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Free will is an illusion
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The language of important disciplines has terms that appear to referto abstract, nonexistent, and ‘possible-but-nonactual’ objects, andeven abstract, nonexistent, and possible-but-nonactual properties andrelations:
0, 1, 2, . . . , π, ∅, {∅}, ω, ℵ0, . . . ; x < y, x ∈ y (math)– possible event x in a probability distribution y, x’s center of mass,the possible planet perturbing the orbit of Pluto; the aether,phlogiston, absolute simultaneity, . . . (science, present and past)– Zeus, Sherlock Holmes, Bilbo Baggins, the monster I dreamtabout last night, x’s concept of y, the possible state of affairs therebeing a communist takeover of the U.S. (literary criticism,psychology)
But if we accept the scientific view about what exists, namely, thephysical entities and forces postulated by our best scientific theories,then what do the above terms refer to, since they aren’t mentioned bythese theories?
Are these just “ideas in our minds” (psychologism).– When we say ‘2 is prime’, ‘Holmes is a detective’ and ‘GeorgeBush is president’, there is a systematicity to our use of language.The suggestion is: in the last case, we are referring to an object inthe external world, but in the first two cases, we are referring toideas.
But ideas are particular to individuals – whose idea of ‘2’ are wereferring to when we say ‘2 is prime’, yours or mine? Instead, itseems like there is something more abstract, which you and I are bothreferring to.
It seems like when we say ‘Holmes is a detective’ and ‘Pinkerton is adetective’, we are, in both cases, truly attributing the property ofbeing a detective to an object. But how can an idea truly be adetective?
For today, let’s temporarily put aside the worry about reconcilingabstract, nonexistent, and possible objects with our best theories.
Instead, our plan is:
– See what the data is we are trying to explain, namely, the truesentences and valid arguments involving terms referring to theseentities. We’ll focus on fictions.
– Examine critically what some philosophers have said about theanalysis of this data.
– Produce a theory of the objects in question and use them our ownanalysis.
– Return to the question of reconciling our theory with our bestscientific theories.
According to the Conan Doyle novels, Holmes is a detective.According to The Tempest, Prospero had a daughter.According to The Iliad, Achilles fought Hector.According to the The Lord of the Rings, Sauron tried to recover themaster ring from Frodo.
Holmes is more famous than any real detective.Holmes still inspires modern criminologists.Kafka wrote about Gregor Samsa.The ancient Greeks worshipped Zeus.Ponce de Leon searched for the fountain of youth.
Teams of scientists have searched for the the Loch Ness monster, butsince it doesn’t exist, no one will ever find it.Ponce de Leon searched for the fountain of youth, and though itdoesn’t exist, he believed that it existed.
uperman = Clark Kent.Zeus = Jupiter.Pegasus is not identical to Zeus.
Some fictional characters are interesting because they findthemselves in situations in which they appear to be able to choosetheir identity, though it inevitably turns out that factors beyond theircontrol, antecedent to the moment of choice, had already determinedwhat they would do.
The ancient Greeks and Romans worshipped the same gods, thoughthey called them by different names.This story is fictional and any similarity between the characters andreal people is unintended and coincidental.None of the characters in this story exist.
Valid Arguments:– The ancient Greeks worshipped Zeus.Zeus is a mythical character.
Mythical characters don’t exist.Therefore, the ancient Greeks worshipped something that doesn’texist.
– Modern Oregonians worshipped Bhagwan Rajneesh.
Bhagwan Rajneesh is a sex-scam artist.Sex-scam artists shouldn’t be trusted.Therefore, modern Oregonians worshipped someone whoshouldn’t be trusted
– Ponce de Leon searched for the fountain of youth.Therefore, Ponce de Leon searched for something.– I searched for the keys in my pocket.I searched for something.
Frege’s (1892) theory: Names like ‘Pegasus’ fail to denote anythingwhatsoever. When a name ‘n’ occurs in a sentence such as ‘n is F’(or ‘x bears relation R to n’ or ‘n bears relation R to x) and it fails todenote, then the sentence as a whole lacks a truth value.
