Question for old-timer's: Peikoff's view on certainty


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Ellen,

The item in Ayn Rand Answers comes from Lecture 6 in Leonard Peikoff's 1976 series on Principles of Objectivism--the same lecture that I've been going over closely because of what Dr. Peikoff says about arbitrary assertions. Rand took over the entire question and answer period to Lecture 6.

The question she was answering was whether there needs to be a perfect correspondence between our knowledge of the world and its object--and, if so, how we could assess the strength or quality of that correspondence.

What I take Rand to be doing in her long answer is trying to separate a correspondence theory of truth (which she favored) from a correspondence theory of knowledge (which made her uneasy, on account of its vulnerabilities to both rationalism and skepticism). A correspondence theory of knowledge is the same as a theory of knowing as encoding.

I won't have time right away to key in long quotes--the "Fall" semester is just about to start. But I will try to get to it in the next few days.

Robert Campbell

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It belatedly occurred to me that some folks here might not be familiar with Aquinas's angels.

Supposedly (this is second-hand, because I haven't studied his philosophy) Thomas Aquinas wanted to explain how angels have greater cognitive powers than mortal human beings, but lesser cognitive powers than God.

So he proposed that angels did need to learn, sort of. Learning for them consisted of getting acquainted with particular ideas in God's mind. But angels could instantly apprehend all of the implications of each idea they encountered.

Robert,

Thank you for that explanation.

So, if I understand it, according to a certain school of Objectivism, Ayn Rand was one of Aquinas's angels during her stay on earth—at least morally. All we have to do is remove the concept "God" and replace it by "Nature." Then spice it up with a little Eastern philosophy and claim that she went through life on earth as some kind of test of her perfect soul. Voila!

Now I understand why they get so upset when they are accused of worshiping Rand as a goddess. They don't do that at all. They worship her as an angel. :)

Michael

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Ellen,

The item in Ayn Rand Answers comes from Lecture 6 in Leonard Peikoff's 1976 series on Principles of Objectivism--the same lecture that I've been going over closely because of what Dr. Peikoff says about arbitrary assertions. Rand took over the entire question and answer period to Lecture 6.

I think I signed up for that course but then wasn't able to attend beyond the first lecture because of severe work pressures at the time.

The question she was answering was whether there needs to be a perfect correspondence between our knowledge of the world and its object--and, if so, how we could assess the strength or quality of that correspondence.

What I take Rand to be doing in her long answer is trying to separate a correspondence theory of truth (which she favored) from a correspondence theory of knowledge (which made her uneasy, on account of its vulnerabilities to both rationalism and skepticism). A correspondence theory of knowledge is the same as a theory of knowing as encoding.

Sorry, but I don't "track" that; I don't understand why you'd equate a "correspondence theory of knowledge" with a "theory of knowing [or, I'd be more likely to write "knowing"] as encoding."

I won't have time right away to key in long quotes--the "Fall" semester is just about to start. But I will try to get to it in the next few days.

I'd certainly be interested to read the question and her reply, but well understand if you don't have time. The "Fall" semester is upon a certain academician here, too. <Groan> ;-)

Ellen

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Here is the quote. Ayn Rand Answers: The Best of Her Q&A, edited by Robert Mayhew, pp. 156-158. (This gave me an excuse to train my voice recognition software.)

Q: My question is about the criteria of correspondence as a test of truth. An idea that corresponds to its object is true, but how do we determine whether an idea in fact bears a perfect correspondence to its object? Doesn't this require some criterion besides correspondence? Further, in asserting a correspondence between an idea and reality, don't we need some test to determine the precise degree of similarity between what we think and what exists?

AR: The error here is the idea that something other than correspondence is needed to establish correspondence. Take the same error in a different realm: if you say someone is beautiful, you'll need a criterion other than beauty to establish beauty. But if you've established that beauty is, say, a perfect harmony of elements, then you don't need something other than beauty to establish that someone is beautiful.

