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Does Objectivism have the concept of a tautology?

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Here is the first paragraph of The Cambridge Dictionary of Philosophy entry on tautologies:

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tautology, a proposition whose negation is inconsistent, or (self-) contradictory, e.g. "Socrates is Socrates", "Every human is either male or non-male", "No human is both male and non-male", "Every human is identical to itself", "If Socrates is human then Socrates is human". A proposition that is (or is logically equivalent to) the negation of tautology is called a (self-) contradiction. According to classical logic, the property of being implied by its own negation is a necessary and sufficient condition for being a tautology and the property of implying its own negation is a necessary and sufficient condition for being a contradiction. Tautologies are logically necessary and contradictions are logically impossible.

Does Objectivism accept the concept of a tautology (that is, consider tautologies an objectively distinct category of proposition)? If so, what is the difference between the concept of a tautology and the concept of an analytic proposition?

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A similar question came up during a Q&A session of the 1976 Objectivism course. I am quoting the exerpt bellow:

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Q. I once took a philosophy course in which the professor said that the Law of Identity is tautological. It doesn't reveal any information about reality. What is meant by this?

A. A tautology is a statement which says the same thing. It's predicate is the same as the subject. A brother is a male. A male sibling is male, would be a tautology. A is A is a tautology. It is part of the post Kantian mystic in philosophy that tautology says nothing about reality. There is no base for that view whatever. I cover it in The Analytic-Synthetic Dichotomy in that article. It's a form of that error, which I alluded to briefly in the lectures. I will not repeat it here in the answer, except simply to say that according to Objectivism all knowledge is ultimately tautological, because a concept stands for and includes every fact about its reference. So, whenever you say, a man has two legs, man includes everything that is true of him, including that he has two legs. This I elaborate in my article on The Analytic-Synthetic Dichotomy. This is particularly a Kantian method of attacking logic.

 

 

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The topic is treated in Peikoff’s “The Analytic-Synthetic Dichotomy”, published in Introduction to Objectivist Epistemology. The man point is that Objectivism rejects the analytic-synthetic dichotomy. This extract well summarizes the point:

Whether one states that "A man is a rational animal," or that "A man has only two eyes"—in both cases, the predicated characteristics are true of man and are, therefore, included in the concept "man." The meaning of the first statement is: "A certain type of entity, including all its characteristics (among which are rationality and animality) is: a rational animal." The meaning of the second is: "A certain type of entity, including all its characteristics (among which is the possession of only two eyes) has: only two eyes." Each of these statements is an instance of the Law of Identity; each is a "tautology"; to deny either is to contradict the meaning of the concept "man," and thus to endorse a self-contradiction.

Along similar lines, “If one wishes to use the term "tautology" in this context, then all truths are "tautological." (And, by the same reasoning, all falsehoods are self-contradictions.)”

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I appreciate both of your responses.

It sounds like Peikoff would probably say that "tautology" is a valid category, but that it's a somewhat subjective distinction because ultimately all knowledge is tautological. He would also insist that tautologies say something substantial about reality. The latter is what distinguishes them from so called "analytic" propositions, which Kantians describe as empty. Objectivism would say that no true proposition is analytic in this sense, although every true proposition is ultimately tautological.

I think I am reading a bit into Peikoff here, since he doesn't explicitly call the distinction subjective or distinguish them from analytic propositions in this way. I don't think Peikoff ever commented on this issue in his article on the analytic-synthetic dichotomy.

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Whether one states that "A man is a rational animal," or that "A man has only two eyes"—in both cases, the predicated characteristics are true of man and are, therefore, included in the concept "man." The meaning of the first statement is: "A certain type of entity, including all its characteristics (among which are rationality and animality) is: a rational animal." The meaning of the second is: "A certain type of entity, including all its characteristics (among which is the possession of only two eyes) has: only two eyes." Each of these statements is an instance of the Law of Identity; each is a "tautology"; to deny either is to contradict the meaning of the concept "man," and thus to endorse a self-contradiction.

