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Frege's Puzzles; Frege's Puzzles; Sense Sense vs. vs. ReferenceReference

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Teaching Assistants Teaching Assistants

Brenden MURPHYBrenden MURPHYbjmurphy@connect.carleton.cabjmurphy@connect.carleton.caoffice h:office h: 12:00-1:00pm12:00-1:00pmPaterson 330APaterson 330A

Mark TOVEYMark TOVEYmtovey@connect.carleton.camtovey@connect.carleton.caoffice h:office h:

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IdentityIdentity

It’s a relation (a = b), but:It’s a relation (a = b), but:

1. 1. between objects?between objects?

2.2. between signs (i.e. names of between signs (i.e. names of objects)?objects)?

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If it’s a relation between objects then:If it’s a relation between objects then:

““a = b” doesn’t differ from “a = a”a = b” doesn’t differ from “a = a”

We would say that an object is identical to We would say that an object is identical to itself.itself.

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If it’s a relation between signs then:If it’s a relation between signs then:

given that signs are arbitrary we would given that signs are arbitrary we would lose contact with what the signs stand for lose contact with what the signs stand for (“the subject matter”) and, again, “a = b” (“the subject matter”) and, again, “a = b” would not differ from “a = a”.would not differ from “a = a”.

It would amount of saying that the word It would amount of saying that the word “a” is identical to the word “b”.“a” is identical to the word “b”.

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Cognitive ValueCognitive Value

““a = b” and “a = a” (e.g.: “Superman is a = b” and “a = a” (e.g.: “Superman is Superman” Superman” vsvs. “Superman is Clark Kent”) . “Superman is Clark Kent”) differ in cognitive value.differ in cognitive value.

If “a = b” merely concerns the objects If “a = b” merely concerns the objects aa and and bb, its cognitive content would not , its cognitive content would not differ from the one of “a = a”. differ from the one of “a = a”.

All we would know is that an object is All we would know is that an object is identical with itself.identical with itself.

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If “a = b” merely concerns the signs “a” If “a = b” merely concerns the signs “a” and “b”, its cognitive content would not and “b”, its cognitive content would not differ from the one of “a = a”. differ from the one of “a = a”.

All we would know is that signs “a” and All we would know is that signs “a” and “b” are identical.“b” are identical.

It seems that identity is neither a relation It seems that identity is neither a relation between objects, nor a relation between between objects, nor a relation between signs (nouns/names).signs (nouns/names).

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Formulating Frege’s Formulating Frege’s ProblemProblem

Terminology:Terminology:

nn = a referring expression [e.g. “Tully”] = a referring expression [e.g. “Tully”]

r(n)r(n) = = rr is is the referent of the referent of nn [e.g. [e.g. Tully(“Tully”)]Tully(“Tully”)]

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SS = a sentence containing the singular = a sentence containing the singular term term [e.g. “Tully smokes” is a sentence [e.g. “Tully smokes” is a sentence containing the singular term “Tully”]containing the singular term “Tully”]

SS// = a sentence obtained by replacing = a sentence obtained by replacing the occurrences of the occurrences of with occurrences of with occurrences of [e.g. “Jane smokes” can be obtained by [e.g. “Jane smokes” can be obtained by replacing occurrences of “Tully” with replacing occurrences of “Tully” with occurrence of “Jane” in “Tully smokes”]occurrence of “Jane” in “Tully smokes”]

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Substitution PrincipleSubstitution Principle ( (BegriffsschriftBegriffsschrift):):

If If SS is about is about r(r()), then if , then if r(r() = r() = r()), ,

SS and and SS// have the same cognitive value. have the same cognitive value.

[if “Tully smokes” is about the referent of [if “Tully smokes” is about the referent of “Tully” then, if “Tully” then, if the referent of “Tully” = the the referent of “Tully” = the referent of “Cicero”referent of “Cicero” , “Tully smokes” and , “Tully smokes” and “Cicero smokes” have the same cognitive “Cicero smokes” have the same cognitive value]value]

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2 Assumptions2 Assumptions

1. Substitution principle1. Substitution principle

2. Identity relates objects2. Identity relates objects

These two assumptions generate the These two assumptions generate the following following paradox:paradox:

““a = b” differs in cognitive value from “a = a = b” differs in cognitive value from “a = a”, yet, according to the substitution a”, yet, according to the substitution principle they do not differ.principle they do not differ.