• Examples: ‘Odysseus is a Greek warrior’, ‘Holmes is a detective’,‘Frodo is a hobbit’ are all truth-valueless, on Frege’s view. This issomething we could live with, given that there is some kind ofdisanalogy to sentences like ‘Bush is president’, etc.
• Counterexamples: ‘Augustus Caesar worshipped Jupiter’, ‘SherlockHolmes is more famous than Alan Pinkerton’ are both true, nottruth-valueless! They are (historical) facts.
Russell’s theory (1905): Names like ‘Pegasus’ abbreviate definitedescriptions, such as ‘the winged horse captured by Bellerophon’.Definite descriptions are analyzed away in terms of existence anduniqueness claims.
Example: ‘Pegasus can fly’ is analyzed as ‘The winged horsecaptured by Bellerophon can fly’, and that in turn becomes analyzedas ‘There exists a unique winged horse captured by Bellerophon andit can fly’. Let ‘W’ abbreviate ‘winged horse captured byBellerophon’:
∃x[Wx & ∀y(Wy → y= x) & Fx]Russell’s theory predicts this latter is false, which is something wecan live with. But,
Counterexample to Russell’s Theory: ‘Augustus Caesar worshippedJupiter’, which is true, is analyzed as ‘Augustus Caesar worshippedthe most powerful Roman god’, which in turn, becomes analyzed as:There exists a unique most powerful Roman god and Caesarworshipped it’:
∃x[Mx & ∀y(My → y= x) & Wcx]
This is false, contrary to historical fact
Meinong’s (1905) naive theory of objects: for any group ofproperties, there is an object which has (instantiates, exemplifies)those properties.∃x∀F(Fx ≡ ϕ).
There is an object which instantiates the properties that Zeus hasin the myth.∃x∀F(Fx ≡ In the myth, Fz).
– There is an object which instantiates the properties that SherlockHolmes has in the Conan Doyle novels.∃x∀F(Fx ≡ In the Conan Doyle novels, Fh)
There is a round square.∃x∀F(Fx ≡ F =R ∨ F =S
Objects x and y are identical whenever they have exactly the sameproperties.x=y ≡ ∀F(Fx ≡ Fy)
Clearly, such objects could be used to give an account of the truthconditions and validity of our data
Russell’s famous objections apply however: Meinong’s theory asserts(contrary to fact) there is an existing golden mountain, and asserts(contrary to the laws of geometry) that there is a round square, andasserts (contrary to the laws of logic) that there is a non-squaresquare.
∃x∀F(Fx ≡ F =E! ∨ F =G ∨ F = M), butFact: ¬∃x(E!x & Gx & Mx)– ∃x∀F(Fx ≡ F =R ∨ F =S ) but,Geometrical Law: ∀x(Rx → ¬S x)– ∃x∀F(Fx ≡ F =S ∨ F =S¯) but,Logical Law: ∀x(S x¯ ≡ ¬S x)
Parsons’ (1980) solution to the Russell objections: (1) distinguishnuclear and extranuclear properties, (2) define objects only relative togroups of nuclear properties, (3) restrict laws of geometry to possibleobjects, and (4) assert that negations of properties are not genuinecomplements, (5) stipulate that existence is extranuclear and not anuclear property
On Parsons’ theory, the quantifier ‘there is’ (‘∃’) is distinguishedfrom the existence predicate E! – the former doesn’t imply existence.One can consistently assert that there are objects which don’t exist(∃x¬E!x). Parsons’ argues that in natural language, we distinguishbetween ‘there is’ and ‘there exists’, as in ‘there are fictionalcharacters (e.g., Iago) which we loathe even though they don’t exist’.(What would Quine say about this?)
