nirgrahamUK: if being a cat has no meaning, then it is not a question to be decided by any logic. one would be mad to ask question of truth about it. you are merely denying that to 'be a cat' is anything knowable, not that things can contradict.
if being a cat has no meaning, then it is not a question to be decided by any logic. one would be mad to ask question of truth about it.
you are merely denying that to 'be a cat' is anything knowable, not that things can contradict.
Hence why I keep bringing up Nietzsche
'Men do not change, they unmask themselves' - Germaine de Stael
Anarcho-Mercantilist: Imagine an animal that looks like a cat, but has three legs. You would assume it "is" still a cat. Imagine an animal that looks like a cat, but has a head shaped like a dog. "Is" it still a cat? Imagine an animal that looks like a cat, except it has a head shaped like a dog, barks, and behaves like a dog. "Is" it still a cat? Two-valued logic would fail at the last two cases. We cannot determine if it "is" either a cat or not a cat.
Imagine an animal that looks like a cat, but has three legs. You would assume it "is" still a cat.
Imagine an animal that looks like a cat, but has a head shaped like a dog. "Is" it still a cat?
Imagine an animal that looks like a cat, except it has a head shaped like a dog, barks, and behaves like a dog. "Is" it still a cat?
Two-valued logic would fail at the last two cases. We cannot determine if it "is" either a cat or not a cat.
The deep end has now been reached: this is a great bolstering to Wittgenstein's thesis that all philosophical problems are nothing but ones of language.
Abstract liberty, like other mere abstractions, is not to be found.
- Edmund Burke
nirgrahamUK:it either is a cat or it isnt, if it means something to 'be a cat'.
We would have more precision if we allow infinite-valued logic rather than the two-valued "is" or "is not."
Let us define the word "cat" as an animal which has four legs, two eyes, two ears, a mouth, meows, purrs, etc. If we define the word "cat" further, we end up defining it with these attributes: covered with hair, has whiskers, produces saliva, likes to eat meat, has red blood flowing through its veins, can hear high-pitched noises, can move all its limbs, has a four-chambered heart, etc.
However, not all cats purr. Not all cats meow, produce saliva, eats meat, can hear high-pitched noises. Not all cats have all these characteristics. Not all cats have genes which express these characteristics.
If we define a "cat" this way, then we cannot label anything as a "cat" because no cat has all those defined characteristics. But we still label an animal as a "cat" if it has an adequate amount of these characteristics. Why?
Let us go back to the above definition of "cat." In prototype theory, the above definition represents a prototype of the term "cat." Prototype theory claims that the more similar the characteristics that an object matches with a prototype, the more likely we would identify it with that prototype. In this scenario, we have defined the prototype of "cat."
Life is filled with misinterpretations, misrepresentations, and prodigal folklore.
laminustacitus:The deep end has now been reached: this is a great bolstering to Wittgenstein's thesis that all philosophical problems are nothing but ones of language.
If he had actually meant that "nothing but one's use of language," then we all would have disagreed with him. But that depends on his definition of "philosophy."
I have read Wittgenstein's works, and I cannot understand most of it. I have no direct influence from him, except his indirect contribution towards prototype theory. He seemed to have advocated "exemplar theory" rather than "prototype theory." I have not even heard of the name "Wittgenstein" before the year 2009.
I have discovered general semantics in early April this year. However, Korzybski developed general semantics before Wittgenstein developed his own ideas. Wittgenstein appeared to have copied a few ideas from general semantics, and then bastardized them.
Korzybski appeared to have similar views towards "philosophy." In Science and Sanity, he claimed that he has solved most "philosophical" problems. However, he still reserved "epistemology" to refer to the study of general semantics.
Wait, what "is" a "cat?"
Such categorical definitions have no real meaning to them and cannot be determined by logic.
Angurse:Wait, what "is" a "cat?"
The term "cat" refers to the prototype which we have defined above.
Anarcho-Mercantilist:The term "cat" refers to the prototype which we have defined above.
And, again, why did we come to that definition?
Angurse: Anarcho-Mercantilist:The term "cat" refers to the prototype which we have defined above. And, again, why did we come to that definition?
