Artifactual Functions: A Plan for Analysis Jesse Hughes - PowerPoint PPT Presentation

A very serious example. Decorative covers: that Martha Stewart touch. Artifactual Functions: A Plan for Analysis – p.6/17

A very serious example. This alternate function arose first as an accidental function. Artifactual Functions: A Plan for Analysis – p.6/17

A very serious example. It became an example of repeated use function (with designed accessories). Artifactual Functions: A Plan for Analysis – p.6/17

A very serious example. Now coreless rolls of toilet paper are available (i.e., designed function). Artifactual Functions: A Plan for Analysis – p.6/17

Accidental functions We regard accidental function as the simplest sort. Artifactual Functions: A Plan for Analysis – p.7/17

Accidental functions We regard accidental function as the simplest sort. An artifact a has the accidental function f if a can be used to do f . Artifactual Functions: A Plan for Analysis – p.7/17

Accidental functions We regard accidental function as the simplest sort. An artifact a has the accidental function f if a can be used to do f . We expect: Repeat use Designed Accidental Artifactual Functions: A Plan for Analysis – p.7/17

Accidental functions We regard accidental function as the simplest sort. An artifact a has the accidental function f if a can be used to do f . We expect: Repeat use Designed Accidental What we say about accidental functions apply to repeated use and designed functions, too. Artifactual Functions: A Plan for Analysis – p.7/17

Accidental functions We regard accidental function as the simplest sort. An artifact a has the accidental function f if a can be used to do f . We expect: Repeat use Designed Accidental What we say about accidental functions apply to repeated use and designed functions, too. (We hope.) Artifactual Functions: A Plan for Analysis – p.7/17

Means and Ends Whatever an accidental function is, it includes a means-end claim. Artifactual Functions: A Plan for Analysis – p.8/17

Means and Ends Whatever an accidental function is, it includes a means-end claim. An artifact a has the accidental function f if a can be used to do f . Artifactual Functions: A Plan for Analysis – p.8/17

Means and Ends Whatever an accidental function is, it includes a means-end claim. An artifact a has the accidental function f if there is a means to f involving a . Artifactual Functions: A Plan for Analysis – p.8/17

Means and Ends Whatever an accidental function is, it includes a means-end claim. An artifact a has the accidental function f if there is a means to f involving a . First step: analyze means-end ascriptions. Artifactual Functions: A Plan for Analysis – p.8/17

Means and Ends Whatever an accidental function is, it includes a means-end claim. An artifact a has the accidental function f if there is a means to f involving a . First step: analyze means-end ascriptions. Aim: conceptual analysis, not tools for practical reasoning. Artifactual Functions: A Plan for Analysis – p.8/17

Means and Ends Whatever an accidental function is, it includes a means-end claim. An artifact a has the accidental function f if there is a means to f involving a . First step: analyze means-end ascriptions. Aim: conceptual analysis, not tools for practical reasoning. What does a means-end claim mean? Artifactual Functions: A Plan for Analysis – p.8/17

Means and Ends Whatever an accidental function is, it includes a means-end claim. An artifact a has the accidental function f if there is a means to f involving a . First step: analyze means-end ascriptions. Aim: conceptual analysis, not tools for practical reasoning. What does a means-end claim mean? Procedure: analysis via formalization. Artifactual Functions: A Plan for Analysis – p.8/17

The Proposed Development Means-end ascriptions • Provide formal semantics for means-end ascriptions. Artifactual Functions: A Plan for Analysis – p.9/17

The Proposed Development Means-end ⇒ Accidental ascriptions functions • Provide formal semantics for means-end ascriptions. • Include artifacts and users. Artifactual Functions: A Plan for Analysis – p.9/17

The Proposed Development Means-end ⇒ Accidental ⇒ Other ascriptions functions functions • Provide formal semantics for means-end ascriptions. • Include artifacts and users. • Additional norms involved? Artifactual Functions: A Plan for Analysis – p.9/17

The Proposed Development Means-end ⇒ Function ⇒ Accidental ⇒ Other ascriptions simpliciter ? functions functions • Provide formal semantics for means-end ascriptions. • Include artifacts and users. • Additional norms involved? • Who knows? Artifactual Functions: A Plan for Analysis – p.9/17

The Proposed Development Means-end ⇒ Function ⇒ Accidental ⇒ Other ascriptions simpliciter ? functions functions • Provide formal semantics for means-end ascriptions. • Include artifacts and users. • Additional norms involved? • Who knows? Today, we restrict our attention to means-end ascriptions. Artifactual Functions: A Plan for Analysis – p.9/17

