Imperatives a judgemental analysis Chris Fox CSEE University of - - PowerPoint PPT Presentation

Background Some issues Proposal

Imperatives

a judgemental analysis Chris Fox

CSEE University of Essex United Kingdom foxcj@essex.ac.uk

Language and Computation Day 8th October 2010

Chris Fox (University of Essex, UK) Judgemental Imperatives 1 / 30

Background Some issues Proposal

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 2 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 3 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 4 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context

Solving conceptual problems (rather than engineering problems or implementation issues) Alternatives to Possible Worlds interpretations of semantic phenomena. (Previous work on fine-grained intentionality without Possible Worlds.) Over the past few years concentrated on reasoning with non-indicative utterances without Possible Worlds. Obligations & Permissions. Questions & Answers. This talk: analysing imperatives (commands).

Chris Fox (University of Essex, UK) Judgemental Imperatives 5 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context

Solving conceptual problems (rather than engineering problems or implementation issues) Alternatives to Possible Worlds interpretations of semantic phenomena. (Previous work on fine-grained intentionality without Possible Worlds.) Over the past few years concentrated on reasoning with non-indicative utterances without Possible Worlds. Obligations & Permissions. Questions & Answers. This talk: analysing imperatives (commands).

Chris Fox (University of Essex, UK) Judgemental Imperatives 5 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context

Solving conceptual problems (rather than engineering problems or implementation issues) Alternatives to Possible Worlds interpretations of semantic phenomena. (Previous work on fine-grained intentionality without Possible Worlds.) Over the past few years concentrated on reasoning with non-indicative utterances without Possible Worlds. Obligations & Permissions. Questions & Answers. This talk: analysing imperatives (commands).

Chris Fox (University of Essex, UK) Judgemental Imperatives 5 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context

Solving conceptual problems (rather than engineering problems or implementation issues) Alternatives to Possible Worlds interpretations of semantic phenomena. (Previous work on fine-grained intentionality without Possible Worlds.) Over the past few years concentrated on reasoning with non-indicative utterances without Possible Worlds. Obligations & Permissions. Questions & Answers. This talk: analysing imperatives (commands).

Chris Fox (University of Essex, UK) Judgemental Imperatives 5 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context

Solving conceptual problems (rather than engineering problems or implementation issues) Alternatives to Possible Worlds interpretations of semantic phenomena. (Previous work on fine-grained intentionality without Possible Worlds.) Over the past few years concentrated on reasoning with non-indicative utterances without Possible Worlds. Obligations & Permissions. Questions & Answers. This talk: analysing imperatives (commands).

Chris Fox (University of Essex, UK) Judgemental Imperatives 5 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context

Solving conceptual problems (rather than engineering problems or implementation issues) Alternatives to Possible Worlds interpretations of semantic phenomena. (Previous work on fine-grained intentionality without Possible Worlds.) Over the past few years concentrated on reasoning with non-indicative utterances without Possible Worlds. Obligations & Permissions. Questions & Answers. This talk: analysing imperatives (commands).

Chris Fox (University of Essex, UK) Judgemental Imperatives 5 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context

Solving conceptual problems (rather than engineering problems or implementation issues) Alternatives to Possible Worlds interpretations of semantic phenomena. (Previous work on fine-grained intentionality without Possible Worlds.) Over the past few years concentrated on reasoning with non-indicative utterances without Possible Worlds. Obligations & Permissions. Questions & Answers. This talk: analysing imperatives (commands).

Chris Fox (University of Essex, UK) Judgemental Imperatives 5 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context: imperatives

Consider how it is possible to reason with imperatives. Allow inconsistent commands without logical collapse. Focus on using a notion of a judgement. This presentation gives a overview of the approach.

Chris Fox (University of Essex, UK) Judgemental Imperatives 6 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context: imperatives

Consider how it is possible to reason with imperatives. Allow inconsistent commands without logical collapse. Focus on using a notion of a judgement. This presentation gives a overview of the approach.

Chris Fox (University of Essex, UK) Judgemental Imperatives 6 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context: imperatives

Consider how it is possible to reason with imperatives. Allow inconsistent commands without logical collapse. Focus on using a notion of a judgement. This presentation gives a overview of the approach.