To establish correspondence means to establish the similarity between, or the identity of, A and B. What other criterion do you need? If you introduce another criterion, the first thing to go is reality. The questioner regards his ideas as something separate from reality. This is extreme rationalism. How are you going to determine the precise degree of similarity between what we think and what exists? Would you say, "My ideas correspond to reality about one-tenth of a percent"? When you speak of ideas, to be exact you must be able to say what in reality your ideas refer to. In using concepts—the minimum tool of ideas—unless you can indicate what's designated by your concept, you have no moral or epistemological right to use it. You must first know what your concept refers to in reality. If you know how to use concepts and organize them into grammatically correct sentences, then you know what it is your sentences denote in reality. The questions you must have in your mind constantly are: "What am I thinking about?" "What am I talking about?" Draw no conclusion until and unless you can point to the facts of reality and say, "I have concluded this about that." That's the test of correspondence. For instance, if you see somebody picking another man's pocket, and say, "This man stole another man's wallet," that's correspondence to reality. If, however, you see this and say: "I don't know; I can't be sure of what I saw," then your statement does not correspond to reality.

No special criterion is needed to establish correspondence. What's needed is reality and the proper kind of intellectual identification. Your thinking is not a separate attribute or collection of Platonic objects that you compare to reality. The idea of the degree of similarity between what we think and what exists is Platonic. Proper thinking is a metal identification or classification of what exists.

Another dangerous Platonic element in this question is the notion of perfect correspondence. Be careful in using "perfect." It's applicable in the realm of ethics; but in the realm of cognition, it is extremely dangerous. It's a mystical concept. What would "perfect correspondence" be? According to some mystical uses, it would have to be "omniscience"—knowing everything about some object. But that's not how the human mind works; that's not rational epistemology.

In regard to correspondence to reality, you need only be concerned with two simple rules: In drawing a conclusion you claim is true you must have (1) included everything relevant to your conclusion, and (2) omitted nothing relevant. In other words, you have considered everything open to your knowledge about a given fact or set of facts, so that when you say, "My conclusion is true," you have used all of the knowledge available to you and have not indulged in any evasion. These are the only rules for establishing that your conclusions correspond to reality. But the real test is what is out there in reality, not some double criteria based on preconceived ideas somehow formed in your mind and detached from reality.

Look at reality. If you find you have ideas detached from reality, that's a sign of rationalism.

I get the impression that by saying "not some double criteria based on preconceived ideas somehow formed in your mind and detached from reality," she is talking about the analytic-synthetic dichotomy (as she and Peikoff have characterized it), i.e., including rules of logic not derived from reality.

Michael

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Here is the quote. Ayn Rand Answers: The Best of Her Q&A, edited by Robert Mayhew, pp. 156-158. (This gave me an excuse to train my voice recognition software.)
Q: My question is about the criteria of correspondence as a test of truth. An idea that x

In regard to correspondence to reality, you need only be concerned with two simple rules: In drawing a conclusion you claim is true you must have (1) included everything relevant to your conclusion, and (2) omitted nothing relevant. In other words, you have considered everything open to your knowledge about a given fact or set of facts, so that when you say, "My conclusion is true," you have used all of the knowledge available to you and have not indulged in any evasion. These are the only rules for establishing that your conclusions correspond to reality. But the real test is what is out there in reality, not some double criteria based on preconceived ideas somehow formed in your mind and detached from reality.

Look at reality. If you find you have ideas detached from reality, that's a sign of rationalism.

Michael

Item (2) above ... "omitted nothing relevant ....".

This can only be known if every possible pertinent fact related to your conclusion were known. Then you could go through the list and see what, if anything, is left out. There is only one problem: the list of pertinent facts is open ended. Once can never be certain one has not left out some essential fact connected with you conclusion.

Until the last fact is known about an a posteriori proposition (don't hold your breath) one cannot be totally certain of the proposition.

That is why the sciences are not closed disciplines. They are always open to newly discovered facts which may refute currently accepted theories. The history of physics contains a long list of theories accepted at one time and discarded when later discoveries showed they were not generally true.

You might start this list with Aristotle's theories on motion of bodies.

Ba'al Chatzaf

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Mike quoted Rand:

AR: The error here is the idea that something other than correspondence is needed to establish correspondence. .

It may be just me, but this passage seems to be mostly empty or redundant verbiage like the above. For another example, Rand advises:

In regard to correspondence to reality, you need only be concerned with two simple rules: In drawing a conclusion you claim is true you must have (1) included everything relevant to your conclusion, and (2) omitted nothing relevant.

But she doesn't realise that (1) is (2)! So there is really just one simple rule - one so banal it is barely worth repeating - that in drawing a conclusion one must consider the relevant facts. The classic problem with this banality that Ba'al raises (ie how do you know when you have all the relevant facts?) is ignored.

Similarly, we have this:

[Look at reality. If you find you have ideas detached from reality, that's a sign of rationalism.