• On Parsons’ theory, you don’t get an existing golden mountain, sincethe property of existence is extranuclear and can’t be used to define anew object
On Parsons’ theory, the round square is asserted to be an ‘impossible’object, and so doesn’t fall within the reconfigured geometrical law:for all possible objects x, if x is round, x fails to be square (i.e.,∀x(Rx → ¬S x)).
On Parsons’ theory, the negation of the property of being square (S¯)works properly only for existing objects: ∀x(E!x → (S x¯ ≡ ¬S x)).By asserting that the non-square square doesn’t exist, you avoid thecontradiction
E. Mally’s (1912) solution to the Russell objections: distinguishbetween the properties that ‘determine’ an abstract object x and theproperties that x satisifes (or instantiates, or exemplifies). Write ‘xF’to say F determines x (or x encodes F) and ‘Fx’ to say x satisfies (orinstantiates, or exemplifies) F.
The existing golden mountain is an object x which is determined by,i.e., encodes, the properties of existence, goldenness, andmountainhood (i.e., xE! & xG & xM), but it doesn’t instantiate theseproperties. It is consistent with the claim ¬∃x(E!x & Gx & Mx).
The round square is an object y which is determined by (encodes)roundness and squareness (i.e., yR & yS ). It is consistent with theunrestricted law: ∀x(Rx → ¬S x).
On Mally’s view, the non-square square is an object z which encodessquareness and non-squareness (i.e., zS & zS¯), and it is consistentwith the unrestricted law: ∀x(S x¯ ≡ ¬S x).
Mally’s theory is formalized and applied in the cited works by Zalta.• x is an ordinary object iff it is possible that x is concrete.O!x ≡
^E!x
x is an abstract object iff it is not possible that x is concrete.A!x ≡ ¬^E!x
Ordinary objects don’t encode properties.O!x → ¬∃FxF• x and y are identical iff either (a) they are both ordinary and theyexemplify the same properties, or (b) they are both abstract and theyencode the same properties.x=y ≡ [O!x & O!y & ∀F(Fx ≡ Fy)] ∨ [A!x & A!y & ∀F(xF ≡ yF)]
For any condition on properties, there is an abstract object thatencodes just the properties meeting the condition.∃x(A!x & ∀F(xF ≡ ϕ))
0, 1, 2, . . . , π, ∅, {∅}, ω, ℵ0, . . . ; x < y, x ∈ y (math)– possible event x in a probability distribution y, x’s center of mass,the possible planet perturbing the orbit of Pluto; the aether,phlogiston, absolute simultaneity, . . . (science, present and past)– Zeus, Sherlock Holmes, Bilbo Baggins, the monster I dreamtabout last night, x’s concept of y, the possible state of affairs therebeing a communist takeover of the U.S. (literary criticism,psychology)
But if we accept the scientific view about what exists, namely, thephysical entities and forces postulated by our best scientific theories,then what do the above terms refer to, since they aren’t mentioned bythese theories?
Are these just “ideas in our minds” (psychologism).– When we say ‘2 is prime’, ‘Holmes is a detective’ and ‘GeorgeBush is president’, there is a systematicity to our use of language.The suggestion is: in the last case, we are referring to an object inthe external world, but in the first two cases, we are referring toideas.
But ideas are particular to individuals – whose idea of ‘2’ are wereferring to when we say ‘2 is prime’, yours or mine? Instead, itseems like there is something more abstract, which you and I are bothreferring to.
It seems like when we say ‘Holmes is a detective’ and ‘Pinkerton is adetective’, we are, in both cases, truly attributing the property ofbeing a detective to an object. But how can an idea truly be adetective?
For today, let’s temporarily put aside the worry about reconcilingabstract, nonexistent, and possible objects with our best theories.
Instead, our plan is:
– See what the data is we are trying to explain, namely, the truesentences and valid arguments involving terms referring to theseentities. We’ll focus on fictions.
– Examine critically what some philosophers have said about theanalysis of this data.
– Produce a theory of the objects in question and use them our ownanalysis.
– Return to the question of reconciling our theory with our bestscientific theories.