Chris Fox (University of Essex, UK) Judgemental Imperatives 6 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Research Context: imperatives

Consider how it is possible to reason with imperatives. Allow inconsistent commands without logical collapse. Focus on using a notion of a judgement. This presentation gives a overview of the approach.

Chris Fox (University of Essex, UK) Judgemental Imperatives 6 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 7 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Examples of Imperatives

Some examples.

1

“Shut the door!”

2

“Jump out of the window and land on the mattress!”

3

“If you see John, say hello!”

4

“Go to the beach or play in the park!”

5

“Jump, or I will shoot you!”

6

“Jump, and I will shoot you!”

Commands may also be expressed in non-imperative form. We are interested in logical rather than linguistic issues.

Chris Fox (University of Essex, UK) Judgemental Imperatives 8 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Examples of Imperatives

Some examples.

1

“Shut the door!”

2

“Jump out of the window and land on the mattress!”

3

“If you see John, say hello!”

4

“Go to the beach or play in the park!”

5

“Jump, or I will shoot you!”

6

“Jump, and I will shoot you!”

Commands may also be expressed in non-imperative form. We are interested in logical rather than linguistic issues.

Chris Fox (University of Essex, UK) Judgemental Imperatives 8 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Examples of Imperatives

Some examples.

1

“Shut the door!”

2

“Jump out of the window and land on the mattress!”

3

“If you see John, say hello!”

4

“Go to the beach or play in the park!”

5

“Jump, or I will shoot you!”

6

“Jump, and I will shoot you!”

Commands may also be expressed in non-imperative form. We are interested in logical rather than linguistic issues.

Chris Fox (University of Essex, UK) Judgemental Imperatives 8 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 9 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Semantics of Imperatives

What formal machinery is required to reason with imperatives? What inferences should be supported? How should natural language imperative be “translated” into such a formal system? Do imperatives even lend themselves to a formal semantic (i.e. logical) analysis? Can we avoid a reduction to possible worlds, or actions, and all the associated problems?

Chris Fox (University of Essex, UK) Judgemental Imperatives 10 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Semantics of Imperatives

What formal machinery is required to reason with imperatives? What inferences should be supported? How should natural language imperative be “translated” into such a formal system? Do imperatives even lend themselves to a formal semantic (i.e. logical) analysis? Can we avoid a reduction to possible worlds, or actions, and all the associated problems?

Chris Fox (University of Essex, UK) Judgemental Imperatives 10 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Semantics of Imperatives

What formal machinery is required to reason with imperatives? What inferences should be supported? How should natural language imperative be “translated” into such a formal system? Do imperatives even lend themselves to a formal semantic (i.e. logical) analysis? Can we avoid a reduction to possible worlds, or actions, and all the associated problems?

Chris Fox (University of Essex, UK) Judgemental Imperatives 10 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Semantics of Imperatives

What formal machinery is required to reason with imperatives? What inferences should be supported? How should natural language imperative be “translated” into such a formal system? Do imperatives even lend themselves to a formal semantic (i.e. logical) analysis? Can we avoid a reduction to possible worlds, or actions, and all the associated problems?

Chris Fox (University of Essex, UK) Judgemental Imperatives 10 / 30

Background Some issues Proposal Introduction Examples of Imperatives Semantics of Imperatives

Semantics of Imperatives

What formal machinery is required to reason with imperatives? What inferences should be supported? How should natural language imperative be “translated” into such a formal system? Do imperatives even lend themselves to a formal semantic (i.e. logical) analysis? Can we avoid a reduction to possible worlds, or actions, and all the associated problems?

Chris Fox (University of Essex, UK) Judgemental Imperatives 10 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 11 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 12 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Jørgensen’s Dilemma

Imperatives seem to support patterns of behaviour resembling entailment.

“Man is mortal”, “Socrates is a man” ⊢ “Socrates is mortal” “Help the poor!”, “Socrates is poor” ⊢ “Help Socrates!”

But only expressions with truth conditions support a notion of entailment (or inference). Imperatives do not have truth conditions. So imperatives should not support a notion of entailment. Therefore: Contradiction? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 13 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Jørgensen’s Dilemma

Imperatives seem to support patterns of behaviour resembling entailment.