This is more than a "sign" of rationalism, "ideas detached from reality" is rationalism! I realise she is speaking extempore, but surely this sort of thing is hardly worth filling a book with, surely?

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In regard to correspondence to reality, you need only be concerned with two simple rules: In drawing a conclusion you claim is true you must have (1) included everything relevant to your conclusion, and (2) omitted nothing relevant.

I think Rand subscribed primarily to the correspondence theory of truth. However, there are some elements of the coherence theory of truth in her position, and this sounds more like one of them.

But she doesn't realise that (1) is (2)! So there is really just one simple rule - one so banal it is barely worth repeating - that in drawing a conclusion one must consider the relevant facts. The classic problem with this banality that Ba'al raises (ie how do you know when you have all the relevant facts?) is ignored.

Daniel, I realize you are extremely eager to dismiss anything Ayn Rand said as banal verbalism, but you could have noticed the difference between her two similar phrases simply by reading her next sentence: "you have used all of the knowledge available to you and have not indulged in any evasion."

As for the banality that Ba'al raises, I suggest caution. It comes mighty close to "no truth w/o omniscience."

For anyone interested I address the coherence theory of truth in Volume 1, Number 5 and the Objectivist theory of truth in Volume 1, Number 6 here:

http://objectivity-archive.com/

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x"you have used all of the knowledge available to you and have not indulged in any evasion."

As for the banality that Ba'al raises, I suggest caution. It comes mighty close to "no truth w/o omniscience."

For anyone interested I address the coherence theory of truth in Volume 1, Number 5 and the Objectivist theory of truth in Volume 1, Number 6 here:

http://objectivity-archive.com/

Matters of truth are raised in the context of what happens to be known at a given time.

If anything I argue against omniscience. All we have at any given time are the facts in hand and there is no platinum plated guarantee that our dearest most believed in truths will not be falsified tomorrow by some newly found fact. All of the statements about the world (i.e. synthetic statements known a posteriori) at best can be held true provisionally. The only guaranteed true statements we have are tautologies and definitions and they tell us NOTHING in particular about the world because they are true in EVERY possible world.

Ba'al Chatzaf

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Michael,

Thank you for posting that quotation.

Ellen,

Here's how I see the connection between coding and correspondence.

A simple example of a real live code would be Morse code.

To use Morse code, human beings need to know:

1) The code itself: i.e., the strings of short and long pulses (dots and dashes)

2) The items that it encodes; i.e., letters of the Roman alphabet, Arabic digits, and punctuation marks.

3) The correspondences between them; e.g., ...- is in one-to-one correspondence with V; --- corresponds one-to-one with O, etc.

All of this works just fine when we learn Morse code.

But if knowing is done by encoding in general, this means that knowing is done via correspondence between structures of symbols in our minds and structures out in the environment.

And the problem with knowing by encoding is that in order to use a code, you already have to know the code itself, you have to know what it encodes, and you have to know the correspondences between them.

Consequently, you would have to know too much, in order to be able to know anything at all.

Robert Campbell

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The only guaranteed true statements we have are tautologies and definitions and they tell us NOTHING in particular about the world because they are true in EVERY possible world.

Bob,

For the moment, let's use your standard. You call that nothing?

Michael

I am either sitting on the Mat (like the Cat) or I am not.

Now what does that tell you. Does it tell you where I am sitting or not sitting?

Tautologies do have one good use. If something implies a contradiction to a tautology you know for sure it is false. So I suppose that is something useful. Tautologies are handy as guardians.

Ba'al Chatzaf

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Bob,

Congratulations. You have just discovered what fundamental axioms are for.

Now if you look real close, you will see that "if something implies a contradiction to a tautology" you can bet your boody that there is a connection. If there is a connection, then a so-called tautology (in the sense we are discussing) is telling you something about the real world.

In fact, it's telling you so much that you can invalidate false impressions. That's quite a lot when you think about it.

Michael

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Bob,

Congratulations. You have just discovered what fundamental axioms are for.

Now if you look real close, you will see that "if something implies a contradiction to a tautology" you can bet your boody that there is a connection. If there is a connection, then a so-called tautology (in the sense we are discussing) is telling you something about the real world.

In fact, it's telling you so much that you can invalidate false impressions. That's quite a lot when you think about it.

Michael

A tautology is something logically equivalent to A or not A or even better Not (A and not-A). A tautology tells you nothing particular about the world. It doesn't tell you price of coffee, the height of Mt. Everest or when the trains run.

