MODAL COGNITIVISM: A REACTION TO LOGIC OF IMPERATIVES
DEBIRUPA BASU� DEPARTMENT OF PHILOSOPHY�SHRI SHIKSHAYATAN COLLEGE, KOLKATA
MANIDIPA SANYAL� PROFESSOR, DEPARTMENT OF PHILOSOPHY�UNIVERSITY OF CALCUTTA, KOLKATA
MADRAS SCHOOL OF ECONOMICS, CHENNAI, 20.01.24
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Area of the discussion
1. Imperative Logic- Introduction and a brief history
2. Non- Cognitivism- Nate Charlow
3. Cognitivism- Its defense in respect of imperative sentence
4. Conclusion
An imperative sentence - expressions like requests or commands.
Imperative sentence:
2. Non-reductionism (non-truth-functional)
NECESSITY FOR CONSTRUCTING A LOGICAL SYSTEM FOR IMPERATIVE SENTENCES:
a) Inconsistency: i] Shut the door. [ !P ]
ii] Do not shut the door. [ !¬P ]
b) Inferential relations: Move all the balls.
So, move this ball.
c) Connection with logical operators (like negation, conjunction, disjunction, implication and equivalence):
Respect your father and respect your mother.
LOGICIANS DEALT WITH IMPERATIVE LOGIC
PETER B.M. VRANAS (2008)�
A declarative sentence deals with propositions.
An imperative sentence deals with prescriptions which include commands, requests, instructions, suggestions.
Two values of a prescription: satisfaction and violation
Prescription = an ordered pair of satisfaction proposition and violation proposition.
I= ˂ S,V ˃
Prescription I = ˂ S, V, A ˃
Context of I = (S ∪ V)
Avoidance of I = ~ (S ∪ V)
Prescriptions may be interpreted with logical connectives, namely, negation, conjunction, disjunction, conditional and bi-conditional in terms of satisfaction, violation and avoidance criteria of prescription.
THREE VALUES OF A CONDITIONAL PRESCRIPTION -SATISFACTION, VIOLATION AND AVOIDANCE�
“If you love him, help him.” or “Help him, if you love him.”
The above prescription is
satisfied, if you love him and help him
violated, if you love him but do not help him
avoided, if you do not love him, no matter you
help him or not.
Reductionism - imperative sentences are reducible to indicative sentences.
Non-reductionism- imperative sentences are irreducible to descriptive sentences due to their performative feature.
Imperative logic can be established in parallel to classical logic by expanding its vocabulary by “!” like case of other extended logics, for example, modal logic.
Cognitivism- imperatives are claimed to express propositions having truth values, truth and falsity.
Non-cognitivism- Imperatives are non-truth-functional.
Nate Charlow (Logic and Semantics for Imperatives, 2013)- Indicative sentences may be treated as functioning to give cognitive instructions , thereby resolving different types of cognitive issues, viz., issues of believing, pursuing etc.
In case of imperative sentences, this account gives stress on a natural understanding of the function. An imperative dictates an agent how to plan and not what to believe.
Semantic notion of imperative language
Let L be a first-order language. The imperative language Limp is the smallest set such that
(i) L is the subset of Limp
(ii) If ɸ ϵ L, then ! ɸ ϵ Limp
Following the imperative language the language of conditional Imperatives (CI) may be formed. Limp may be used to represent the form !(ɸ→ψ) . For example,
Semantic methodology
An imperative !ф expresses a function - a plan which determines a modal proposition. It is the proposition that the plan requires the imperative’s prejacent ф.
A plan has a property when the plan is in line with how the imperative tells the agent to plan.
The property a plan has if it is decided on ф.
In case of ! ¬ф, it expresses a property when it is not decided of ¬ф.
A declarative sentence ф holds at S iff ∀w ϵ S, ф ϵ w [ф is a sentence, S is the set of possible world, w is world]
Recursive characterization:
S╞ ф iff ∀wϵS : {w}╞ ф
S╞ ¬ф iff ∀wϵS : {w} |≠ ф
S╞ (ф ᴧ ψ) iff S╞ ф and S╞ ψ
In case of imperative:
i) Imperatives tell a person what to plan
ii) Imperative of the form !ф tells this by encoding the property a plan has if it is decided on ф. Its semantic function is to specify plans along the expected lines.
