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##### General Discussion / Re: Counting

« Last post by**Eberhard & Yvonne Jonath**on

*March 15, 2018, 08:55:17 AM*»

That means, on the other hand: No figure ("Zählzeichen") without counted objects ("Zählobjekte")!

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That means, on the other hand: No figure ("Zählzeichen") without counted objects ("Zählobjekte")!

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„…we want our numbers to be such as can be used for counting common objects, and this requires that our numbers should have a definite meaning, not merely that they should have certain formal properties.“ [B.R.: Introduction to Mathematical Philosophy, p.10]

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Since 9 > 7, by substitutivity of identity, Quine says it follows:

Necessarily (the number of planets > 7)

But there are two ways the scope of the definite description can be interpreted:

Necessarily (Ex)(y)((y numbers the planets equ x = y) & x > 7)

Which is false - but that is not a problem.

Or

(Ex)((y) (y numbers the planets equ x = y) & Necessarily (x > 7))

Which is true & is not a problem.

As both Quine and Russell thought names should be replaced by definite descriptions (although Russell allowed logically proper names).

It is not unfair to exclude names from consideration.

This is discussed (a little differently)by Haack - Philosophy of Logics, location 3991 in kindle)

Necessarily (the number of planets > 7)

But there are two ways the scope of the definite description can be interpreted:

Necessarily (Ex)(y)((y numbers the planets equ x = y) & x > 7)

Which is false - but that is not a problem.

Or

(Ex)((y) (y numbers the planets equ x = y) & Necessarily (x > 7))

Which is true & is not a problem.

As both Quine and Russell thought names should be replaced by definite descriptions (although Russell allowed logically proper names).

It is not unfair to exclude names from consideration.

This is discussed (a little differently)by Haack - Philosophy of Logics, location 3991 in kindle)

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I was aware of that quote, and what you say about it true. I don't remember much discussion of it here. I am trying to get some discussion of the philosophy of logic & PM started here.

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Dear Dennis,

please excuse me for using this way to send my message. I didn't succeed in finding the appropriate entrance.

Yours truly

Eberhard

Dear Russellians,

your present discussion about B.R. as philosopher in P.M. is a great temptation for me:

The most horrible and disillusioning but correct fact about mathematics I have ever learned is the following Russell-dictum :

„In mathematics, the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point; hence the early deductions, until they reach this point, give reasons rather for believing the premisses because true consequences follow from them, than for believing the consequences because they follow from the premisses.“

(Whitehead and) Russell in the PREFACE to „PRINCIPIA MATHEMATICA [TO *56]“

Has there ever been a discussion about that dictum in the BRS?

"Ich bin ein Berliner" in Switzerland

Eberhard Jonath

please excuse me for using this way to send my message. I didn't succeed in finding the appropriate entrance.

Yours truly

Eberhard

Dear Russellians,

your present discussion about B.R. as philosopher in P.M. is a great temptation for me:

The most horrible and disillusioning but correct fact about mathematics I have ever learned is the following Russell-dictum :

„In mathematics, the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point; hence the early deductions, until they reach this point, give reasons rather for believing the premisses because true consequences follow from them, than for believing the consequences because they follow from the premisses.“

(Whitehead and) Russell in the PREFACE to „PRINCIPIA MATHEMATICA [TO *56]“

Has there ever been a discussion about that dictum in the BRS?

"Ich bin ein Berliner" in Switzerland

Eberhard Jonath

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But really "the evening star = the morning star" in PM is (according to definitions) See PM *14.03

(let Fx = x is an evening star & Gx = x is a morning star.)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Gx equ x = c) & b = c)

This is an empirical fact, but if predicates are interpreted extensionally, then F = G.

Then F may be substituted for G and it is not a significant statement.

For it to be significant, predicates must be interpreted intensionally.

(let Fx = x is an evening star & Gx = x is a morning star.)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Gx equ x = c) & b = c)

This is an empirical fact, but if predicates are interpreted extensionally, then F = G.

Then F may be substituted for G and it is not a significant statement.

For it to be significant, predicates must be interpreted intensionally.

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"Necessarily (the Evening Star = the Evening Star)"

Susan Haack takes this example up on Kindle location 1326 of*Philosophy of Logics*.

But really "the evening star = the evening star" in PM is (according to definitions) See PM *14.03

(let Fx = x is an evening star)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Fx equ x = c) & b = c)

But this is not true unless the evening star exists, so it is not necessarily true.

I think all Quine's objections to modal logic rest on this sort of error.

I have not, of course, had time to review all his objections.

Susan Haack takes this example up on Kindle location 1326 of

But really "the evening star = the evening star" in PM is (according to definitions) See PM *14.03

(let Fx = x is an evening star)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Fx equ x = c) & b = c)

But this is not true unless the evening star exists, so it is not necessarily true.

I think all Quine's objections to modal logic rest on this sort of error.

I have not, of course, had time to review all his objections.