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SolutionSolution: :

reject either (1) or (2), reject either (1) or (2),

i.e. either the substitution principle or the i.e. either the substitution principle or the view that identity relates objects.view that identity relates objects.

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Solution 1: Early FregeSolution 1: Early Frege ( (BegriffsshriftBegriffsshrift 1879)1879)

Rejection of assumption 2: Rejection of assumption 2:

Identity is not a relation between objects Identity is not a relation between objects (it’s a relation between signs).(it’s a relation between signs).

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Solution 2: Later FregeSolution 2: Later Frege

(“(“ÜÜber Sinn und Bedeutungber Sinn und Bedeutung “ / “ “ / “Sense and Sense and Reference”Reference” 1892) 1892)

The sense/reference solution.The sense/reference solution.

Rejection of assumption 1, i.e. the Rejection of assumption 1, i.e. the substitution principle.substitution principle.

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Substitution of coreferential singular terms Substitution of coreferential singular terms preserves truth value but not cognitive preserves truth value but not cognitive value.value.

In substituting terms with the same sense In substituting terms with the same sense cognitive value is preserved .cognitive value is preserved .

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Frege’s PuzzlesFrege’s Puzzles

Cognitive valueCognitive value

““Hesperus = Hesperus” is trivial and non-Hesperus = Hesperus” is trivial and non-informative, whereas “Hesperus = informative, whereas “Hesperus = Phosphorus” is Phosphorus” is informativeinformative. .

So, the cognitive value of these sentences So, the cognitive value of these sentences ought to differ. Where does the difference ought to differ. Where does the difference come in?come in?

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Frege’s solutionFrege’s solution

““Hesperus” and “Phosphorus” express two Hesperus” and “Phosphorus” express two distinct senses (distinct senses (SinneSinne), ),

I.e. the I.e. the modes of presentationsmodes of presentations of the of the referent (Bedeutung), i.e. Venus, referent (Bedeutung), i.e. Venus, associated with both terms are different.associated with both terms are different.

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Proper NamesProper Names

A proper name A proper name expressesexpresses a sense and a sense and refersrefers to an object. to an object.

The The sensesense of a proper name, say “Tully”, is of a proper name, say “Tully”, is the the mode of presentationmode of presentation of the object, of the object, Tully, it stands for. Intuitively, a sense is Tully, it stands for. Intuitively, a sense is that property of a linguistic expression in that property of a linguistic expression in virtue of which it is understood (grasped) virtue of which it is understood (grasped) by a competent speaker.by a competent speaker.

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Sense and thoughtSense and thought

The sense of a sentence (thought) is The sense of a sentence (thought) is determined by the senses of its determined by the senses of its constituents. constituents.

Different senses make different Different senses make different contributions to a thought.contributions to a thought.

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Sense Sense vsvs. Reference. Reference

Sense Sense determinesdetermines reference reference

r(n) = r(s)n)) r(n) = r(s)n))

[e.g. the referent of “Tully” is the referent [e.g. the referent of “Tully” is the referent of the sense of “Tully”]of the sense of “Tully”]

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Reference is a Reference is a functionfunction

Any two terms having the same sense Any two terms having the same sense refer to the same object, i.e.refer to the same object, i.e.

If s(n) = s(m), then r(n) = r(m)If s(n) = s(m), then r(n) = r(m)

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Frege’s SemanticsFrege’s Semantics

Three worldsThree worlds

1. Language1. Language

2. World of senses/thoughts2. World of senses/thoughts

3. Reality3. Reality

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1.1. sign proper name predicate sentencesign proper name predicate sentence

2. sense/thought sense sense thought2. sense/thought sense sense thought

3. referent object concept Truth 3. referent object concept Truth ValueValue

object object

falling falling under the concept under the concept

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A A proper names is a linguistic expression is a linguistic expression which: which:

(i) expresses a sense and (i) expresses a sense and

(ii) stands for/refers to/designates an (ii) stands for/refers to/designates an objectobject..