“Man is mortal”, “Socrates is a man” ⊢ “Socrates is mortal” “Help the poor!”, “Socrates is poor” ⊢ “Help Socrates!”

But only expressions with truth conditions support a notion of entailment (or inference). Imperatives do not have truth conditions. So imperatives should not support a notion of entailment. Therefore: Contradiction? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 13 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Jørgensen’s Dilemma

Imperatives seem to support patterns of behaviour resembling entailment.

“Man is mortal”, “Socrates is a man” ⊢ “Socrates is mortal” “Help the poor!”, “Socrates is poor” ⊢ “Help Socrates!”

But only expressions with truth conditions support a notion of entailment (or inference). Imperatives do not have truth conditions. So imperatives should not support a notion of entailment. Therefore: Contradiction? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 13 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Jørgensen’s Dilemma

Imperatives seem to support patterns of behaviour resembling entailment.

“Man is mortal”, “Socrates is a man” ⊢ “Socrates is mortal” “Help the poor!”, “Socrates is poor” ⊢ “Help Socrates!”

But only expressions with truth conditions support a notion of entailment (or inference). Imperatives do not have truth conditions. So imperatives should not support a notion of entailment. Therefore: Contradiction? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 13 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Jørgensen’s Dilemma

Imperatives seem to support patterns of behaviour resembling entailment.

“Man is mortal”, “Socrates is a man” ⊢ “Socrates is mortal” “Help the poor!”, “Socrates is poor” ⊢ “Help Socrates!”

But only expressions with truth conditions support a notion of entailment (or inference). Imperatives do not have truth conditions. So imperatives should not support a notion of entailment. Therefore: Contradiction? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 13 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Jørgensen’s Dilemma

Imperatives seem to support patterns of behaviour resembling entailment.

“Man is mortal”, “Socrates is a man” ⊢ “Socrates is mortal” “Help the poor!”, “Socrates is poor” ⊢ “Help Socrates!”

But only expressions with truth conditions support a notion of entailment (or inference). Imperatives do not have truth conditions. So imperatives should not support a notion of entailment. Therefore: Contradiction? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 13 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Jørgensen’s Dilemma

Imperatives seem to support patterns of behaviour resembling entailment.

“Man is mortal”, “Socrates is a man” ⊢ “Socrates is mortal” “Help the poor!”, “Socrates is poor” ⊢ “Help Socrates!”

But only expressions with truth conditions support a notion of entailment (or inference). Imperatives do not have truth conditions. So imperatives should not support a notion of entailment. Therefore: Contradiction? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 13 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 14 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Ross’s Paradox

Assume that imperatives do support a notion of entailment that

1

mirrors that of valid arguments with propositions.

2

captures the notion of satisfaction conditions.

There is now a problem. For example, disjunction introduction: p ⊢ (p ∨ q) “Post the letter!” ⊢ “Post the letter or burn the letter!” But although burning the letter satisfies the conclusions, it does not satisfy the original command. Therefore: validity and satisfaction cannot be captured by any notion of entailment . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 15 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 16 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Free Choice Disjunction

“Go to the beach or play in the park!” They appear to give permission to do either option (but not both). Free choice imperatives should not be derivable by way of disjunction introduction. How can a formal theory capture these facts? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 17 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Free Choice Disjunction

“Go to the beach or play in the park!” They appear to give permission to do either option (but not both). Free choice imperatives should not be derivable by way of disjunction introduction. How can a formal theory capture these facts? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 17 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Free Choice Disjunction

“Go to the beach or play in the park!” They appear to give permission to do either option (but not both). Free choice imperatives should not be derivable by way of disjunction introduction. How can a formal theory capture these facts? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 17 / 30

Background Some issues Proposal Jørgensen’s Dilemma Ross’s Paradox Free Choice

Free Choice Disjunction

“Go to the beach or play in the park!” They appear to give permission to do either option (but not both). Free choice imperatives should not be derivable by way of disjunction introduction. How can a formal theory capture these facts? . . .