P implies False implies (P is false) is a tautology. It has limited use. You can't design machinery using it. You might be able to reject a design with a built in contradiction, but that is a negative use.

Ba'al Chatzaf

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Ellen,

Here's how I see the connection between coding and correspondence.

A simple example of a real live code would be Morse code.

To use Morse code, human beings need to know:

1) The code itself: i.e., the strings of short and long pulses (dots and dashes)

2) The items that it encodes; i.e., letters of the Roman alphabet, Arabic digits, and punctuation marks.

3) The correspondences between them; e.g., ...- is in one-to-one correspondence with V; --- corresponds one-to-one with O, etc.

All of this works just fine when we learn Morse code.

But if knowing is done by encoding in general, this means that knowing is done via correspondence between structures of symbols in our minds and structures out in the environment.

And the problem with knowing by encoding is that in order to use a code, you already have to know the code itself, you have to know what it encodes, and you have to know the correspondences between them.

Consequently, you would have to know too much, in order to be able to know anything at all.

Robert Campbell

Let's back up. Earlier I mentioned the disagreement between Dragonfly and Bob K. as to whether or not the genetic code is properly called a "code." Bob says no, since he thinks of a code as a set of symbols for communicating between conscious beings, both of whom know the meanings of the symbols. Dragonfly says yes, since he thinks of a code as an instructional scheme without prejudice as to a requirement of conscious interpretation at either end of the instruction. Thus he says the genetic code is properly a code and that it's legitimate to think of this code as being "read" by the cell mechanism, although there's neither a conscious coder or "reader."

If I understand you correctly, you'd agree with Bob's negative in regard to the genetic code -- that it isn't properly a "code" -- since you view as a requirement for a "code" symbols the meaning of which is known at least by the interpreting recipient.

However, even if one were to define "code" in the way you indicate, I'm still not sure if I'm understanding you, since I think you've reversed the statement you earlier made which I said I wasn't tracking. In your post above you're claiming that encoding "is done via" correspondence between the symbolic structure and the referent structure. But your earlier statement was: "A correspondence theory of knowledge is the same [emphasis added] as a theory of knowing as encoding." So I'm still not following why you'd say "the same as." It seems that what you've explained is why you'd consider "a theory of knowing as encoding" to involve a type of "correspondence" but not why you'd see it as equivalent to "a correspondence theory of knowledge."

Ellen

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Ellen,

Here's how I see the connection between coding and correspondence.

A simple example of a real live code would be Morse code.

To use Morse code, human beings need to know:

1) The code itself: i.e., the strings of short and long pulses (dots and dashes)

2) The items that it encodes; i.e., letters of the Roman alphabet, Arabic digits, and punctuation marks.

3) The correspondences between them; e.g., ...- is in one-to-one correspondence with V; --- corresponds one-to-one with O, etc.

All of this works just fine when we learn Morse code.

But if knowing is done by encoding in general, this means that knowing is done via correspondence between structures of symbols in our minds and structures out in the environment.

And the problem with knowing by encoding is that in order to use a code, you already have to know the code itself, you have to know what it encodes, and you have to know the correspondences between them.

Consequently, you would have to know too much, in order to be able to know anything at all.

Robert Campbell

Let's back up. Earlier I mentioned the disagreement between Dragonfly and Bob K. as to whether or not the genetic code is properly called a "code." Bob says no, since he thinks of a code as a set of symbols for communicating between conscious beings, both of whom know the meanings of the symbols. Dragonfly says yes, since he thinks of a code as an instructional scheme without prejudice as to a requirement of conscious interpretation at either end of the instruction. Thus he says the genetic code is properly a code and that it's legitimate to think of this code as being "read" by the cell mechanism, although there's neither a conscious coder or "reader."

If I understand you correctly, you'd agree with Bob's negative in regard to the genetic code -- that it isn't properly a "code" -- since you view as a requirement for a "code" symbols the meaning of which is known at least by the interpreting recipient.

However, even if one were to define "code" in the way you indicate, I'm still not sure if I'm understanding you, since I think you've reversed the statement you earlier made which I said I wasn't tracking. In your post above you're claiming that encoding "is done via" correspondence between the symbolic structure and the referent structure. But your earlier statement was: "A correspondence theory of knowledge is the same [emphasis added] as a theory of knowing as encoding." So I'm still not following why you'd say "the same as." It seems that what you've explained is why you'd consider "a theory of knowing as encoding" to involve a type of "correspondence" but not why you'd see it as equivalent to "a correspondence theory of knowledge."