According to the Conan Doyle novels, Holmes is a detective.According to The Tempest, Prospero had a daughter.According to The Iliad, Achilles fought Hector.According to the The Lord of the Rings, Sauron tried to recover themaster ring from Frodo.
Holmes is more famous than any real detective.Holmes still inspires modern criminologists.Kafka wrote about Gregor Samsa.The ancient Greeks worshipped Zeus.Ponce de Leon searched for the fountain of youth.
Teams of scientists have searched for the the Loch Ness monster, butsince it doesn’t exist, no one will ever find it.Ponce de Leon searched for the fountain of youth, and though itdoesn’t exist, he believed that it existed.
uperman = Clark Kent.Zeus = Jupiter.Pegasus is not identical to Zeus.
Some fictional characters are interesting because they findthemselves in situations in which they appear to be able to choosetheir identity, though it inevitably turns out that factors beyond theircontrol, antecedent to the moment of choice, had already determinedwhat they would do.
The ancient Greeks and Romans worshipped the same gods, thoughthey called them by different names.This story is fictional and any similarity between the characters andreal people is unintended and coincidental.None of the characters in this story exist.
Valid Arguments:– The ancient Greeks worshipped Zeus.Zeus is a mythical character.
Mythical characters don’t exist.Therefore, the ancient Greeks worshipped something that doesn’texist.
– Modern Oregonians worshipped Bhagwan Rajneesh.
Bhagwan Rajneesh is a sex-scam artist.Sex-scam artists shouldn’t be trusted.Therefore, modern Oregonians worshipped someone whoshouldn’t be trusted
– Ponce de Leon searched for the fountain of youth.Therefore, Ponce de Leon searched for something.– I searched for the keys in my pocket.I searched for something.
Frege’s (1892) theory: Names like ‘Pegasus’ fail to denote anythingwhatsoever. When a name ‘n’ occurs in a sentence such as ‘n is F’(or ‘x bears relation R to n’ or ‘n bears relation R to x) and it fails todenote, then the sentence as a whole lacks a truth value.
• Examples: ‘Odysseus is a Greek warrior’, ‘Holmes is a detective’,‘Frodo is a hobbit’ are all truth-valueless, on Frege’s view. This issomething we could live with, given that there is some kind ofdisanalogy to sentences like ‘Bush is president’, etc.
• Counterexamples: ‘Augustus Caesar worshipped Jupiter’, ‘SherlockHolmes is more famous than Alan Pinkerton’ are both true, nottruth-valueless! They are (historical) facts.
Russell’s theory (1905): Names like ‘Pegasus’ abbreviate definitedescriptions, such as ‘the winged horse captured by Bellerophon’.Definite descriptions are analyzed away in terms of existence anduniqueness claims.
Example: ‘Pegasus can fly’ is analyzed as ‘The winged horsecaptured by Bellerophon can fly’, and that in turn becomes analyzedas ‘There exists a unique winged horse captured by Bellerophon andit can fly’. Let ‘W’ abbreviate ‘winged horse captured byBellerophon’:
∃x[Wx & ∀y(Wy → y= x) & Fx]Russell’s theory predicts this latter is false, which is something wecan live with. But,
Counterexample to Russell’s Theory: ‘Augustus Caesar worshippedJupiter’, which is true, is analyzed as ‘Augustus Caesar worshippedthe most powerful Roman god’, which in turn, becomes analyzed as:There exists a unique most powerful Roman god and Caesarworshipped it’:
∃x[Mx & ∀y(My → y= x) & Wcx]
This is false, contrary to historical fact
Meinong’s (1905) naive theory of objects: for any group ofproperties, there is an object which has (instantiates, exemplifies)those properties.∃x∀F(Fx ≡ ϕ).
There is an object which instantiates the properties that Zeus hasin the myth.∃x∀F(Fx ≡ In the myth, Fz).