Chris Fox (University of Essex, UK) Judgemental Imperatives 17 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 18 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 19 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements

The proposal is to use a theory in which we make judgements about expressions, and give patterns of entailments between such judgements.

p True — p is true. a Commandedα — a is commanded (by α). a Satisfiedσ — a is satisfied (by σ).

a Satisfiedσ does not imply, or presuppose a Commandedα. For imperatives, entailments involving satisfaction will be the “strongest”. Commanding can be seen to be highly inscriptional in character (cf. asserting, or saying).

Chris Fox (University of Essex, UK) Judgemental Imperatives 20 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements

The proposal is to use a theory in which we make judgements about expressions, and give patterns of entailments between such judgements.

p True — p is true. a Commandedα — a is commanded (by α). a Satisfiedσ — a is satisfied (by σ).

a Satisfiedσ does not imply, or presuppose a Commandedα. For imperatives, entailments involving satisfaction will be the “strongest”. Commanding can be seen to be highly inscriptional in character (cf. asserting, or saying).

Chris Fox (University of Essex, UK) Judgemental Imperatives 20 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements

The proposal is to use a theory in which we make judgements about expressions, and give patterns of entailments between such judgements.

p True — p is true. a Commandedα — a is commanded (by α). a Satisfiedσ — a is satisfied (by σ).

a Satisfiedσ does not imply, or presuppose a Commandedα. For imperatives, entailments involving satisfaction will be the “strongest”. Commanding can be seen to be highly inscriptional in character (cf. asserting, or saying).

Chris Fox (University of Essex, UK) Judgemental Imperatives 20 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements

The proposal is to use a theory in which we make judgements about expressions, and give patterns of entailments between such judgements.

p True — p is true. a Commandedα — a is commanded (by α). a Satisfiedσ — a is satisfied (by σ).

a Satisfiedσ does not imply, or presuppose a Commandedα. For imperatives, entailments involving satisfaction will be the “strongest”. Commanding can be seen to be highly inscriptional in character (cf. asserting, or saying).

Chris Fox (University of Essex, UK) Judgemental Imperatives 20 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements

The proposal is to use a theory in which we make judgements about expressions, and give patterns of entailments between such judgements.

p True — p is true. a Commandedα — a is commanded (by α). a Satisfiedσ — a is satisfied (by σ).

a Satisfiedσ does not imply, or presuppose a Commandedα. For imperatives, entailments involving satisfaction will be the “strongest”. Commanding can be seen to be highly inscriptional in character (cf. asserting, or saying).

Chris Fox (University of Essex, UK) Judgemental Imperatives 20 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements

The proposal is to use a theory in which we make judgements about expressions, and give patterns of entailments between such judgements.

p True — p is true. a Commandedα — a is commanded (by α). a Satisfiedσ — a is satisfied (by σ).

a Satisfiedσ does not imply, or presuppose a Commandedα. For imperatives, entailments involving satisfaction will be the “strongest”. Commanding can be seen to be highly inscriptional in character (cf. asserting, or saying).

Chris Fox (University of Essex, UK) Judgemental Imperatives 20 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements

The proposal is to use a theory in which we make judgements about expressions, and give patterns of entailments between such judgements.

p True — p is true. a Commandedα — a is commanded (by α). a Satisfiedσ — a is satisfied (by σ).

a Satisfiedσ does not imply, or presuppose a Commandedα. For imperatives, entailments involving satisfaction will be the “strongest”. Commanding can be seen to be highly inscriptional in character (cf. asserting, or saying).

Chris Fox (University of Essex, UK) Judgemental Imperatives 20 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma

We can undermine Jørgensen’s dilemma by viewing entailments as being between judgements. Entailments between propositions are just an abbreviation for entailments between judgements of truth. Inference rules involving imperatives can then be seen to be of essentially the same kind as rules involving propositions; provided the rules are expressed in terms of the appropriate kind of judgements. Imperatives seem to support patterns of behaviour resembling entailment.

Chris Fox (University of Essex, UK) Judgemental Imperatives 21 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma

We can undermine Jørgensen’s dilemma by viewing entailments as being between judgements. Entailments between propositions are just an abbreviation for entailments between judgements of truth. Inference rules involving imperatives can then be seen to be of essentially the same kind as rules involving propositions; provided the rules are expressed in terms of the appropriate kind of judgements. Imperatives seem to support patterns of behaviour resembling entailment.

