Decision

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Account

Components of a Decision

Claim

Judgement

Response

The first statement is called the claim of the decision. In the diagram above, the claim is the upper arch of occasions.

Claims have necessary modality.

Response

Judgement

Response

The second statement is called the response of the decision. In the diagram above, the response is the lower arch of occasions.

Responses have necessary modality.

Judgement

The third statement is called the judgement of the decision. It relates the claim to the response. In the diagram above, the judgement runs through the middle.

Judgements have necessary modality.

Subject

Predicate

Judgement

The claim and the response start at a given subject which may be a logical variable or a constant. In the diagram above, the subject is at 9 o'clock.

Constants have necessary modality.

Variables have possible modality.

Predicate

The claim and the response terminate at a given predicate. In the diagram above, the predicate is at 3 o'clock.

Predicates have contingent modality.

Rationale

Predicate

The rationale of a decision is how the claim and the response are handled in producing the truth claims of the the judgement. In the diagram, the occasions found within the outer ring compose the rationale.

Quantification in Decisions

Subject and Predicate

Each logical term in any statement that follows the “general form” is quantified before its participation in the copula. However, only two of the ten pattern logic quantifiers are available in decision making:

existential quantification
non-existential quantification.

Claim and Response

Subject and Predicate

The claim and the response may be rendered as monadic predicate statements with quantified subjects. These statements have no truth value until they become quantified in the formation of the judgement. At that point in the pattern’s composition,

existential quantification corresponds to an affirmation (TRUE value)
non-existential quantification corresponds to a denial (FALSE value).

Rationale

Subject and Predicate

Rationale

Within the judgement, the aggregate form of the quantification-assigned truth values and the copula are called the rationale. There are eight possible rationales:

narrowly affirming: ∃(claim)∧∃(response)
broadly affirming: ∃(claim)∨∃(response)
broadly denying: ∄(claim)∨∄(response)
narrowly denying: ∄(claim)∧∄(response)
claim including: ∄(claim)∨∃(response)
response excluding: ∃(claim)∧∄(response)
response including: ∃(claim)∨∄(response)
claim excluding: ∄(claim)∧∃(response)

About Decisions

Pattern Notation for Decisions

Here is an example of a decision in pattern logic notation. We could assign “x” to be a variable assigned to the concept “sky” or just the constant “sky”, and assign “P” to be a predicate “is blue”.

∃(∃x ∧ ∃P) ∨ ∃(∄x ∨ ∃P)

The claim is within the first set of parenthesis and the response is within the second set of parenthesis. We can label the symbols in this expression as follows.

[quantifier of claim in judgement] “(“ [quantifier of subject in claim] [subject] [copula of claim] [quantifier of predicate in claim] [predicate] “)” [copula of judgement] [quantifier of response in judgement] “(“ [quantifier of subject in response] [subject] [copula of response] [quantifier of predicate in response] [predicate] “)”

Counting and Grouping Decisions

We can calculate the total count of the species of decision by granting two degrees of freedom to each quantifier (∃|∄) and copula (∧|∨) which occur in the pattern logic notation.

2x(2x1x2x2x1)x2x2x(2x1x2x1x2) = 512

The rationales divide the 512 species of decision into eight groups of 64.

There are 8 claims (similar for the 8 responses) which can also divide the 512 species of decision into a different eight groups of 64.

Truth

Decisions as Propositional Truths

If a “proposition” is philosophically defined as a statement that may be true or false, then it is correct to see the simple logical statements of the claim and the response of a decision, as propositions in the potential sense. The judgement of the decision then represents the realization of the truth of these propositions. The claim is considered to be the base proposition, or the topic of the decision’s sense-making. While there are decisions that produce simple truth values for single propositions, there are also more complex scenarios of judging truth and disambiguating to various degrees, the relation between the subject and the predicate. We can enumerate these scenarios for truth under the following proposed labels and with these technical descriptions (list to the right).

What, exactly does the “truth value” of the claim or the response describe? Simple statements such as the claim and the response which relate a subject and a predicate have eight possible propositional forms. These are enumerated both in pattern logic statements and in a predicate notation below.