Dynamic components m is a means to the end ϕ . Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic components m is a means to the end ϕ . m is an action, the result of which is (likely) ϕ . Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic components m is a means to the end ϕ . m is an action, the result of which is (likely) ϕ . ϕ is a condition, i.e., a formula. Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic components m is a means to the end ϕ . m is an action, the result of which is (likely) ϕ . ϕ is a condition, i.e., a formula. Dynamic logic is an appropriate setting for us. Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic components m is a means to the end ϕ . m is an action, the result of which is (likely) ϕ . ϕ is a condition, i.e., a formula. Dynamic logic is an appropriate setting for us. act m, n, . . . actions Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic components m is a means to the end ϕ . m is an action, the result of which is (likely) ϕ . ϕ is a condition, i.e., a formula. Dynamic logic is an appropriate setting for us. act m, n, . . . actions prop atomic propositions P, Q, . . . Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic components m is a means to the end ϕ . m is an action, the result of which is (likely) ϕ . ϕ is a condition, i.e., a formula. Dynamic logic is an appropriate setting for us. act m, n, . . . actions prop atomic propositions P, Q, . . . ME all propositions ϕ, ψ, . . . Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic components m is a means to the end ϕ . m is an action, the result of which is (likely) ϕ . ϕ is a condition, i.e., a formula. Dynamic logic is an appropriate setting for us. act m, n, . . . actions prop atomic propositions P, Q, . . . ME all propositions ϕ, ψ, . . . ME → prop | ¬ ME | ME ∧ ME | [ act ] ME Artifactual Functions: A Plan for Analysis – p.10/17

Dynamic operators We interpret [ m ] ϕ as: After doing m , the condition ϕ holds/is likely. Artifactual Functions: A Plan for Analysis – p.11/17

Dynamic operators We interpret [ m ] ϕ as: After doing m , the condition ϕ holds/is likely. Dynamic logic interprets actions as transitions between worlds. Artifactual Functions: A Plan for Analysis – p.11/17

Dynamic operators We interpret [ m ] ϕ as: After doing m , the condition ϕ holds/is likely. Dynamic logic interprets actions as transitions between worlds. m is a means to ϕ iff doing m changes the world so that ϕ . Artifactual Functions: A Plan for Analysis – p.11/17

Dynamic operators We interpret [ m ] ϕ as: After doing m , the condition ϕ holds/is likely. Dynamic logic interprets actions as transitions between worlds. m is a means to ϕ iff doing m changes the world so that ϕ . m is a means to ϕ in world w iff w | = [ m ] ϕ Artifactual Functions: A Plan for Analysis – p.11/17

Dynamic operators We interpret [ m ] ϕ as: After doing m , the condition ϕ holds/is likely. Dynamic logic interprets actions as transitions between worlds. m is a means to ϕ iff doing m changes the world so that ϕ . m is a means to ϕ in world w iff w | = [ m ] ϕ But this is a bit too simple... Artifactual Functions: A Plan for Analysis – p.11/17

Conditional components Means/end attributions come with (implicit) preconditions. Artifactual Functions: A Plan for Analysis – p.12/17

Conditional components Means/end attributions come with (implicit) preconditions. Firing the starter pistol will start the race... Artifactual Functions: A Plan for Analysis – p.12/17

Conditional components Means/end attributions come with (implicit) preconditions. Firing the starter pistol will start the race... but only if there are bullets in the pistol. Artifactual Functions: A Plan for Analysis – p.12/17

Conditional components Means/end attributions come with (implicit) preconditions. Firing the starter pistol will start the race... but only if there are bullets in the pistol. Formally: Loaded ⇒ [fire] Race Artifactual Functions: A Plan for Analysis – p.12/17

Conditional components Means/end attributions come with (implicit) preconditions. Firing the starter pistol will start the race... but only if there are bullets in the pistol. Formally: Loaded ⇒ [fire] Race Clearly, ⇒ is not material implication. Artifactual Functions: A Plan for Analysis – p.12/17

Conditional components Means/end attributions come with (implicit) preconditions. Firing the starter pistol will start the race... but only if there are bullets in the pistol. Formally: Loaded ⇒ [fire] Race Clearly, ⇒ is not material implication. It is evidently not monotone: � � ¬ ( Loaded ∧ RunnersDeaf ) ⇒ [fire] Race Artifactual Functions: A Plan for Analysis – p.12/17

Conditional components Means/end attributions come with (implicit) preconditions. Firing the starter pistol will start the race... but only if there are bullets in the pistol. Formally: Loaded ⇒ [fire] Race Clearly, ⇒ is not material implication. It is evidently not monotone: � � ¬ ( Loaded ∧ RunnersDeaf ) ⇒ [fire] Race We will ignore ⇒ hereafter. Artifactual Functions: A Plan for Analysis – p.12/17

Dynamic semantics A simple model. Artifactual Functions: A Plan for Analysis – p.13/17

Dynamic semantics Race Worlds in which the race has started... Artifactual Functions: A Plan for Analysis – p.13/17

Dynamic semantics Race Loaded and those in which the gun is loaded. Artifactual Functions: A Plan for Analysis – p.13/17

Dynamic semantics Race shoot Loaded W × act → W The transition structure for shoot ... Artifactual Functions: A Plan for Analysis – p.13/17

Dynamic semantics Race shoot load Loaded W × act → W and the structure for load . Artifactual Functions: A Plan for Analysis – p.13/17

Dynamic semantics Race shoot load Loaded W × act → 1 + W Maybe not every action can be performed in every state. (You can’t load a loaded gun.) Artifactual Functions: A Plan for Analysis – p.13/17