Chris Fox (University of Essex, UK) Judgemental Imperatives 21 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma

We can undermine Jørgensen’s dilemma by viewing entailments as being between judgements. Entailments between propositions are just an abbreviation for entailments between judgements of truth. Inference rules involving imperatives can then be seen to be of essentially the same kind as rules involving propositions; provided the rules are expressed in terms of the appropriate kind of judgements. Imperatives seem to support patterns of behaviour resembling entailment.

Chris Fox (University of Essex, UK) Judgemental Imperatives 21 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma

We can undermine Jørgensen’s dilemma by viewing entailments as being between judgements. Entailments between propositions are just an abbreviation for entailments between judgements of truth. Inference rules involving imperatives can then be seen to be of essentially the same kind as rules involving propositions; provided the rules are expressed in terms of the appropriate kind of judgements. Imperatives seem to support patterns of behaviour resembling entailment.

Chris Fox (University of Essex, UK) Judgemental Imperatives 21 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma — Examples

“Man is mortal” True “Socrates is a man” True “Socrates is mortal” True “Help the poor!” Commandedα “Socrates is poor” True “Help Socrates!” Commandedα Arguably there are some conceptual difficulties if we allow entailments between judgements concerning what has been commanded. We may prefer the following: “Help the poor!” Satisfiedσ “Socrates is poor” True “Help Socrates!” Satisfiedσ

Chris Fox (University of Essex, UK) Judgemental Imperatives 22 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma — Examples

“Man is mortal” True “Socrates is a man” True “Socrates is mortal” True “Help the poor!” Commandedα “Socrates is poor” True “Help Socrates!” Commandedα Arguably there are some conceptual difficulties if we allow entailments between judgements concerning what has been commanded. We may prefer the following: “Help the poor!” Satisfiedσ “Socrates is poor” True “Help Socrates!” Satisfiedσ

Chris Fox (University of Essex, UK) Judgemental Imperatives 22 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma — Examples

“Man is mortal” True “Socrates is a man” True “Socrates is mortal” True “Help the poor!” Commandedα “Socrates is poor” True “Help Socrates!” Commandedα Arguably there are some conceptual difficulties if we allow entailments between judgements concerning what has been commanded. We may prefer the following: “Help the poor!” Satisfiedσ “Socrates is poor” True “Help Socrates!” Satisfiedσ

Chris Fox (University of Essex, UK) Judgemental Imperatives 22 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Judgements and Jørgensen’s Dilemma — Examples

“Man is mortal” True “Socrates is a man” True “Socrates is mortal” True “Help the poor!” Commandedα “Socrates is poor” True “Help Socrates!” Commandedα Arguably there are some conceptual difficulties if we allow entailments between judgements concerning what has been commanded. We may prefer the following: “Help the poor!” Satisfiedσ “Socrates is poor” True “Help Socrates!” Satisfiedσ

Chris Fox (University of Essex, UK) Judgemental Imperatives 22 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 23 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding

By making explicit the distinct kinds of judgements being made, we can avoid certain kinds of confusion. The judgement of Satisfaction can support many of the inferences of Truth (or “validity”, in the language of Ross) (but we may need to take some care about this.) In contrast, we can treat Commanding as highly inscriptional in nature.

Chris Fox (University of Essex, UK) Judgemental Imperatives 24 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding

By making explicit the distinct kinds of judgements being made, we can avoid certain kinds of confusion. The judgement of Satisfaction can support many of the inferences of Truth (or “validity”, in the language of Ross) (but we may need to take some care about this.) In contrast, we can treat Commanding as highly inscriptional in nature.

Chris Fox (University of Essex, UK) Judgemental Imperatives 24 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding

By making explicit the distinct kinds of judgements being made, we can avoid certain kinds of confusion. The judgement of Satisfaction can support many of the inferences of Truth (or “validity”, in the language of Ross) (but we may need to take some care about this.) In contrast, we can treat Commanding as highly inscriptional in nature.

Chris Fox (University of Essex, UK) Judgemental Imperatives 24 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding & Ross

We avoid Ross’ Paradox by distinguishing between judgements

• f satisfaction and commanding.