 

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A tautology is a statement which says the same thing. It's predicate is the same as the subject. A brother is a male. A male sibling is male, would be a tautology. A is A is a tautology. It is part of the post Kantian mystic in philosophy that tautology says nothing about reality. There is no base for that view whatever. I cover it in The Analytic-Synthetic Dichotomy in that article. It's a form of that error, which I alluded to briefly in the lectures. I will not repeat it here in the answer, except simply to say that according to Objectivism all knowledge is ultimately tautological, because a concept stands for and includes every fact about its reference. So, whenever you say, a man has two legs, man includes everything that is true of him, including that he has two legs. This I elaborate in my article on The Analytic-Synthetic Dichotomy. This is particularly a Kantian method of attacking logic.

 

Peikoff is hopelessly confused.

A tautology is a statement that is true by virtue of its form alone. For example, "The moon is made of cheese or it is not made of cheese" is a tautology. You don't have to know ANYTHING about the moon, cheese, or any part of reality to know that it is true.

An analytic statement is one that, once you replace its subject by its definition, the result is a tautology.

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according to Objectivism all knowledge is ultimately tautological,

He doesn't even realize that this is 100% unadulterated Leibnizian rationalism.

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On 10/29/2017 at 2:58 PM, KyaryPamyu said:

A. A tautology is a statement which says the same thing. It's predicate is the same as the subject. A brother is a male. A male sibling is male, would be a tautology. A is A is a tautology. It is part of the post Kantian mystic in philosophy that tautology says nothing about reality. There is no base for that view whatever. I cover it in The Analytic-Synthetic Dichotomy in that article. It's a form of that error, which I alluded to briefly in the lectures. I will not repeat it here in the answer, except simply to say that according to Objectivism all knowledge is ultimately tautological, because a concept stands for and includes every fact about its referents. So, whenever you say, a man has two legs, man includes everything that is true of him, including that he has two legs. This I elaborate in my article on The Analytic-Synthetic Dichotomy. This is particularly a Kantian method of attacking logic.

This has to be a transcription error.

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On 11/1/2017 at 5:49 PM, SpookyKitty said:

 

 

Peikoff is hopelessly confused.

A tautology is a statement that is true by virtue of its form alone. For example, "The moon is made of cheese or it is not made of cheese" is a tautology. You don't have to know ANYTHING about the moon, cheese, or any part of reality to know that it is true.

An analytic statement is one that, once you replace its subject by its definition, the result is a tautology.

He doesn't even realize that this is 100% unadulterated Leibnizian rationalism.

Are you saying that tautologies are statements that have no content? If so then how is that different from saying they aren't statements? Also, isn't your example about the moon a dichotomy rather than a tautology? "Either the moon is made of cheese or it isn't" is different from "moons made of cheese are comprised of cheese".

I know what rationalism is, and I know Lebniz had some belief about monads, but know little beyond that about "Leibnizian rationalism". Would you care to clarify or elaborate, since I know quite a bit about Objectivism and would be very surprised to find out it has a lot in common with rationalism of any variety. My understanding is that rationalism requires no observation of physical reality, no induction, but only deduction from presupposed postulates. It's like a non-religious philosophical version of theology. If that is what you think then it's not surprising you view tautologies as statements having form but devoid of content.

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14 hours ago, Doug Pridgen said:

Are you saying that tautologies are statements that have no content? If so then how is that different from saying they aren't statements?

 

An empty glass is still a glass.
 

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Also, isn't your example about the moon a dichotomy rather than a tautology? "Either the moon is made of cheese or it isn't" is different from "moons made of cheese are comprised of cheese".

 

 

Something can be both a dichotomy and a tautology.

 

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I know what rationalism is, and I know Lebniz had some belief about monads, but know little beyond that about "Leibnizian rationalism". Would you care to clarify or elaborate, since I know quite a bit about Objectivism and would be very surprised to find out it has a lot in common with rationalism of any variety. My understanding is that rationalism requires no observation of physical reality, no induction, but only deduction from presupposed postulates. It's like a non-religious philosophical version of theology. If that is what you think then it's not surprising you view tautologies as statements having form but devoid of content.

