B)
If A and B are WFFs, then define (A <-> B) to be ((A -> B) & (B ->A))
No other strings are WFFs
</pre>
That defines our "grammar" for our fake little language that will turn into the propositional logic.

Now define 21 rules of inference to allow us to move between WFFs:

http://upload.wikimedia.org/wikipedia/commons/3/34/Propositional_Logic.png

Then we define a function that maps each propositional variable to two values: "True" or "false" (or 1 and 0, or "your mom" and "your dad" - it doesn't matter from a formal point of view).

Then come the soundness (if you can derive a string from a set of strings above, then it must be "true") and completeness (all "true" strings can be derived from the rules above) proofs, and we're done! The system is both sound and complete.

All this in much more detail can be found at:

http://www.algebra.com/algebra/about/history/Propositional-logic.wikipedia#Axioms

The point is that there can be no axioms in this logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally.

This system even allows us to create a proof for the law of non contradiction:
<pre>
Proof (by reductio):

1) (A & ~A) [Proposition]
2) A [Conjunction elimination from 1]
3) ~A [Conjunction elimination from 1]
4) ~(A & ~A) [Reductio, 1 - 3]

QED
</pre>

This is a proof of the [[law of noncontradiction]] (LNC) using the simplest logical system there is, which is called sentential, or [[propositional]] logic. The rules used in the proof were cited in square brackets. The LNC is line 4 of the proof. In short, the argument shows that the LNC is derivable from logic in the most rigorous way possible: a deductive proof.

This said, there are cases where certain logics don't "work" (for example, "all men are mortal, Socrates is a man, therefore Socrates is mortal" is an invalid argument under the logic given above. I'll leave it as an exercise for the interested to figure out why)2.

Those taking the [[Course in Logic 101]] will want to proceed to the next section:
[[The Difference Between Believing and Knowing]]

----

====Footnotes====

1. Metaphysics is a term also invented by [[Aristotle]]; and it has to do with theories concerning how existence itself 'works'.

2. Ok, here's the answer: http://en.wikipedia.org/wiki/First-order_logic

Propositional logic is not adequate for formalizing valid arguments that rely on the internal structure of the propositions involved. For example, a translation of the valid argument

* All men are mortal * Socrates is a man * Therefore, Socrates is mortal

into propositional logic yields

* A * B * therefore C

which is invalid, as there is no connection between the premises and the conclusion.
----

==References==

* Copi, I. M, Cohen, C., (2001), "Introduction to Logic", 11th Edition.

Indeterminate

Admin — Mon, 18 Jun 2007 23:17:22 GMT

Admin:

A reason for postulating a third truth-value 'indeterminate' is the problem of vagueness. Vagueness exists in the real world, because the real world is not a set of discrete catergories - it is a continuum. Therefore, attempts to apply deductive logic to the real world are always as imperfect as attempts to apply geometrical patterns like squares and circles to a world filled with ovals and rectangles.

Consider a color spectrum between red and orange. Let us also call the statement, 'It is red here', 'p'. Now, it is obvious that there are cases where 'p' is true (the red case) and clear cases where 'p' is false (the orange case). However, between the two extremes there seems to be a large class of colours where we just cannot say whether 'p' is true or false. Hence, some have suggested that in such cases 'p' is neither true nor false and that a third truth-value — indeterminate — is needed. Such a suggestion would rule out bivalence but retain the law of excluded middle. The best book on this distinction and the problem of vagueness is Timothy Williamson's book Vagueness.

Admin — Mon, 18 Jun 2007 22:49:43 GMT

Admin:

In [[Propositional Logic]], a '''tautology''' is a statement that is truth-functionally valid—i.e. it is universally true, or true in every interpretation). For example, the statement "If it rains, then it rains" is a tautology. Every theorem of propositional logic is a tautology, and so we can equivalently define 'tautology' as any theorem of propositional logic—i.e. any statement that is deducible from the empty set in some system of deduction of propositional logic, such as a natural deduction system. The term is often mistakenly applied to any validity (or theorem) of [[first-order logic]], though it applies only to a proper subset of such validities. The term was originally introduced by [[Ludwig Wittgenstein]].

The negation of a tautology is clearly a [[Contradiction]], and the negation of a contradiction is clearly a tautology. A sentence that is neither a tautology (always true) nor a contradiction (always false) is logically [[Necessity and Contingency|contingent]], i.e., possible of being true or false .

==Discovering tautologies==

An effective procedure for checking whether a propositional formula is a tautology or not is by means of a [[Truth Tables|Truth Table]]

== References ==

Tautology

Admin — Mon, 18 Jun 2007 22:48:46 GMT

Admin:

Tautology

Admin — Mon, 18 Jun 2007 22:44:48 GMT

Admin:

In [[Popositional Logic]], a '''tautology''' is a [[statement]] that is truth-functionally valid—i.e. it is universally true, or true in every interpretation). For example, the statement "If it rains, then it rains" is a tautology. Every theorem of propositional logic is a tautology, and so we can equivalently define 'tautology' as any theorem of propositional logic—i.e. any statement that is deducible from the empty set in some system of deduction of propositional logic, such as a [[natural deduction]] system. The term is often mistakenly applied to any validity (or theorem) of [[first-order logic]], though it applies only to a proper subset of such validities. The term was originally introduced by [[Ludwig Wittgenstein]].

The negation of a tautology is clearly a [[Contradiction]], and the negation of a contradiction is clearly a tautology. A sentence that is neither a tautology (always true) nor a contradiction (always false) is logically [[Necessity and Contingency|contingent]], i.e., possible of being true or false .

== Tautologies versus validities ==

The use of 'tautology', however, can be extended to [[first-order logic]] since it includes propositional logic. It can be further extended to include sentences that are quantified in the following sense. Call any statement that is not a truth-functional compound (i.e. not a conjunction, disjunction, conditional, etc.) a 'Boolean atom'. Then every [[atomic sentence]] is a Boolean atom, as is every quantified sentence—i.e. those of the form <math>\\forall x\\phi</math> or <math>\\exists x\\phi</math>. For example, <math>P(x)</math> and <math>\\forall x(P(x)\\land Q(y))</math> are Boolean atoms, while <math>\\forall xP(x)\\land Q(y)</math> is not. Then a statement of first-order logic is a tautology if the uniform relettering of each of its Boolean atoms yields a tautology in the propositional sense. Thus <math>\\forall x(P(x) \\lor\\lnot P(x))</math> is not a tautology, since its Boolean relettering yields <math>p</math>, while <math>\\forall xP(x)\\lor\\lnot\\forall xP(x)</math> is a tautology. One could further extend this notion by taking statements to be equivalence classes of statements, each of which is closed under the property of its elements being variants of each other (e.g. ''∀xP(x)'' is a variant of ''∀yP(y)'', and likewise upon substituting any other variable for ''x'' in the former). Then the Boolean relettering of <math>\\forall xP(x)\\lor\\lnot\\forall yP(y)</math> yields a tautology, since each disjunct falls under the same equivalence class.

==Discovering tautologies==

An effective procedure for checking whether a propositional formula is a tautology or not is by means of a [[Truth Tables|Truth Table]]

== References ==

Admin — Mon, 18 Jun 2007 22:02:10 GMT

Admin:

I hope you have enjoyed this encounter as much as I have. If you have a need for further assistance, please feel free to contact Christopher Smith at hanniballecturer@gmail.com. Otherwise, I will assume that you have understood and benefited from this page. It is my humble hope that a few will learn from this page, and make the world a tad bit more... logical.

http://www.candleinthedark.com/drsmith_peaceful.jpg
Adieu
[[Logic]]