As you have stated previously:
Angurse: Do the laws logic even apply to categorizing entities? Prototype theory just seems to be an approach to linguistics that differs from the conditions used in Aristotelian logic, not necessarily a rebuke of Aristotelian logic itself.
Do the laws logic even apply to categorizing entities? Prototype theory just seems to be an approach to linguistics that differs from the conditions used in Aristotelian logic, not necessarily a rebuke of Aristotelian logic itself.
As mentioned before, prototype theory extends Aristotelian logic because it allows infinite values instead of two values. Alternatively, prototype theory has more generality than Aristotelian logic. Prototype theory therefore does not "reject" the laws of Aristotelian logic itself in the sense of completely rebuking them.
The laws of logic does indeed apply to identifying or categorizing entities. However, the "laws of logic" does not necessarily refer to only the Aristotelian type. The "laws of logic" could refer to the rules from prototype theory or general semantics, because the non-Aristotelian forms of logic (prototype theory, general semantics) extends Aristotelian logic.
Seems like you had conflated my 'metaphysical' rejection to the laws of logic with my 'epistemological' criticisms of two-valued logic.
And, again, no flaw in Aristotelian logic has been shown then.
Angurse: And, again, no flaw in Aristotelian logic has been shown then.
I have used the term "flaw" to mean that Aristotelian logic lacks the accuracy and precision of infinite-valued logic.
So let me rephrase my question: Do you believe that infinite-valued logic has greater accuracy and precision than two-valued logic?
AM: You're not even addressing logic here, you're addressing semantics.
Brainpolice: AM: You're not even addressing logic here, you're addressing semantics.
Would you explain to me why my last 20 posts addressed about 'semantics' and not on the laws of logic? Prototype theory and other forms of non-Aristotelian logic deals with infinite values. Two-valued logic only deals with two values: true or false.
Anarcho-Mercantilist: Juan:Well, show a flaw in the laws of logic then. I will show the flaws of the Aristotelian laws of logic below. In categorizing entities, the law of the excluded middle does not have as much precision as prototype theory. The law of the excluded middle says: a thing is either completely A or not-completely-A. Prototype theory says: a thing can have many degrees of similarity towards the category A. The law of the excluded middle is two-valued logic, while prototype theory is infinite-valued logic. The mutant monotreme and the three-legged cat does not quite fit into two-valued logic. Infinite-valued logic deals with them better.
Juan:Well, show a flaw in the laws of logic then.
I will show the flaws of the Aristotelian laws of logic below.
In categorizing entities, the law of the excluded middle does not have as much precision as prototype theory.
The law of the excluded middle says: a thing is either completely A or not-completely-A.
Prototype theory says: a thing can have many degrees of similarity towards the category A.
The law of the excluded middle is two-valued logic, while prototype theory is infinite-valued logic.
The mutant monotreme and the three-legged cat does not quite fit into two-valued logic. Infinite-valued logic deals with them better.
The logic is uneffected. Its the premise "all cats have four legs" that is disproved.
"If all cats have four legs, then fluffy has four legs" is valid logic, but an inaccurate premise. The conclusion is as accurate as the premise is. That is precisely why statements begin with if.
If A, then B is a shorthand way of saying the transitive property: If A=B and B=C, then A=C. With the middle premise that fluffy is a cat being unstated.
If cat = four legged animal
and fluffy = cat
then fluffy= four legged animal
As I said, the logical form is always valid , but the conclusion is as accurate as the premises are. There may be a case where a premise, even though not entirelly accurate, is accurate enough to still be useful. For example, all cats have four legs.