Ellen

_

Can you guys practicalize this out?

--Brant

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Here is an abstract of Merlin Jetton's 1992-93 essay in Objectivity:

Theories of Truth

Part 1 (V1N4, pp. 1–30)

Only what-is is thought in the true thought, says Parmenides. But nothing can be thought that is not what-is, for only what-is is. This is the existence theory of truth, and it launches Jetton’s comprehensive essay of theories of truth. The principals of Part 1 are Plato, Aristotle, the Stoics, Aquinas, Ockham, Hobbes, Spinoza, Locke, Leibniz, and Kant.

Jetton lays out the critical issues to be looked for in any theory of truth. These are the definition of truth, the criteria of truth, the bearers of truth, the makers of truth, and the account a theory of truth gives of falsity. From texts of the Greek philosophers to texts of a thirteenth-century theologian, Jetton assembles the various treatments of these issues within what today is called the correspondence theory of truth.

We are shown tendencies towards a nominalist theory blossoming in the fourteenth century and again in the seventeenth century. We are shown the beginnings of the coherence theory of truth in the texts of Spinoza, Leibniz, and Kant. Spinoza has tendencies towards the older, existence theory as well, and he inherits the special thorniness of accounting for falsity that comes with this rose. Nonetheless, their texts show that for these three coherence-leaning philosophers the correspondence theory remains the basic account of truth.

Part 2 (V1N5, pp. 109–49)

In Hegel’s texts, Jetton finds truth being turned to mean the agreement of object with its concept. Hegel argues that conformity of thought to object—the correspondence theory—is not an adequate account of truth. It misses the boat. Jetton takes the reader through Hegel’s arguments and through the elements of Hegel’s theory of truth, which is integral to the grand ship of metaphysical idealism.

Elements of Hegel’s theory are then carried forward to Bradley, Joachim, and Blanshard, who sail explicitly with the coherence theory of truth, the theory of truth-as-system. Jetton shows its timbers, ropes, blocks, and pulleys. He then selects parts for salvage.

Coherence theories hold out the possibility of “truth without true foundations.” Jetton charts the twentieth-century debates over foundational truths and the possibility of attaining truth without them. He concludes Part 2 with a discussion of the special nature of the truths we call scientific. This includes a close inspection of the views of Popper.

Part 3 (V1N6, pp. 73–106)

Now come forward the pragmatist theories of truth. Here with Peirce is truth as “that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief.” Here with James is emphasis on “truth’s cash-value in experimental terms.” Here with Dewey is truth as “that which is accepted upon adequate evidence” and as “warranted assertability.”

