More Human Mind Revealed!

Aquiring beliefs

A belief is an attitude that something is the case, or that some proposition about the world is true. We aquire and maintain our beliefs by observing the world or by reading or listening to a mentor or by inference.  We segregate knowledge into three types: episodic, semantic, and procedural. Here we will discuss aquiring and maintaining semantic beliefs from a mentor and by inference.  For a statement to be accepted as a belief it must pass one or more belief tests.

Input tests

Each statement from a mentor must be understood, unopposed, unrefuted, new or supported.

Understanding: Matches a known pattern in English.

New: not already in beliefs.

Opposition: The negation is not present in beliefs.

Refutation: No opposing proposition in beliefs. Below is an example of this type of reasoning.

Given: Jane is a human.

Given: Humans are animals.

Given: Animals are [either] male or female.

Given: Jane is female.

Q: [remember] Jane is male.

A: No, Jane is not male because Jane is female.

Supported by trusted authority: Mentor provided the proposition.

Supported by prior beliefs: Syllogistic logic.

New beliefs by inference

Now that we have a new belief we can check to see if we can discover a new statement from using the new belief.  Here are some inference methods we can use. The most prevalent method of discovery is logical inference. Deductive logic lets us infer the truth and validity of arguments and infer new information from known information. Inductive logic lets us infer general relationships from observations with some probability of truth. Abductive logic lets us infer the possible minor premises that support a conclusion. A syllogism is a set of statements that lets us apply these logic methods to infer a new statement.

 Inference by syllogism

Since one of our project objectives is to discover new ideas from old ideas (inference), we shall look at some ways that humans accomplish this task. First lets look at some methods used for inference: deduction, induction, and abduction. We'll start by introducing the syllogism: a representation of facts in three parts: a rule, a case, and a result. The syllogism indicates the relationship of two statements to a third. In deduction, given a rule and a case, you may infer a result. In Induction, given a case and a result, you may infer a rule. In Abduction, given a result and a rule, you may infer a case. In our example we will only use statements of a certain type, each containing a subject and predicate.

Using our example, in the deduction column, we use the subject from the case (Socrates) to fill in the subject of the result. Then we use the predicate of the rule (mortal) to fill in the predicate of the result. Our new statement is now “Socrates is mortal”.

In the induction column, we use the predicate of the case (Greek) to fill in the subject of the rule. Then we use the predicate of the result (mortal) to fill in the predicate of the rule. Our new statement is now “Maybe all Greeks are mortal”.

In the Abduction column, we use the subject of the result (Socrates) to fill in the subject of the case. Then we use the subject of the rule (Greek) to fill in the predicate of the case. Our new statement is now “Possibly Socrates is a Greek”.

Create a syllogism starting with one premise

Now that we have inferred a new proposition, let us use it to create our own syllogism to see if something else can be inferred. If we have a result we can search our memory for a rule that will let us deduce a new proposition.  If we have a rule, we can search our memory for a case that will let deduce a new proposition. If we have a case, we can search our memory for a rule that will let us deduce a new proposition. This an be used for inductive or abductive searches, as well.

If this technique works for new propositions, then it can be used with any input proposition.

Inference using the Square of Opposition

Categorical logic lets us infer relationships between sets of objects.  The square of opposition is a diagram representing the relations between the four basic categorical propositions: some S are P, some S are not P, All S are P, and No S are P.  Here are some inferences from the Square of opposition. 

When a proposition of singular type is encountered, it is assumed to be true if neither refuted nor opposed.

When a proposition of singular type is encountered, it is assumed to be false if refuted or opposed.

When a classification proposition of singular type is encountered, it may be associated with characteristic proposition to infer its particular proposition.

When a characteristic proposition of singular type is encountered, it may be associated with classification proposition to infer its particular proposition.

When a proposition of particular type is encountered and its negation is unknown, then one may infer the probable universal proposition and remove the negative universal proposition.

When a proposition of particular type is encountered and its negation is known, then one may remove the universal proposition.

Some reasoning terms

Argument has three parts: 2 premises, 1 conclusion. Asks for belief of the conclusion.

Inference has 2 premises. Asks for a conclusion.

Prove has 1 conclusion, asks for the premises.

Analyze Argument asks for soundness of the argument. 

Singular: Tom is a person. Tom is alive.

Particular: some person is alive.

Universal: all persons are alive.

2020-07-27 Added reasoning table.

2019-03-03 Revised page format.