Peace
JonBostwick: Anarcho-Mercantilist: Juan:Well, show a flaw in the laws of logic then. I will show the flaws of the Aristotelian laws of logic below. In categorizing entities, the law of the excluded middle does not have as much precision as prototype theory. The law of the excluded middle says: a thing is either completely A or not-completely-A. Prototype theory says: a thing can have many degrees of similarity towards the category A. The law of the excluded middle is two-valued logic, while prototype theory is infinite-valued logic. The mutant monotreme and the three-legged cat does not quite fit into two-valued logic. Infinite-valued logic deals with them better. The logic is uneffected. Its the premise "all cats have four legs" that is disproved. "If all cats have four legs, then fluffy has four legs" is valid logic, but an inaccurate premise. The conclusion is as accurate as the premise is. That is precisely why statements begin with if. If A, then B is a shorthand way of saying the transitive property: If A=B and B=C, then A=C. With the middle premise that fluffy is a cat being unstated. If cat = four legged animal and fluffy = cat then fluffy= four legged animal As I said, the logical form is always valid , but the conclusion is as accurate as the premises are. There may be a case where a premise, even though not entirelly accurate, is accurate enough to still be useful. For example, all cats have four legs.
You have recently entered into this discussion, so you probably missed several previous posts. Previously, I had accepted the assertion that Aristotelian logic may be logically valid. However this does not imply that Arostotelian logic may be logically sound. You have just demonstrated that Aristotelian logic may not be logically sound, but still retain its logical consistency. I "reject" two-valued logic because of its logical unsoundness.
This implies that the performative contradiction argument may be logically valid, but not necessarily logically sound. Applying the performative contradiction argument to ethics does not guarantee the logically soundness of the system itself. Hence, this demonstrates some of the inaccuarcies of the performative contradiction argument
By the way, I have read James A. Donald's defense of 'natural law' and 'natural rights.' Donald has defined the terms 'truth', 'logical consistency', 'utilitarianism', 'relativism' differently that what some of its respective proponents have defined them, and has conflated the multiple meanings of each term. For example, he has strawmanned some, but not all, utilitarians. He has defined 'utilitarianism' as the system which maximizes the utility for 'society' by mathematical calculations, but not all 'utilitarians' define it that way. However, I still agree with his article if I go by his unique definitions. It seems that most of the conflict revolves around definitions itself.
In fact, Donald's article has noted me that wilderness and Anarchist Cain have different definitions of the 'fact-value dichotomy.' For example, I agree with Anarchist Cain's point that biological facts can partially derive some aspects of ethics. Anarchist Cain has pointed out that ethics requires grounding from 'agent-neutral values' from 'nature'. However, I have pointed out that ethics requires grounding form 'agent-relative values.'
Juan, Night, Anarchist Cain, wilderness, and Jon had classified the Aristotelian laws of logic as 'axioms' and 'necessary givens'. If you also classify scientific facts as 'axioms' and 'necessary givens', then it would imply that we still have unclear terminology. Therefore, I would like to ask four questions to clarify what you mean by an 'axiom' and a 'necessary given'.
Do you guys classify the law of gravity as an 'axiom'? Do you classify the law of gravity also as a 'necessary given'?
How about the law of natural selection? Does that fit into both the criterions of an 'axiom' and a 'necessary given'?
Anarcho-Mercantilist:Do you guys classify the law of gravity as an 'axiom'? Do you classify the law of gravity also as a 'necessary given'?
What is the point of this? Are you trying to establishing the 'subjectivity' of gravity throughout the universe? [ Gravity on earth but not necessarily space ] I would also not like to confusion the discussion with an a priori axiom and an a posteri axiom.
I don't know about all, but certainly most of them seem to revolve around definitions. And about the cat with a dog's head, it's not that two-valued logic necessarily fails, it's that we have to have an absolute definition of a cat in order to use two-valued logic.
Why anarchy fails
Anarcho-Mercantilist: Previously, I had accepted the assertion that Aristotelian logic may be logically valid. However this does not imply that Arostotelian logic may be logically sound. You have just demonstrated that Aristotelian logic may not be logically sound, but still retain its logical consistency. I "reject" two-valued logic because of its logical unsoundness.
Let me know if I missed something earlier, but your use of the term logically sound seems non-standard. A deductive argument can be logically sound or unsound, but two-valued logic in itself cannot be logically sound or unsound. "A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound."
So whether an argument is sound or unsound simply depends on whether its premises are true. What criticism of Aristotelian logic is it to say that it "may not be logically sound," if that merely means that it is possible to word an argument starting from a false premise?
Anarchist Cain:I would also not like to confusion the discussion with an a priori axiom and an a posteri axiom.