There may only still be one notion of entailment, but it covers different judgements. We cannot infer “Post the letter or burn the letter!” Commandedα from “Post the letter!” Commandedα. We can infer “Post the letter or burn the letter!” Satisfiedσ from “Post the letter!” Satisfiedσ. Remember that a Satisfiedσ does not presuppose or imply a Commandedα.

Chris Fox (University of Essex, UK) Judgemental Imperatives 25 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding & Ross

We avoid Ross’ Paradox by distinguishing between judgements

• f satisfaction and commanding.

There may only still be one notion of entailment, but it covers different judgements. We cannot infer “Post the letter or burn the letter!” Commandedα from “Post the letter!” Commandedα. We can infer “Post the letter or burn the letter!” Satisfiedσ from “Post the letter!” Satisfiedσ. Remember that a Satisfiedσ does not presuppose or imply a Commandedα.

Chris Fox (University of Essex, UK) Judgemental Imperatives 25 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding & Ross

We avoid Ross’ Paradox by distinguishing between judgements

• f satisfaction and commanding.

There may only still be one notion of entailment, but it covers different judgements. We cannot infer “Post the letter or burn the letter!” Commandedα from “Post the letter!” Commandedα. We can infer “Post the letter or burn the letter!” Satisfiedσ from “Post the letter!” Satisfiedσ. Remember that a Satisfiedσ does not presuppose or imply a Commandedα.

Chris Fox (University of Essex, UK) Judgemental Imperatives 25 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding & Ross

We avoid Ross’ Paradox by distinguishing between judgements

• f satisfaction and commanding.

There may only still be one notion of entailment, but it covers different judgements. We cannot infer “Post the letter or burn the letter!” Commandedα from “Post the letter!” Commandedα. We can infer “Post the letter or burn the letter!” Satisfiedσ from “Post the letter!” Satisfiedσ. Remember that a Satisfiedσ does not presuppose or imply a Commandedα.

Chris Fox (University of Essex, UK) Judgemental Imperatives 25 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Satisfaction v. Commanding & Ross

We avoid Ross’ Paradox by distinguishing between judgements

• f satisfaction and commanding.

There may only still be one notion of entailment, but it covers different judgements. We cannot infer “Post the letter or burn the letter!” Commandedα from “Post the letter!” Commandedα. We can infer “Post the letter or burn the letter!” Satisfiedσ from “Post the letter!” Satisfiedσ. Remember that a Satisfiedσ does not presuppose or imply a Commandedα.

Chris Fox (University of Essex, UK) Judgemental Imperatives 25 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

1 Background

Introduction Examples of Imperatives Semantics of Imperatives

2 Some issues

Jørgensen’s Dilemma Ross’s Paradox Free Choice

3 Proposal

Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Chris Fox (University of Essex, UK) Judgemental Imperatives 26 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Incoherence v. Inconsistency

We wish to avoid entailments between commands, even to the extent that “Jump out of the window!” does not follow from “Jump out of the window and land on the mattress!” We don’t have (a ∧ b) Commandedα ⊢ a Commandedα But it seems odd to combine (a ∧ b) Commandedα with ¬ a Commandedα. (Entailments between commands would capture this, indirectly.) We can try to capture it more directly and say (a ∧ b) Commandedα, a Commandedα ⊢ α Incoherent. A judgement that authority α is incoherent does not mean that the logic is inconsistent. We could define incoherence in terms of the inconsistency of satisfaction conditions.

Chris Fox (University of Essex, UK) Judgemental Imperatives 27 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Incoherence v. Inconsistency

We wish to avoid entailments between commands, even to the extent that “Jump out of the window!” does not follow from “Jump out of the window and land on the mattress!” We don’t have (a ∧ b) Commandedα ⊢ a Commandedα But it seems odd to combine (a ∧ b) Commandedα with ¬ a Commandedα. (Entailments between commands would capture this, indirectly.) We can try to capture it more directly and say (a ∧ b) Commandedα, a Commandedα ⊢ α Incoherent. A judgement that authority α is incoherent does not mean that the logic is inconsistent. We could define incoherence in terms of the inconsistency of satisfaction conditions.