– There is an object which instantiates the properties that SherlockHolmes has in the Conan Doyle novels.∃x∀F(Fx ≡ In the Conan Doyle novels, Fh)
There is a round square.∃x∀F(Fx ≡ F =R ∨ F =S
Objects x and y are identical whenever they have exactly the sameproperties.x=y ≡ ∀F(Fx ≡ Fy)
Clearly, such objects could be used to give an account of the truthconditions and validity of our data
Russell’s famous objections apply however: Meinong’s theory asserts(contrary to fact) there is an existing golden mountain, and asserts(contrary to the laws of geometry) that there is a round square, andasserts (contrary to the laws of logic) that there is a non-squaresquare.
∃x∀F(Fx ≡ F =E! ∨ F =G ∨ F = M), butFact: ¬∃x(E!x & Gx & Mx)– ∃x∀F(Fx ≡ F =R ∨ F =S ) but,Geometrical Law: ∀x(Rx → ¬S x)– ∃x∀F(Fx ≡ F =S ∨ F =S¯) but,Logical Law: ∀x(S x¯ ≡ ¬S x)
Parsons’ (1980) solution to the Russell objections: (1) distinguishnuclear and extranuclear properties, (2) define objects only relative togroups of nuclear properties, (3) restrict laws of geometry to possibleobjects, and (4) assert that negations of properties are not genuinecomplements, (5) stipulate that existence is extranuclear and not anuclear property
On Parsons’ theory, the quantifier ‘there is’ (‘∃’) is distinguishedfrom the existence predicate E! – the former doesn’t imply existence.One can consistently assert that there are objects which don’t exist(∃x¬E!x). Parsons’ argues that in natural language, we distinguishbetween ‘there is’ and ‘there exists’, as in ‘there are fictionalcharacters (e.g., Iago) which we loathe even though they don’t exist’.(What would Quine say about this?)
• On Parsons’ theory, you don’t get an existing golden mountain, sincethe property of existence is extranuclear and can’t be used to define anew object
On Parsons’ theory, the round square is asserted to be an ‘impossible’object, and so doesn’t fall within the reconfigured geometrical law:for all possible objects x, if x is round, x fails to be square (i.e.,∀x(Rx → ¬S x)).
On Parsons’ theory, the negation of the property of being square (S¯)works properly only for existing objects: ∀x(E!x → (S x¯ ≡ ¬S x)).By asserting that the non-square square doesn’t exist, you avoid thecontradiction
E. Mally’s (1912) solution to the Russell objections: distinguishbetween the properties that ‘determine’ an abstract object x and theproperties that x satisifes (or instantiates, or exemplifies). Write ‘xF’to say F determines x (or x encodes F) and ‘Fx’ to say x satisfies (orinstantiates, or exemplifies) F.
The existing golden mountain is an object x which is determined by,i.e., encodes, the properties of existence, goldenness, andmountainhood (i.e., xE! & xG & xM), but it doesn’t instantiate theseproperties. It is consistent with the claim ¬∃x(E!x & Gx & Mx).
The round square is an object y which is determined by (encodes)roundness and squareness (i.e., yR & yS ). It is consistent with theunrestricted law: ∀x(Rx → ¬S x).
On Mally’s view, the non-square square is an object z which encodessquareness and non-squareness (i.e., zS & zS¯), and it is consistentwith the unrestricted law: ∀x(S x¯ ≡ ¬S x).
Mally’s theory is formalized and applied in the cited works by Zalta.• x is an ordinary object iff it is possible that x is concrete.O!x ≡
^E!x
x is an abstract object iff it is not possible that x is concrete.A!x ≡ ¬^E!x
Ordinary objects don’t encode properties.O!x → ¬∃FxF• x and y are identical iff either (a) they are both ordinary and theyexemplify the same properties, or (b) they are both abstract and theyencode the same properties.x=y ≡ [O!x & O!y & ∀F(Fx ≡ Fy)] ∨ [A!x & A!y & ∀F(xF ≡ yF)]
For any condition on properties, there is an abstract object thatencodes just the properties meeting the condition.∃x(A!x & ∀F(xF ≡ ϕ))
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