Anarchist Cain, you classified the law of gravity as an 'a priori' 'axiom' and an 'a priori' 'necessary given'. I will assume that you classify an 'a priori axiom' as a type of 'axiom'. This means that you had defined an 'axiom' and a 'necessary given' sufficiently with these three attributes: 'non-normative', 'scientific', and 'factual'.
We had defined 'science' as necessary 'non-normative'. In addition, we will assume the term 'scientific' as the mere adjectival form of science'. Therefore, we can leave out the 'non-normative' attribute as the definitions for an 'axiom' and a 'necessary given'.
We also had defined 'science' as necessary 'factual', but not sufficient. For example, 'moral realists' might attribute ethical commands as 'factual', but not as 'scientific'. For example, we often hear statements such as "it is a fact that taxation is theft", or "it is a fact that the free market is the only ethical system".
However, some might deny those statements as 'scientific', because the scientific method does not derive them. Consequentially, 'moral realists' might distinguish 'moral facts' from 'scientific facts' by determining if 'facts' themselves require verification by 'empirical' research such as the scientific method. If the 'facts' do require verification by 'empirical' research such as the scientific method, they will classify them as 'scientific facts'. If not, they will possibly classify them as 'moral facts'.
However, Mises denied praxeology as a 'science', because it does not utilize 'empirical' research to explain phenomenon. Instead, praxeology uses cause-effect analysis to predict the results from the initial assumptions. Praxeology differs from 'science', which helps us to explain phenomenon, not to predict the effects of a theory as in praxeology.
This means that you might classify 'moral facts' as necessarily 'a priori axioms', and 'scientific facts' as necessarily 'a posteriori axioms'. By the term 'axiom' you define it as a 'necessary given' 'truth'. You might also had defined a 'fact' necessarily as a 'truth'.
Therefore, if you classified both 'scientific facts' and 'moral facts' as 'necessary givens', then it would, by definition, follow that you must have defined both 'scientific' and 'moral facts' as 'necessary givens'.
I classify both the laws of logic and ethics as normative. However, that does not preclude the possibility that I will deny these normative ideas as 'facts'. For instance, I can define 'facts' as compatible with normative ideologies. However, normative ideologies represent the 'opinions' of human beings. Because an idea cannot represent both a 'fact' and an 'opinion' at the same time, we should not define 'facts' as compatible with normative ideologies.
However, we could theorize that the law of non-contradiction actually applies to the universe. For example, stones do not fall both up and down. The color of the water does not 'contradict' the color of the atmosphere, at least in some sense. However, does the law of non-contradiction deny 'contradiction' in general or specifically deny 'logical contradiction'? Can we say that "the color of the water does not 'logically contradict' the color of the atmosphere"?
I deny the law of non-contradiction in this sense, because I the blue color of water does not 'logically contradict' the blue color of the atmosphere. Something that 'contradicts' itself does not follow that the same thing 'logically contradicts' itself. The law of non-contradiction, because of its logicality, does not explain the universe. Therefore, the law of non-contradiction reflect normative values.
We should recall that this thread conflates the two senses of the laws of logic: the 'metaphysical' sense and the 'epistemological' sense. The last paragraph rejects the law of non-contradiction in the 'metaphysical' sense, not in the 'epistemological sense'. We specifically stated that although entities within our universe does not 'contradict' themselves in a sense, it implies a category error to further assert that the same entities do not 'logically contradict' themselves.
Even though the previous paragraph 'rejected' the laws of logic in the 'metaphysical' sense, it does not imply that we 'reject' the laws of logic in the 'epistemological' sense. Indeed, we actually do not 'reject' the laws of logic in the 'epistemological' sense. We only 'reject' two-valued logic in the 'epistemological' sense because of its inaccuracy and imprecision'. We do not 'reject' 'infinite-valued logic in the 'epistemological' sense. However, we reject all forms of logic in the 'metaphysical' sense, regardless of whether it allows two or infinite values.