 

Objectivism is not ratioanlism. Peikoff, on the other hand, is a rationalist who doesn't know that he is a rationalist.

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On 11/1/2017 at 2:49 PM, SpookyKitty said:

A tautology is a statement that is true by virtue of its form alone. For example, "The moon is made of cheese or it is not made of cheese" is a tautology. You don't have to know ANYTHING about the moon, cheese, or any part of reality to know that it is true.

You have to know that A cannot be both A and not A at the same time. Otherwise you have no basis for saying that the moon cannot be both cheese and not cheese. It might very well be both simultaneously for all you know, since you know nothing about reality.

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1 hour ago, MisterSwig said:

You have to know that A cannot be both A and not A at the same time. Otherwise you have no basis for saying that the moon cannot be both cheese and not cheese. It might very well be both simultaneously for all you know, since you know nothing about reality.

That's not knowledge about reality, that's knowledge about logic.

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6 hours ago, SpookyKitty said:

 

An empty glass is still a glass.
 

 

Something can be both a dichotomy and a tautology.

 

 

Objectivism is not ratioanlism. Peikoff, on the other hand, is a rationalist who doesn't know that he is a rationalist.

Why are you fixated on Peikoff? Ayn Rand chose him as her intellectual heir. She read and approved the article on the analytic/synthetic dichotomy. Therefore, by your reasoning, Ayn Rand is a rationalist. But why are you talking about people instead of ideas? I think that tendency is in itself telling.

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7 minutes ago, Doug Pridgen said:

Why are you fixated on Peikoff? Ayn Rand chose him as her intellectual heir. She read and approved the article on the analytic/synthetic dichotomy. Therefore, by your reasoning, Ayn Rand is a rationalist. But why are you talking about people instead of ideas? I think that tendency is in itself telling.

Why are you fixated on me? Why are you talking about people instead of ideas? I think that tendency is in itself telling.

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Rational discussion typically involves two or more peoples. Otherwise it is a monologue. So your analogy is inaccurate. I chose to talk to you because you said something that piqued my curiosity. If you are unable or unwilling to participate, to answer honest questions, then so be it. You are the one who accused Peikoff of being a rationalist without providing evidence and rational argument to support the assertion. Are you still confused?

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10 hours ago, SpookyKitty said:

That's not knowledge about reality, that's knowledge about logic.

Isn't knowledge about logic itself knowledge of reality?

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On 11/1/2017 at 5:49 PM, SpookyKitty said:

 

 

Peikoff is hopelessly confused.

A tautology is a statement that is true by virtue of its form alone. For example, "The moon is made of cheese or it is not made of cheese" is a tautology. You don't have to know ANYTHING about the moon, cheese, or any part of reality to know that it is true.

An analytic statement is one that, once you replace its subject by its definition, the result is a tautology.

He doesn't even realize that this is 100% unadulterated Leibnizian rationalism.

All true statements have the tautological form.  The tautological form is the only form a true statement can take on.  These two assertions rest on the premise of Rand's theory of concepts, which establishes the proper relationship between words, concepts and things-in-the -world, and which is definitely not Leibniz's theory of concepts.

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1 hour ago, Eiuol said:

Isn't knowledge about logic itself knowledge of reality?

Yes, but ...

Be careful of equivocating here.  Recall the distinction between of the metaphysical versus the man-made.  Logic is man-made and thus is not a given,  but the metaphysically given is what the most references to "reality" are invoking.

Logic only continues to exist and be studied because it is a valid way to think about reality.  Its valid because the law of identity is true in the sense that it corresponds to reality in the appropriate way.  So, knowledge of logic is knowledge of reality in that the concept of logic derives from reality, or restated that the law of identity is a true statement about reality.  

The law of identity is not an arbitrary given, it is validated, justified and even provoked or prompted by reality. 

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3 hours ago, Grames said:

 

 

All true statements have the tautological form.  The tautological form is the only form a true statement can take on.  These two assertions rest on the premise of Rand's theory of concepts, which establishes the proper relationship between words, concepts and things-in-the -world, and which is definitely not Leibniz's theory of concepts.