Pattern Logic Notation --> Quantified Monadic Predicate Notation

(∃x ∧ ∄P) --> ꓱx [¬P(x)]

(∃x ∧ ∃P) --> ꓱx [P(x)]

(∄x ∧ ∃P) --> ꓱx [P(¬x)]

(∄x ∧ ∄P) --> ꓱx [¬P(¬x)]

(∄x ∨ ∄P) --> ∀x [¬P(x)]

(∄x ∨ ∃P) --> ∀x [P(x)]

(∃x ∨ ∃P) --> ∀x [P(¬x)]

(∃x ∨ ∄P) --> ∀x [¬P(¬x)]

Truth Values

Unasserted – no truth claim of the state has been made or inferred by the claim or the response.

Simply (TRUE | FALSE) – the truth value is doubly stated by the claim and the response.

Assumed (TRUE | FALSE) – the truth value of the claim or the response is disjunctively related to an unasserted state in the other.

Presumed (TRUE | FALSE) – the truth value of the claim or the response is conjunctively related to an unasserted state in the other.

Undecided – the truth value is disjunctively related opposing values for the claim and the response.

Contradicted –the truth value is conjunctively related opposing values for the claim and the response.

Inference of Truth

Infer a De Morgan Dual

An existential quantification of a statement of overlap, or alternatively, a non-existential quantification of a statement of union have De Morgan duality inferred.

For example: ∃(∃x ∧ ∃P) infers ∄(∄x ∨ ∃P) and vice versa.

or alternatively, ꓱx [P(x)] is TRUE infers ∀x [¬P(x)] is FALSE and vice versa.

Do Not Infer a De Morgan Dual

Existential quantification of a statement of union or the non-existential quantification of a statement of overlap do not have De Morgan duality inferred.

For example: ∄(∃x ∧ ∃P) does not infer ∃(∄x ∨ ∄P)

or alternatively, ꓱx [P(x)] is FALSE does not infer ∀x [¬P(x)] is TRUE

Pattern Logic vs. Modern Logic

Ambiguity of Propositions

Monadic predicates with quantification - which are the propositions of this system - are ambiguous statements of truth. We observe that any single monadic predicate cannot complete a Venn diagram. There are latent logical scenarios behind any monadic predicate given in isolation. Pattern logic decisions work to reduce the latent ambiguity within these scenarios. Even so, no pattern logic decision is able to resolve every latent ambiguity in a given quantified monadic predicate. However, multiple decisions may fully resolve this ambiguity.

Emergence of Truth

Truth values are emergent, not a separate, arbitrary “interpretation of the model” as is found in the model-theoretic approaches to logic. A pattern logic instance structurally embodies this emergent truth.

Partial Inference of Truth

Inference of truth values only occurs in half (eight of sixteen) of the truth-valued propositions (where we define a proposition as a quantified monadic predicate).

Nuanced Aspects of Truth

Decisions may express more nuanced aspects of truth aside from simple truth or falsehood. These included unasserted-ness, simple-ness, assumption, presumption, undecided-ness and contradiction.

Not a Correspondence Theory of Truth

Truth, as developed so far, has no requirement for correspondence to representations of “physical entities”. Rather, it is emergent from particular iterative pattern sets, composed of occasions and their defining limitations, and which are merely representations of “conceptual entities”.

Pattern Logic Primer

Decisions

Decision-Making

The Pattern of a Decision

Decision Patterns

Components of a Decision

Claim

Judgement

Response

Response

Judgement

Response

Judgement

Judgement

Judgement

Subject

Predicate

Judgement

Predicate

Predicate

Predicate

Rationale

Predicate

Predicate

Quantification in Decisions

Subject and Predicate

Subject and Predicate

Subject and Predicate

Claim and Response

Subject and Predicate

Subject and Predicate

Rationale

Subject and Predicate

Rationale

About Decisions

Pattern Notation for Decisions

Counting and Grouping Decisions

Truth

Decisions as Propositional Truths

Truth Values

Inference of Truth

Infer a De Morgan Dual

Do Not Infer a De Morgan Dual

Decisions: ambiguous truths of quantified monadic predicates

Pattern Logic vs. Modern Logic

Ambiguity of Propositions

Emergence of Truth

Partial Inference of Truth

Nuanced Aspects of Truth

Not a Correspondence Theory of Truth

Reasoning

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