AJ: Anarcho-Mercantilist: Previously, I had accepted the assertion that Aristotelian logic may be logically valid. However this does not imply that Arostotelian logic may be logically sound. You have just demonstrated that Aristotelian logic may not be logically sound, but still retain its logical consistency. I "reject" two-valued logic because of its logical unsoundness. Let me know if I missed something earlier, but your use of the term logically sound seems non-standard. A deductive argument can be logically sound or unsound, but two-valued logic in itself cannot be logically sound or unsound. "A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound." So whether an argument is sound or unsound simply depends on whether its premises are true. What criticism of Aristotelian logic is it to say that it "may not be logically sound," if that merely means that it is possible to word an argument starting from a false premise?
The premises of an argument may not be 'true' in the first place. For example, some people would identify the cat with a head shaped like a dog as a 'cat', while others would identify it as a 'dog'. If the cat with a head of a dog also barks, then more people would identify that thing as a 'dog' instead of a 'cat'. If the cat has gained more and more attributes of a 'dog', then more and more people would start identifying it as a 'dog' instead of a 'cat'.
In Aristotelian logic, the premises of any argument only assumes two values: either true or false. It can either assume an entity as entirely true (100% a cat) or entirely false (0% a cat).
However, prototype theory gives it more accuracy and precision by allowing infinite-values of truth. For example, it can assume an entity as either 80% a cat, 60% a cat, or 10% a cat. The cat that merely barks may be 80% of a cat, while the cat with a head shaped like a dog may be 60% a cat. The cat that has both a head shaped like a dog and barks may be 10% a cat, for example.
Prototype theory therefore refines the accuracy and precision of Aristotelian logic. It makes the premises more presise, therefore allowing the premises to be more logically sound. It allows degrees and uncertainties in the truth of its premises. The conclusions of the argument may be more presise and logically sound, for example.
Anarcho-Mercantilist: Anarchist Cain, you classified the law of gravity as an 'a priori' 'axiom' and an 'a priori' 'necessary given'. I will assume that you classify an 'a priori axiom' as a type of 'axiom'. This means that you had defined an 'axiom' and a 'necessary given' sufficiently with these three attributes: 'non-normative', 'scientific', and 'factual'.
Actually I never classified gravity as an a priori given...we are still talking about natural law here right? On the other hand gravity is certainly an a posteri axiom.
Anarcho-Mercantilist:However, Mises denied praxeology as a 'science', because it does not utilize 'empirical' research to explain phenomenon. Instead, praxeology uses cause-effect analysis to predict the results from the initial assumptions. Praxeology differs from 'science', which helps us to explain phenomenon, not to predict the effects of a theory as in praxeology.
Actually the Austrian approach is not merely praxeology alone. It is in fact a combination of praxeology, historiography and positivism. So I would very much like to see this quote where Mises denied his own method as a science, for we do not know which science you are discussing. Natural or Social?
Anarcho-Mercantilist:I deny the law of non-contradiction in this sense, because I the blue color of water does not 'logically contradict' the blue color of the atmosphere
So you deny the law of contradiction because it does not make a contradictionary destinction betweeen sea water and sky?
Anarcho-Mercantilist:In Aristotelian logic, the premises of any argument only assumes two values: either true or false.
Yes.
Anarcho-Mercantilist:It can either assume an entity as entirely true (100% a cat) or entirely false (0% a cat). However, prototype theory gives it more accuracy and precision by allowing infinite-values of truth. For example, it can assume an entity as either 80% a cat, 60% a cat, or 10% a cat.
So can Aristotelian logic: "If an entity is 80% cat, then..." All you have to do is clearly define what "80% cat" means, then regular logic works fine. The prototype system seems interesting, but it's not a new type of logic, it's just an interesting and possibly useful way to form definitions.
Anarcho-Mercantilist:Prototype theory therefore refines the accuracy and precision of Aristotelian logic. It makes the premises more presise, therefore allowing the premises to be more logically sound. It allows degrees and uncertainties in the truth of its premises. The conclusions of the argument may be more presise and logically sound, for example.
Again, you're talking about a more precise way to define premises, not a departure from Aristotelian logic.
Prototype theory, which allows infinite values, is different than Aristotelian logic, which allows two values. You are merely pointing out that two-valued logic can "emulate" infinite-valued logic.