An object is the ontological reflection of a An object is the ontological reflection of a name.name.

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SentencesSentences are compound proper names are compound proper names whose referents are either the Truth or the whose referents are either the Truth or the False which are objects.False which are objects.

The The BedeutungBedeutung of a sentenceof a sentence (the truth (the truth value) is determined by the value) is determined by the BedeutungBedeutung of of its constituents, just as the sense of a its constituents, just as the sense of a sentence (the thought expressed) is sentence (the thought expressed) is determined by the senses of its determined by the senses of its constituents.constituents.

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Oratio ObliquaOratio Obliqua Oratio obliquaOratio obliqua vs oratio rectavs oratio recta; i.e indirect ; i.e indirect

discoursediscourse vs vs direct discourse; inten direct discourse; intenssional ional contexts contexts vs vs extensional contextextensional context

(1) Sue believes that Hesperus is a star(1) Sue believes that Hesperus is a star (2) Hesperus = Phosphorus(2) Hesperus = PhosphorusSo: (3) Sue believes that Phosphorus is a starSo: (3) Sue believes that Phosphorus is a star

How to block this inference, i.e. the substitution How to block this inference, i.e. the substitution salva veritatesalva veritate of ‘Hesperus’ and ‘Phosphorus’? of ‘Hesperus’ and ‘Phosphorus’?

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Frege’s SolutionFrege’s Solution

(i) “Hesperus” and “Phosphorus” express (i) “Hesperus” and “Phosphorus” express different sedifferent sensesnses;;

(ii) (ii) SensesSenses are the constituents of thoughts are the constituents of thoughts ((GedankeGedanke),),

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(iii) an attitude ascription relates a subject (iii) an attitude ascription relates a subject with a thought; with a thought;

So: (iv) (1) and (3) do not relate Sue with So: (iv) (1) and (3) do not relate Sue with the same thought and, therefore, may the same thought and, therefore, may differ in truth value. differ in truth value.

The moral is that the names “Hesperus” The moral is that the names “Hesperus” and “Phosphorus” cannot be substituted and “Phosphorus” cannot be substituted salva veritatesalva veritate in in oratio obliquaoratio obliqua constructions.constructions.

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Ordinary Senses Ordinary Senses vsvs. . Indirect SensesIndirect Senses

The ordinary sense is what is referred to, via The ordinary sense is what is referred to, via an indirect sense, by embedded expressions. an indirect sense, by embedded expressions.

Since embedded expressions switch Since embedded expressions switch reference, Frege gives up reference, Frege gives up semantic semantic innocenceinnocence. .

E.g.: “Hesperus” in (1) and “Phosphorus” in E.g.: “Hesperus” in (1) and “Phosphorus” in (3) do not refer to Venus, but to their ordinary (3) do not refer to Venus, but to their ordinary sense, which differ.sense, which differ.

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(1) gets represented as: (1) gets represented as:

(1a) (1a) BEL BEL (Sue, <MP(Hesperus), MP(being a (Sue, <MP(Hesperus), MP(being a star)>) star)>)

while (3) as:while (3) as:

(1b) (1b) BEL BEL (Sue, < MP(Phosphorus), (Sue, < MP(Phosphorus), MP(being a MP(being a star)>)star)>)

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MP(Hespeus) differs from MP(Phosphorus)MP(Hespeus) differs from MP(Phosphorus)

Thus as (1a) and (3a) show, (1) and (3) do Thus as (1a) and (3a) show, (1) and (3) do not relate Sue with the same thought. not relate Sue with the same thought.

Thus, they may well differ in truth value. Thus, they may well differ in truth value.

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Moral:Moral:

Coreferring expressions / terms / names Coreferring expressions / terms / names cannot be substituted salva veitate in cannot be substituted salva veitate in oblique / oblique / oratio obliquaoratio obliqua / intensional / intensional contexts.contexts.