After critiquing the pragmatist theories of truth, Jetton addresses truth theory after the linguistic turn in twentieth-century philosophy. He looks especially at the seminal work of Tarski and its relations to the correspondence and coherence theories of truth. Lastly, Jetton recounts Rand’s brief writings on the nature of truth, elaborates their intersections with earlier theories, and offers his own synthesis.

~~~~~~~~~~~~~~~~

A seminal work on the correspondence theory appearing since Merlin's essay is

The Correspondence Theory of Truth

An Essay on the Metaphysics of Predication

by Andrew Newman, published by Cambridge in 2002.

The book comprises these eight chapters:

1. Universals, Predication, and Truth

2. The Univocity of Truth

3. The Correspondence Theory of Predicative Sentences

4. Russell's Theory of Truth and Its Principal Problems

5. How Predicative Beliefs Correspond to the World

6. The Metaphysics of Facts

7. The Metaphysics of Propositions

8. The Correspondence Theory of Complex Propositions

Edited by Stephen Boydstun
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Stephen,

Thanks for the reference to the book by Newman. I looked for it on Amazon and found another book that looked even more interesting -- Bare Facts And Naked Truths: A New Correspondence Theory Of Truth by George Englebretsen.

Both this book and Newman's are pretty expensive.

Englebretsen is also the author of Something To Reckon With: The Logic of Terms, which is about Fred Sommers' term logic. I read it a few years ago and liked it.

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I've been reading Merlin's article "Theories of Truth" and finding it very interesting. I got up through section VII, but my eyes have given out, so I can't continue tonight -- and I probably won't have time to finish the article till a couple days from now.

Meanwhile, to alert Merlin and others, methinks there's one of those (especially irritating to an author) missing-not typos on page 137 of Part 2.

The sentence:

"Popper is content with taking direct or immediate observational experiences as good starting points, as long as we do make a commitment to their truth or certainty and maintain a critical attitude."

I do believe should be:

"Popper is content with taking direct or immediate observational experiences as good starting points, as long as we do not make a commitment to their truth or certainty and maintain a critical attitude."

Ellen

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Ellen,

You are correct. There is a missing "not." Aaarrrggh! (At myself.)

Hopefully other readers will take it to be a typo, too. It is fairly evident from the rest of what is said about Popper.

Edited by Merlin Jetton
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Merlin,

A funny thing happened...

Wednesday evening I reported having read up through section VII of your "Theories of Truth" article. The next day, mulling over various issues of theories of truth, it occurred to me that maybe it would be of help with some of the problems in such theories if mathematical schema and demonstrations were thought of in terms of being correct (or not) rather than in terms of being true (or not).

I was pleased and entertained to read this on the next-to-last page of your article:

Theories of Truth - Part 3

Objectivity, Volume 1, Number 6, 1993

pg. 102

Is there some knowledge in which coherence might be the nature of truth? Is there some truth that cannot be exemplified in terms of correspondence? Many propositions in higher mathematics seem to have this property. There are theorems that are considered true, even proven, yet their truth cannot be shown by pointing to facts of reality. Their truth rests on logical principles and on coherence with certain definitions, postulates, and other theorems. Some are validated only by showing that assuming the contrary proposition would lead to contradiction. These are truths of reason rather than truths of fact. Perhaps we should call such propositions correct rather than true (an Hegelian idea inverted).

I wonder: Do you (or any of the other mathematically informed members) know of any source in the general literature on issues of mathematics and truth where this suggestion is raised and discussed? Have you done anything further with it yourself?

I'm grateful for your article. It's nice to have an overview like that of the history of theories of truth. The article is amongst those in Objectivity which because of their length I didn't have time to read when they appeared and am only now belatedly catching up to reading.

I was sad to discover at the end that you'd left out your anticipated discussion of Ruth Millikan's theory. As best I recall, I've read nothing about that theory (I don't even recall having encountered her name before, though I might have and forgotten), but my curiosity was aroused by your describing her approach in the 2nd paragraph of your opening remarks as "an impressive, biologically based theory of truth." I'm surmising that the section on her work was omitted for space reasons. Have you published (or posted) elsewhere what you'd been planning to say?

Ellen

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Addendum and Correction:

I have (barely) heard of Ruth Millikan before. The name started to ring a dim bell, and on a hunch I looked in the index of Darwin's Dangerous Idea. She is referenced there.

Here's what Dennett says on pg. 403:

More recently, several other philosophers and I have articulated specifically evolutionary accounts of the birth and maintenance of meaning, both linguistic and prelinguistic [references skipped]. Ruth Millikan's account is by far the most carefully articulated, bristling with implications about the details of the other philosophical approaches to meaning mentioned above. Her differences with my position have loomed larger for her than for me, but the gap is closing fast [reference skipped] and I expect the present book to close the gap further, but this is not the place to expose our remaining differences, for they are minor in the context of a larger skirmish, a battle we have not yet won: the battle for any evolutionary account of meaning.

There are a couple other mentions of her name; and there's a bibliography entry in Consciousness Explained, though not an index entry.

She sounds like someone by whom I'd be interested, since I might think of myself as in a sense another ally in the "battle" Dennett speaks of, though I think he skips the crucial stages (and gets his understanding of the outlines wrong in certain ways). Long subject. Just correcting my reported non-memory of having heard Millikan's name.

Ellen

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Ellen asked in #96 about sources in the literature on issues of mathematics and truth, especially the notion that the concept of mathematical truth might be replaced with a concept of mathematical correctness. Here are three that work along those lines. They are the leading forms of objective nominalism concerning mathematical knowledge.

Field, Hartry 1980. Science without Numbers: A Defence of Nominalism. Princeton.

Chihara, Charles 1990. Constructibility and Mathematical Existence. Oxford.

Azzouni, Jody 2004. Deflating Existential Consequence: A Case for Nominalism. Oxford.

PS

There is a fourth:

Hellman, Geoffrey. 1989. Mathematics without Numbers: Towards a Modal-Structural Interpretation. Oxford.

Edited by Stephen Boydstun
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Hey guys. Thanks for bringing up Ruth Millikan. I have had her on my "to read" list for some time. I have just move her name to first place.

Ba'al Chatzaf

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