However, the law of identity does not hold for such statements. We cannot possibly define everything an '80% cat' 'is'. Let us go back to a post of mine:
Anarcho-Mercantilist: Let us define the word "cat" as an animal which has four legs, two eyes, two ears, a mouth, meows, purrs, etc. If we define the word "cat" further, we end up defining it with these attributes: covered with hair, has whiskers, produces saliva, likes to eat meat, has red blood flowing through its veins, can hear high-pitched noises, can move all its limbs, has a four-chambered heart, etc. However, not all cats purr. Not all cats meow, produce saliva, eats meat, can hear high-pitched noises. Not all cats have all these characteristics. Not all cats have genes which express these characteristics. If we define a "cat" this way, then we cannot label anything as a "cat" because no cat has all those defined characteristics. But we still label an animal as a "cat" if it has an adequate amount of these characteristics. Why? Let us go back to the above definition of "cat." In prototype theory, the above definition represents a prototype of the term "cat." Prototype theory claims that the more similar the characteristics that an object matches with a prototype, the more likely we would identify it with that prototype. In this scenario, we have defined the prototype of "cat."
Unfortunately, language must leave out some details of an entity to define it. For example, we have excluded the attribute 'has 38 chromosomes' in the definition of the 'cat' prototype. Some cats even have 36 chromosomes, but they function and look like normal cats. In two-valued logic, we cannot label anything as a 'cat' if we define 'cat' with this much detail. Prototype theory solves this by allowing variations of the identified cat from the 'cat' prototype.
AJ: Anarcho-Mercantilist:It can either assume an entity as entirely true (100% a cat) or entirely false (0% a cat). However, prototype theory gives it more accuracy and precision by allowing infinite-values of truth. For example, it can assume an entity as either 80% a cat, 60% a cat, or 10% a cat. So can Aristotelian logic: "If an entity is 80% cat, then..." All you have to do is clearly define what "80% cat" means, then regular logic works fine. The prototype system seems interesting, but it's not a new type of logic, it's just an interesting and possibly useful way to form definitions.
Sorry, but prototype theory does not deal with cardinal percentages. I have used cardinal percentages to mean the percentage of people who still labeled the entity as a 'cat'. An '80% cat' means that 80% of people still identify a cat that barks as a cat; a '60% cat' means that 60% of people still identify a cat that has a head shaped like a dog as a 'cat'.
Even if we allow percentages in prototype theory, it still does not follow that we can define an '80% cat'. Prototype theory only defines the prototype 'cat' first, and only then it allows the individual's judgment to determine the similarity of the specified entity to the prototype 'cat'. An individual can label multiple different entities as an '80% cat'. An '80% cat' does not necessarily mean that it must bark; it can have a three-chambered heart, or 40 chromosomes. Hence, we cannot define an '80% cat', because lots of variations can fall under the definition of an '80% cat'.
Prototype theory allows variations in human judgment. It differs from two-valued logic because two-valued logic specifies a 'cut-off point' between a cat and not-a-cat. Individuals differently specify these 'cut-off points'; some people will not label a cat as a 'cat' if it merely barks; some people will keep it under the label 'cat' until the same entity acquires a dog-head in addition to its barking noises.
Human judgments vary because of different 'cut-off points' in identifying an object as a 'cat'. However, we cannot eliminate differences in 'cut-off points' because of the impossibility of defining every feature of a cat, as the above quote shows. Prototype theory differs from Aristotelian logic because it allows more precision of the differences in human judgement, which we cannot explicate in definitions.
It's still just an issue of definitions within everyday Aristotelian logic: "If X is an entity that 80% of people identify as a cat, then..." or "If X is an entity that you identify as a cat, then..."
I no not downplay the potential utility of this novel form of definition. It could well be supremely and amazingly useful, but I don't see what value there is in calling it a new type of logic when it's perfectly handled under the regular type.
I think its disingenious to talk about Aristotlean logic. Propositional logic please.
and you are confused between schema's of categorizing, on the one hand and logic on the other.
Where there is no property there is no justice; a proposition as certain as any demonstration in Euclid
Fools! not to see that what they madly desire would be a calamity to them as no hands but their own could bring
You had expanded the definition of Aristotelian logic to describe all reasoning. However, reasoning does not confine itself to Aristotelian logic.