You show me a playing card in your hand, which card it is you are unaware of. 

You make two statements:

"This card is suited red."

and then 10 seconds later

"This card is suited black"

One statement is true.  Is the statement which is true "tautological" in form?  Is the statement which is false, not "tautological" in "form"?

What does it mean for a statement to be tautological in form?  How is the "form" of a statement distinguished from its status as true or false?

Is the assessment of "tautological" form (or no tautological form) of a statement identical with a statement's status as true (or false)?

Edit: (Follow up)  What is the difference between a concept and a proper noun?  Is "this card" an identification of a concrete instance which is conceptual or an identification of a concrete instance which is more akin to a proper noun?

Edited by StrictlyLogical

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19 hours ago, Doug Pridgen said:

Rational discussion typically involves two or more peoples. Otherwise it is a monologue. So your analogy is inaccurate. I chose to talk to you because you said something that piqued my curiosity. If you are unable or unwilling to participate, to answer honest questions, then so be it. You are the one who accused Peikoff of being a rationalist without providing evidence and rational argument to support the assertion. Are you still confused?

1) I did give evidence and arguments for Peikoff's rationalism.

2) Answering honest questions? You're the one who is making the discussion about ME and MY supposed tendencies

10 hours ago, Eiuol said:

Isn't knowledge about logic itself knowledge of reality?

No. When I refer to knowledge of reality I'm usually referring to knowledge of the current state of the external world.

9 hours ago, Grames said:

All true statements have the tautological form. 

This is demonstrably false.

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The tautological form is the only form a true statement can take on. 

This is also demonstrably false.

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These two assertions rest on the premise of Rand's theory of concepts, which establishes the proper relationship between words, concepts and things-in-the -world, and which is definitely not Leibniz's theory of concepts.

I strongly disagree. There's no way you can get from Rand's theory of concepts to the above two statements unless you're as sloppy a thinker as Peikoff.

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To briefly get back to the original question, it is clear that Peikoff rejects the standard philosophical concept "tautology". The problem with the transcription which KyaryPamyu cited is that it doesn't represent what Peikoff wrote, it's what he said. In his writings, you can see that he abjures the term because he always puts scare quotes around it (plus, of course, what he says about so-called tautologies). It's possible but unlikely that he did air quotes when he said "tautology", and the quotes were not transcribed.

"Tautology" is an invalid concept (though you may plead for validity, by removing the thing that makes it invalid). To be valid, there has to be a definition: it has to identify a specific range of things. We don't know what "tautology" refers to, and until we do, it's pointless to get into an extended discussion of it. Since the term is widely used in philosophy, I am inclined to attribute some meaning to it, thus I would more or less accept William O's initial quote from the Cambridge Dictionary of Philosophy: it is

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a proposition whose negation is inconsistent, or (self-) contradictory, e.g. "Socrates is Socrates", "Every human is either male or non-male", "No human is both male and non-male", "Every human is identical to itself", "If Socrates is human then Socrates is human".

The pure form of these statements does not render them always true. A formula which is "always true" is something like "P ∨ ¬ P", but these are meaningless formulas. The proffered tautologies are not of this form. In the Cambridge examples, there might be a valid method of translating the statements into a symbolic form such that these are "tautologies". For example, you have to add a special stipulation of referential identity in these cases (see the last example: we must additionally assert that the first Socrates is the same individual as the second Socrates – we're not mixing Socrates the philosopher and Socrates my dog). Examples like "A brother is a male" is "tautological" not by dint of the form, but because of what we know of the referents of words "male" and "brother", and we know that experientially. It is particularly obvious that one cannot arrive at a formalization of "tautology" by simply inserting the definition of a word, when you are dealing with names, which have no definition.

As for concepts and proper nouns, to quote ITOE, "A concept is a mental integration of two or more units which are isolated by a process of abstraction and united by a specific definition". A noun is the label by which we access a concept. A proper noun is a noun identifying units that name that name – they have no CCD. "Cow" identifies a range of existents with certain characteristics; "William" simply is a conventional label that some people have.