Dynamic semantics Race shoot load Loaded W × act → PW Or maybe outcomes are not determined (say, a gun can jam). Artifactual Functions: A Plan for Analysis – p.13/17

Dynamic semantics Race shoot load Loaded W × act → PW But a jam is less likely than a successful shot. Our semantics should reflect this fact. Artifactual Functions: A Plan for Analysis – p.13/17

Likelihood semantics A likelihood model has a transition structure W × act → D ( W ) , where D ( W ) is the set of discrete distributions on W . Artifactual Functions: A Plan for Analysis – p.14/17

Likelihood semantics A likelihood model has a transition structure W × act → D ( W ) , where D ( W ) is the set of discrete distributions on W . We define a likelihood function l : W × ME → [0 , 1] . Artifactual Functions: A Plan for Analysis – p.14/17

Likelihood semantics A likelihood model has a transition structure W × act → D ( W ) , where D ( W ) is the set of discrete distributions on W . We define a likelihood function l : W × ME → [0 , 1] . Fixing α ∈ [ 1 2 , 1] , we write w | = ϕ ⇔ l ( w, ϕ ) ≥ α Artifactual Functions: A Plan for Analysis – p.14/17

Likelihood functions For actions m � = n , we require l ( w, [ m ] ϕ ∧ [ n ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ n ] ψ ) } . Artifactual Functions: A Plan for Analysis – p.15/17

Likelihood functions For actions m � = n , we require l ( w, [ m ] ϕ ∧ [ n ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ n ] ψ ) } . As long as m is likely enough to yield ϕ and n likely enough to yield ψ , then w | = [ m ] ϕ ∧ [ n ] ψ. Artifactual Functions: A Plan for Analysis – p.15/17

Likelihood functions For actions m � = n , we require l ( w, [ m ] ϕ ∧ [ n ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ n ] ψ ) } . As long as m is likely enough to yield ϕ and n likely enough to yield ψ , then w | = [ m ] ϕ ∧ [ n ] ψ. This is perhaps controversial. Certainly, our likelihood functions are not probability distributions. Artifactual Functions: A Plan for Analysis – p.15/17

Likelihood functions For actions m � = n , we require l ( w, [ m ] ϕ ∧ [ n ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ n ] ψ ) } . Now what if m = n ? We offer two alternatives. Artifactual Functions: A Plan for Analysis – p.15/17

Likelihood functions For actions m � = n , we require l ( w, [ m ] ϕ ∧ [ n ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ n ] ψ ) } . Now what if m = n ? We offer two alternatives. Simple semantics: l ( w, [ m ] ϕ ∧ [ m ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ m ] ψ ) } . Artifactual Functions: A Plan for Analysis – p.15/17

Likelihood functions For actions m � = n , we require l ( w, [ m ] ϕ ∧ [ n ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ n ] ψ ) } . Now what if m = n ? We offer two alternatives. Simple semantics: l ( w, [ m ] ϕ ∧ [ m ] ψ ) = min { l ( w, [ m ] ϕ ) , l ( w, [ m ] ψ ) } . Distributive semantics: l ( w, [ m ] ϕ ∧ [ m ] ψ ) = l ( w, [ m ]( ϕ ∧ ψ )) . Artifactual Functions: A Plan for Analysis – p.15/17

Comparison P r o p o s i t i o n a l Simple semantics Distributive semantics For every purely propositional ϕ , we have l ( w, ϕ ) ∈ { 0 , 1 } . Artifactual Functions: A Plan for Analysis – p.16/17

Comparison P r o M p o o s t i i v t i a o t n i o a n l Simple semantics Distributive semantics A simple and compelling argument that the semantics are the right semantics. Artifactual Functions: A Plan for Analysis – p.16/17

Comparison M P o r o d M p u s o o s t p i i v o t i a n o t e n i o n a n s l Simple semantics Distributive semantics If w | = ϕ → ψ and w | = ϕ , then w | = ψ . Artifactual Functions: A Plan for Analysis – p.16/17

Comparison M P o r o d M T p u a s o o u s t p i i t v o t o i a n l o o t e n i g o n a y n s l Simple semantics Distributive semantics For every tautology ϕ , we have l ( w, ϕ ) = 1 . Artifactual Functions: A Plan for Analysis – p.16/17

Comparison M P o E r o d M q T p u u a s o o i u v s t p i i t a v o t o l i a e n l o o t n e n i g o n c a y e n s l Simple semantics Distributive semantics Whenever ⊢ ϕ ↔ ψ , we have l ( w, ϕ ) = l ( w, ψ ) . Artifactual Functions: A Plan for Analysis – p.16/17

Concluding remarks Progress: • A broad strategy for analyzing functions. Artifactual Functions: A Plan for Analysis – p.17/17

Concluding remarks Progress: • A broad strategy for analyzing functions. • A syntax for means-end ascriptions. Artifactual Functions: A Plan for Analysis – p.17/17

Concluding remarks Progress: • A broad strategy for analyzing functions. • A syntax for means-end ascriptions. • Several semantic options for same, including: Artifactual Functions: A Plan for Analysis – p.17/17