I will define Aristotelian logic as necessarily incorporating the laws of identity, the excluded middle, and non-contradiction. The law of the excluded middle only applies to two-valued logic, not to infinite-valued logic. The law of the excluded middle therefore contradicts with infinite-valued logic.
Prototype theory allows infinite values in the sense that it categorizes entities based on their similarity to a prototype. By definition, the law of the excluded middle does not know how to deal with infinite values of similarity, only two-valued true or false.
you dont understand the difference between classification strategies and logic.
prototype theory is not a theory of logic but of classification.
nirgrahamUK: you dont understand the difference between classification strategies and logic. prototype theory is not a theory of logic but of classification.
However, we can apply some ideas from prototype theory into the laws of logic to challenge the soundness of the premises.
your wordplay is tedious
Aristotelian logic also categorizes premises as either 'true' or 'false'. However, infinite-valued logic categorizes premises with more precision.
is that true or false? or will i need a Cantorian calculator to figure it out?
Can you cite an academic source that concurs with you in this nonsense>, perhaps they can state their position with more rigour and thus allow me the possibility to engage.
So we have a nifty way of making premises more precise. Suppose we accept that this prototyping is useful. Can you give an example of how it's useful for the purposes of this discussion (natural law, etc.)?
basically without the principle of contradiction. (which is what the impossibility of true contradiction is called) you cannot prove any thing. you can not argue validly let alone soundly.
if you took first year logic at college/university you would understand that if (P&~P) = true, anything follows. anything. P follows, ~P follows, Q follows, X follows. ad infinitum.
once you abandon the principle you abandon thinking rationally. good luck with that.
Can you cite an academic source that concurs with you in this nonsense ?
February 17 - 1600 - Giordano Bruno is burnt alive by the catholic church. Aquinas : "much more reason is there for heretics, as soon as they are convicted of heresy, to be not only excommunicated but even put to death."
nirgrahamUK: if you took first year logic at college/university you would understand that if (P&~P) = true, anything follows. anything. P follows, ~P follows, Q follows, X follows. ad infinitum. once you abandon the principle you abandon thinking rationally. good luck with that.
Yep, I think a lot of thinking people (especially math people) figure that out soon enough. Even Aristotle's rules and propositional logic are like training wheels. If people don't understand logic, I don't think any amount of symbols or rules will help them. There's no substitute for just pondering for long hours by yourself.
nirgrahamUK:if you took first year logic at college/university you would understand that if (P&~P) = true, anything follows.
The law of the excluded middle can only work if P equals either 100% true or 100% false. It does not allow fuzzy values such as 90% true or 30% true.
AJ:It's still just an issue of definitions within everyday Aristotelian logic: "If X is an entity that 80% of people identify as a cat, then..."
In Aristotelian logic, if you change the '80%' to an '81%', then you must create a new conditional for this specific instance. Aristotelian logic does not recognize the '80%' as a variable, but as a constant. We must therefore enumerate conditionals indefinitely for it to match infinite-valued logic.
If you try to change the constant into a variable, then Aristotelian logic only allows you to use two variables: either '100%' or '0%'.
Prototype theory explains how the mind categorizes entities. This makes it useful for artificial intelligence research. nirgraham made a valid point that prototype theory does not explicitly try to reformulate the Aristotelian laws of logic.
However, I borrowed some ideas from prototype theory in order to extend Aristotelian logic to allow infinite values. I also borrowed my idea that one cannot possibly define anything in full detail, my idea that judgments can change, and my idea about 'cut-off points' all from general semantics.
General semantics does not 'disprove' nor 'reject' Aristotelian logic in the sense that it rejects it entirely. I already had repeated this in this thread for about ten times. Rather, it cites that these rules of logic can create potential problems. It merely notes that the Aristotelian laws of logic do not always hold in terms of logical soundness in relation to the real-world. It therefore extends Aristotelian logic with some principles that helps to increase accuracy and precision.
Please note that the word 'semantics' in 'general semantics' does not have anything to do with 'semantics' in the sense of the study of meaning. General semantics does not necessarily have anything to do with my terminological clarifications in this thread. I used to clarify about terminology long before I had discovered general semantics.