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1 hour ago, SpookyKitty said:

This is demonstrably false.

This is also demonstrably false.

Then demonstrate it.  Put up or shut up.  I will take any example you proffer and prove my point while disproving yours.

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ghhgh

8 hours ago, StrictlyLogical said:

You show me a playing card in your hand, which card it is you are unaware of. 

If I do not know which card it is then I can make no statement about the card's color and claim it to be knowledge or true (or at least neither of the two possibilities you offered).  They are arbitrary statements that cannot be assessed.

8 hours ago, StrictlyLogical said:

One statement is true.  Is the statement which is true "tautological" in form?  Is the statement which is false, not "tautological" in "form"?

What does it mean for a statement to be tautological in form?  How is the "form" of a statement distinguished from its status as true or false?

Is the assessment of "tautological" form (or no tautological form) of a statement identical with a statement's status as true (or false)?

Edit: (Follow up)  What is the difference between a concept and a proper noun?  Is "this card" an identification of a concrete instance which is conceptual or an identification of a concrete instance which is more akin to a proper noun?

An obvious tautology is one in which the subject and predicate are identical.  Take the classic "All S is P".  The obvious tautological form of that proposition is "All S is S".  This a pure example of the form so long as S has no referent, but is also not a claim about the world that has a truth status.  So long as S has no referent it makes no sense to claim "All S is S" is either true or false.  Truth depends on correspondence between and abstraction and reality but since there is nothing that S references there can be no correspondence (or non-correspondence) possible. 

Having tautological form is not what makes a proposition true.  Instead of "true or false", shift to thinking of method and "valid or invalid" form as one might when learning syllogisms.

A less obvious tautology relies on Rand's theory of concepts, specifically that a concept refers to all of its units in an open-ended manner from the past, present or future and known and unknown and also all of its attributes known and unknown. "Carbon 14 is an isotope of Carbon" is tautological because the Randian concept Carbon refers to all atoms with 12 protons including all of its various isotopes.  Carbon is carbon.   

A false proposition such as "All whales are fish" is not a tautology because the sets of referents pointed out by the concepts of whale and fish have no common members.   A proposition which is not a tautology must be false (if it makes claims about what exists, i.e. has meaning by having referents of its concepts).

The difference between a concept and a proper noun is that a concept has an open-ended number of units but a proper noun has a single unit.  The similarity between a concept and a proper noun is that both refer to all of its referents' attributes open-endedly, known and unknown.  The proposition "Grames weighed 202.7 pounds when measured" is tautological because the proper noun Grames refers to all of the attributes of Grames including the weight produced by his mass in a 1g gravity field (to a non-relativistic observer blah blah...).  "This card" singles out a particular concrete for treatment as a proper noun.

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23 hours ago, SpookyKitty said:

That's not knowledge about reality, that's knowledge about logic.

I see. A tautology isn't true by virtue of its form alone, like you said. Its form must also be part of your knowledge about logic. So if you didn't have this knowledge, the tautology would be false, right? 

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17 hours ago, Grames said:

Then demonstrate it.  Put up or shut up.  I will take any example you proffer and prove my point while disproving yours.

Here is an example of a true statement which is not a tautology:

"For all integers x, there exists an integer y such that 2x + 3 = y."

I don't understand what's so complicated about the concept of a tautology. Have any of you ever studied any formal logic? Who here knows what a truth table is?

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22 minutes ago, SpookyKitty said:

Here is an example of a true statement which is not a tautology:

"For all integers x, there exists an integer y such that 2x + 3 = y."

I don't understand what's so complicated about the concept of a tautology. Have any of you ever studied any formal logic? Who here knows what a truth table is?

The mathematical assertion of the equality of the two expressions on either side of the equal sign is tautological by definition.  The valid values y can take on for the independently variable value of x are limited by what makes the equality true.  Equality is a degenerate case of the tautological relation.  (Degenerate in the sense of only a single attribute need be considered, and there are no unknowns).

Truth tables simply map inputs and outputs and have little to do with truth in the epistemological sense relevant to philosophy.

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