Semantic methodology
REFLECTIONS ON CHARLOW’S THEORY OF IMPERATIVES
a) Imperatives are not evaluable in terms of truth-values: they do not have propositional content.
b) A semantic theory for a sentence of any type is considered as a theory about what sort of cognitive instruction is made by that sentence.
Charlow refers to two kinds of cognitivism —
i) Explicit Performative Cognitivism (EPC)
ii) Modal Cognitivism
i)Two models of EPC: (David Lewis’s view)
a) Explicit Performative Analysis
b)Explicit Performative Cognitivism
A declarative sentence-
The cat is on the mat.
→ assert (x) (that the cat is on the mat.)
The value of the sentence is fixed by the context of utterance, c. The semantic value of a declarative sentence ‘the cat is on the mat’ is given by the proposition that the speaker asserts that the cat is on the mat.
An imperative sentence
Shut the window.
→ command (x) (y shuts the window)
Here the values of x and y are fixed by the context of utterance, c. The semantic value of an imperative ‘Shut the window’ is given by the proposition the speaker commands that the addressee shuts the window.
ii) Modal Cognitivism
In the Modal analysis there is an identification in meaning between the following two following sentences.
Attack at dawn!
You should attack at dawn.
[[ !ɸ ]]= [[ םɸ ]]
Modal Cognitivism represents the logical form of an imperative with the corresponding modal sentence.
Objection 1
Following example is invalid though EPC considers it to valid.
a) Attack at dawn.
b) Therefore, someone commands something.
It is invalid because the conclusion is not an imperative sentence.
It awaits further discussion whether this example can be treated as a proper imperative inference. ‘b’ can be rather an interpretation of ‘a’.
Objection 2
The argument against flexible explanatory pragmatism about truth is highly debatable. It is not the question of manner or style attached to truth or falsity of an imperative. It is more a matter of prescribing some action which is a different kind of speech-act. It is more serious an issue than the issue of calling such an ascription as ungrammatical.
Objection 3
In respect of the theory of modal non-cognitivism there are also some other issues which need clarification.
a) It is disputable to accept that cognitive instructions are “relatively thin things”.
The force of cognitive instruction is to provoke the addressee to accept the content of proposition. But when there is conflict with the agent’s prior information, then the agent has to revise his stock of information in order to carry out the instruction.
b) Imperatives get significance not by themselves, but by being able to be united with other imperatives or declaratives in order to yield further conclusion. Human communication remains incomplete without this implicative consequence.
It is more a matter of cognitivism to determine whether the conclusion they seem to lead is really derivable or not. It is a collective discourse rather than an individual affair.
Examples
i) Put all the balls of different colours into the box.
So, put only red balls into the box. [ Pure imperative inference]
ii) If you want your car not to be stolen, keep your car alarm on.
You want your car not to be stolen.
So, keep your car alarm on. [Mixed imperative inference].
Similarity between an imperative and a declarative sentence
There is a semantical specification of a property which the respective agent can try to “psychologically approximate”.
Imperative sentence !ф, an agent approximates the property which is semantically specified by the sentence. Here the plans are so adjusted that they could be represented as being such that ф is required with respect to them.
There is a general connection between semantics and characteristic function.
Charlow’s theory should get advantage of Modal cognitivism. The theory is close to assign truth-conditions to imperatives in the sense that it ascribes truth-of-a-plan conditions. An imperative is true of a plan Ax just if its corresponding modal sentence is true relative to Ax.
Is an imperative true or false?
Charlow - this question definitely is not speaking of grammatical ascription. In fact, an imperative encodes a picture of the world to-be. Imperatives have so to speak, ‘directional’ perspective, they may have truth of a plan conditions, but they are neither true nor false.
CONCLUSION
1. The function of resolving cognitive issues is not something that falls within the area of declarative sentences only. This function is very well witnessed in inferences involving imperative sentences. With respect to his truth-of a-plan condition it is evident that such cognitive issues are very well involves in such context implicitly.
2. Taken individually an imperative sentence may be interpreted in the model of modal non-cognitivism, but it remains a question whether such model can explain the cases of imperative inferences and more importantly the issue of validity of such inferences.
Thank You
�REFERENCES
1. Charlow, Nate. (2014) “Logic and Semantics for Imperatives”, Journal of Philosophical Logic;43, [617-664]
2. Hare, R.M. The Language of Morals, Oxford University Press, Great Britain (15
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