You can learn more about general semantics by reading Alfred Korzybski's work Science and Sanity. I read that book twice, and it is well-worth a read. If you read this 800-page book, you will acquire vast knowledge of the state of science in the year 1933. In addition, you may find these two other books useful in learning general semantics: S. I. Hawakaya's Language in Thought and Action, and Susan and Bruce Kodish's book Drive Yourself Sane: Using the Uncommon Sense of General Semantics. Although the latter two leaves out many details, you might read them more easily than reading Korzybski's Science and Sanity.
Anarcho-Mercantilist: AJ:It's still just an issue of definitions within everyday Aristotelian logic: "If X is an entity that 80% of people identify as a cat, then..." In Aristotelian logic, if you change the '80%' to an '81%', then you must create a new conditional for this specific instance. Aristotelian logic does not recognize the '80%' as a variable, but as a constant. We must therefore enumerate conditionals indefinitely for it to match infinite-valued logic.
It's still just, "Let 0 <= N <= 100. If X is an entity that N% of people identify as a cat, then..." I'd really prefer to call this just normal everyday logic where one is applying a basic trick from highschool algebra to describe a set of propositions - an infinite set to be sure, but again, can we get an example of an application of this "infinite valued logic" that is so substantialy useful as to warrant its own special designation?
Anarcho-Mercantilist: It merely notes that the Aristotelian laws of logic do not always hold in terms of logical soundness in relation to the real-world.
I think this could be better stated as, "An over-simplified formulation of premises in everyday logic creates practical problems in the real world." No argument here, but I think you're running into opposition on this forum because of statements like the bolded portion above, where it sounds like you're saying everyday (Aristotelian? Propositional? I would just say "obvious" or "self-evident") logic is not logically sound, which again would be a mismatch of terms. Logical soundness refers only to the premises of an argument, not to the system of logic. Citing sources won't change that, although they may be very interesting in their own right and I'd like to check them out. The issue in contention appears to be how to best state premises, and in that I don't think anyone is necessarily disagreeing with you.
As an aside, AM, I read up a bit on general semantics, and it seems Korzybski's problem with Aristotelian logic was that it claimed that "the word is the essence of the thing defined," which of course is the fallacy that "the map is the territory." So if you consider that part of Aristotelian logic, then it is wrong - but everyday logic still stands. Korzybski's efforts to eliminate such basic cognative biases from logic are certainly headed in the right direction. However, I have not read his book, so I cannot say if he goes too far and throws out everyday logic along with Aristotle's mistaken notion. I'm all for the "Jim seems to be acting foolish," instead of "Jim is a fool," and agree that this pathology pervades modern thought and even science, but this is all just about being more accurate. Still, logic stands, or else nothing can be proven. Most of all, show me an application of the infinite-valued logic so amazing that it warrants a special designation. And let's stop using the term Aristotelian logic. Propositional logic or just "logic" would be better, because then there are no map-territory fallacies implied.
Both Aristotelian logic and propositional logic presupposes elementalism. Elementalism, a term coined by Korzybski, refers to the idea that we can identify, categorize, and label entities in the world into clear-cut categories, separate entities into black-and-white values, assume the all-or-nothingness of entities, and reduce complex interactions into linear relations. Besides the Aristotelian system, Korzybski criticized propositional logic and intuitionist logic for its elementalism.
General semantists practice non-elementalism, which implies the idea of categorization imperfections, fuzzy boundaries, and the dynamicism of language. Non-elementalism does not disprove elementalism. In practice, non-elementalism extends elementalism in a way which resolves many of the imperfections of elementalism.
You seem to have read very little about general semantics. Korzybski has discovered much more imperfections of propositional logic and intuitionist logic.
I have seen no web sources which completely summarizes general semantics. They only reveal a meager fraction of what Korzybski has ascribed about general semantics. You can read his book Science and Sanity here.
Rothbardian natural law requires us to presume propositional logic. Revealing the flaws of propositional logic will challenge Rothbardian natural law.
obviously you dont understand propositional logic. you only understand classification schemas