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A class or collection may be defined in two ways that at first might seem like something quite distinct. We may enumerate its members, as you say, “The collection I mean is Brown, Jones, and Robinson.” Or we may mention a defining property, as when we speak of “mankind” or “the inhabitants of London.” The definition which enumerates is called definition by “extension,” and the one which mentions a defining property called a definition by “intension.” Of these two kinds of definition, the one by intension is logically more fundamental. This is shown by two considerations: (1)that the extensional definition can always be reduced to an intensional one; (2) that the intensional one often cannot even theoretically be reduced to the extensional one.

This is from page 12 of my Touchstone paperback edition or page 14 of the Kindle version (where I found it by searching.)

Russell explains both cases further, but I think this quote sufficient.

This is from page 12 of my Touchstone paperback edition or page 14 of the Kindle version (where I found it by searching.)

Russell explains both cases further, but I think this quote sufficient.

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On the statement Cicero believes "Catiline saw the evening star."

(I'm constructing an example for my purposes, for I want an example with belief and 2 definite descriptions - really I only need 1 description).

I think Quine used the example more regarding modal logic - that does not matter here.

Quine, in*word and object* (and elsewhere) would say that since "the evening star = the morning star.", we should be able to infer:

Cicero believes "Catiline saw the morning star."

But, in fact, Cicero might not believe this. (I realized they are expired - but this is hypothetical anyway.)

Quine bases this inference on substitutivity of identity. (*word & object*, p. 142).

But really "the evening star = the morning star" in PM is (according to definitions) See PM *14.03

(let Fx = x is an evening star & Gx = x is a morning star.)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Gx equ x = c) & b = c)

Now this is not of the form of identity statement to which substitutivity of identity applies. That is x=y where x and y are singular terms.

The identity statement involving descriptions must be analyzed.

If this were not true, then "On Denoting" would not have solved Russell's puzzle about George IV and the author of Waverley.

See CPBR Vol 4. p. 414.)

Note: It is believed BR used this example because his grandparents used to make fun of George IV, rather than any significance of Sir Scott.

If one could substitute "Sir Scott" for "the author of Waverley" in "George IV wondered whether Sir Scott was the author of Waverley,"

then "On Denoting" would not have achieved BR's purpose. BR did not think George IV had such an interest in the law of identity.

Most similar problems can be solved by using definite descriptions such as:

the thing meant by the name n by person p at time t.

This is how such names should be analyzed.

This does not mean people consciously think of this.

Also one might need:

the universal meant by the predicate f by person p at time t

I think it is really even more complicated.

One must distinguish objects, mental symbols, words, tokens of words, etc.

(I'm constructing an example for my purposes, for I want an example with belief and 2 definite descriptions - really I only need 1 description).

I think Quine used the example more regarding modal logic - that does not matter here.

Quine, in

Cicero believes "Catiline saw the morning star."

But, in fact, Cicero might not believe this. (I realized they are expired - but this is hypothetical anyway.)

Quine bases this inference on substitutivity of identity. (

But really "the evening star = the morning star" in PM is (according to definitions) See PM *14.03

(let Fx = x is an evening star & Gx = x is a morning star.)

(Eb)((x)(Fx equ x = b)) & (Ec) ((x) Gx equ x = c) & b = c)

Now this is not of the form of identity statement to which substitutivity of identity applies. That is x=y where x and y are singular terms.

The identity statement involving descriptions must be analyzed.

If this were not true, then "On Denoting" would not have solved Russell's puzzle about George IV and the author of Waverley.

See CPBR Vol 4. p. 414.)

Note: It is believed BR used this example because his grandparents used to make fun of George IV, rather than any significance of Sir Scott.

If one could substitute "Sir Scott" for "the author of Waverley" in "George IV wondered whether Sir Scott was the author of Waverley,"

then "On Denoting" would not have achieved BR's purpose. BR did not think George IV had such an interest in the law of identity.

Most similar problems can be solved by using definite descriptions such as:

the thing meant by the name n by person p at time t.

This is how such names should be analyzed.

This does not mean people consciously think of this.

Also one might need:

the universal meant by the predicate f by person p at time t

I think it is really even more complicated.

One must distinguish objects, mental symbols, words, tokens of words, etc.

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Once again I am violating my view that it should be forbidden to provide links on the BRS Forum without at least some discussion of contents. However, my situation now precludes discussion, even apart from the amply defensible consideration that this link points to a very important set of analyses complementary to this compelling, detailed, and very informative posting by Laurie E. Thomas (she has made other valuable postings as I hope all recall) posted with supporting links. Moreover, I urge constant, even incessant reading of this profoundly significant, utterly pertinent, and acutely disturbing site to which the link below is given. Pardon my Janus-faced comportment in this connection. I beg indulgence. Consider this to be an exigent plea if you will. Would that we could have a Kierkegaard of the history of science, technology, pharmacology, microbiology, medicine and so forth to address this "present age"! (I dare say Ludwig Wittgenstein would have approved.)

Weekend reads: 20th anniversary of a fraud; uses and misuses of doubt; how common is scooping?

https://retractionwatch.com/2018/03/03/weekend-reads-20th-anniversary-of-a-fraud-uses-and-misuses-of-doubt-how-common-is-scooping/

Regards, Jack Clontz in Bangkok, Kingdom of Thailand