Chris Fox (University of Essex, UK) Judgemental Imperatives 27 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Incoherence v. Inconsistency

We wish to avoid entailments between commands, even to the extent that “Jump out of the window!” does not follow from “Jump out of the window and land on the mattress!” We don’t have (a ∧ b) Commandedα ⊢ a Commandedα But it seems odd to combine (a ∧ b) Commandedα with ¬ a Commandedα. (Entailments between commands would capture this, indirectly.) We can try to capture it more directly and say (a ∧ b) Commandedα, a Commandedα ⊢ α Incoherent. A judgement that authority α is incoherent does not mean that the logic is inconsistent. We could define incoherence in terms of the inconsistency of satisfaction conditions.

Chris Fox (University of Essex, UK) Judgemental Imperatives 27 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Incoherence v. Inconsistency

We wish to avoid entailments between commands, even to the extent that “Jump out of the window!” does not follow from “Jump out of the window and land on the mattress!” We don’t have (a ∧ b) Commandedα ⊢ a Commandedα But it seems odd to combine (a ∧ b) Commandedα with ¬ a Commandedα. (Entailments between commands would capture this, indirectly.) We can try to capture it more directly and say (a ∧ b) Commandedα, a Commandedα ⊢ α Incoherent. A judgement that authority α is incoherent does not mean that the logic is inconsistent. We could define incoherence in terms of the inconsistency of satisfaction conditions.

Chris Fox (University of Essex, UK) Judgemental Imperatives 27 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Incoherence v. Inconsistency

We wish to avoid entailments between commands, even to the extent that “Jump out of the window!” does not follow from “Jump out of the window and land on the mattress!” We don’t have (a ∧ b) Commandedα ⊢ a Commandedα But it seems odd to combine (a ∧ b) Commandedα with ¬ a Commandedα. (Entailments between commands would capture this, indirectly.) We can try to capture it more directly and say (a ∧ b) Commandedα, a Commandedα ⊢ α Incoherent. A judgement that authority α is incoherent does not mean that the logic is inconsistent. We could define incoherence in terms of the inconsistency of satisfaction conditions.

Chris Fox (University of Essex, UK) Judgemental Imperatives 27 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Incoherence v. Inconsistency

We wish to avoid entailments between commands, even to the extent that “Jump out of the window!” does not follow from “Jump out of the window and land on the mattress!” We don’t have (a ∧ b) Commandedα ⊢ a Commandedα But it seems odd to combine (a ∧ b) Commandedα with ¬ a Commandedα. (Entailments between commands would capture this, indirectly.) We can try to capture it more directly and say (a ∧ b) Commandedα, a Commandedα ⊢ α Incoherent. A judgement that authority α is incoherent does not mean that the logic is inconsistent. We could define incoherence in terms of the inconsistency of satisfaction conditions.

Chris Fox (University of Essex, UK) Judgemental Imperatives 27 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Incoherence & Free Choice

The permissive sense of free choice “Go to the beach or play in the park!” can be captured by saying that combining (a ∨FC b) Commandedα with ¬ a Commandedα (or ¬ b) allows us to derive α Incoherent.

Chris Fox (University of Essex, UK) Judgemental Imperatives 28 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Conclusions

The use of explicit judgements helps us be more precise in exactly what we mean when we talk of inference and entailment with none propositional expressions. This precision can make it easier to explore solutions to long standing conundrums.

Chris Fox (University of Essex, UK) Judgemental Imperatives 29 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

Conclusions

The use of explicit judgements helps us be more precise in exactly what we mean when we talk of inference and entailment with none propositional expressions. This precision can make it easier to explore solutions to long standing conundrums.

Chris Fox (University of Essex, UK) Judgemental Imperatives 29 / 30

Background Some issues Proposal Use of Judgements Satisfaction v. Commanding Incoherence v. Inconsistency

[The ideas presented here are distilled from a journal article that is currently under review. That paper considers some of these issues in more depth. It also remains neutral on some subtle questions, such as taking “unsatisfied” to be contrary to “satisfied”, rather than contradictory.]

Chris Fox (University of Essex, UK) Judgemental Imperatives 30 / 30