Informal "Immediate Inference"

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Informal Immediate Inference

(1) Formal Immediate Inference and Its Informal Extensions
(2) Added Determinant
— Subject and predicate are identically qualified with a “determinant.”
(3) Omitted Determinant
— A “determinant” is removed.
(4) Complex Conception
— Subject and predicate determine a new third term.
(5) Converse Relation
— A conversion of subject and predicate take place with relative terms.

(1) Formal Immediate Inference
and Its Informal Extensions

Both the “equivalent” and “traditional” type of formal inference is always valid.

Their validity is not determined by the particular content of the given propositions.
For example, any proposition of the form SEP will always validly convert to PES.

In contrast, informal immediate inference is not always valid.
Validity here depends upon the particular content of the given propositions.
So, the meaning of the given propositions is vital to understand.

But even with formal immediate inference, we can add informal considerations. . .

First: Definitions as A-type propositions can be “simply converted.”
It’s formally invalid to move from SAP to PAS.
Yet if SAP is a good definition, it can be simply converted.

“All squares are equilateral rectangles”
can be simply converted to “all equilateral rectangles are squares”
(because it is a good definition).

Using Euler’s Circles, a good definition is represented with Figure Two.
It visually shows why a simple conversion is allowable.

Second: Complements can be taken into account.

For example, “no man is incorruptible” can be obverted to “all men are corruptible.” This just takes into account that “incorruptible” is the complemented form of “corruptible.” It is a more pleasing obversion than writing “all men are non-incorruptible.”

(2) Inference via Added Determinant

The subject and predicate are identically qualified with a “determinant” in an inference by added determinant. This determinant narrows the scope of both subject and predicate in the same exact way.

It goes from the form “All S is P” to “All XS is XP.”
Sometimes this move is valid; sometimes this move is invalid.
As in all informal immediate inferences, it depends upon the context.

“All writers are wordsmiths.” Thus, “all clever writers are clever wordsmiths.”
The determinant here is “clever.”
It narrowed down the subject and predicate in the same exact way.

An invalid argument: “All writers are men.” Thus, “all good writers are good men.”
The determinant here is “good.”
It’s invalid because the determinant is applied in different ways to the subject and predicate. The “goodness” of a writer is different than the “goodness” of a man. A good writer might be a bad man. So, an inference via added determinant is not always valid.

In general, caution is advised.
Use of comparison will often change when applied to the subject and predicate.

“All reporters are people.” Thus, “all tall reporters are tall people.”
The determinant here is “tall.”
It’s valid. It narrowed down the subject and predicate in the same exact way.

But this is invalid: “All giraffes are animals.” Thus, “a small giraffe is a small animal.”
Here’s a comparison gone bad.
All that can be validly inferred is that a small giraffe is small for a giraffe.

An inference via added determinant gone bad can be viewed in light of the fallacy of equivocation. Consider the previous example. The word “small” is being used in two different ways. Thus, it is equivocating. Being “small” as a giraffe is different from being “small” as any average animal.

(3) Inference via Omitted Determinant

Determinants can be added or omitted. Thus, for the latter, the inferred proposition is broadened in scope (rather than narrowed) because the determinant is removed.

It goes from the form “All XS is XP” to “All S is P.”

“All clever writers are clever wordsmiths.” Thus, “all writers are wordsmiths.”
The determinant here is “clever.” It was omitted.
The new proposition broadened in scope the subject and predicate in the same exact way.

“Kasper Gutman is a fat man.”
Thus, “Kasper Gutman is a man.”

A reference to The Maltese Falcon! 🙂

“Men are rational mortals.”
Thus, “men are mortals.”

But this is invalid: “She looks like an angel .” Thus, “she is an angel.”
This is also invalid: “This is a representation of gold.” Thus, “this is gold.”

In the first example, the determinant of “looks like” cannot be removed (especially if the derived proposition treats the predicate “angel” literally). And in the second example, obviously, a representation of gold and gold itself are not the same thing.

So, there are certain determinants that cannot be validly removed. Context matters!

(4) Inference via Complex Conception

No determinant modifies the subject and predicate in complex conception. What rather happens is that the original subject and predicate themselves determine a third term.

It roughly goes from the form “All S is P” to “All X of S is X of P.”

W. Stanley Jevons gives the examples (p. 87 in Elementary Lessons in Logic):
“All metals are elements.” “Thus, “a mixture of metals are a mixture of elements.”
“A horse is a quadruped.” Thus, “the skeleton of a horse is the skeleton of a quadruped.”

In both examples the subject and predicate determine (or modify) the new third term. Horse and quadruped, for example, determine the added term of skeleton.

This is invalid: “All libertarians are independent thinkers.” Thus, “a majority of libertarians are the majority of independent thinkers.” It is an inference via complex conception, but it goes beyond what is warranted from what’s given.

(5) Inference via Converse Relation

This type of inference deals with the “logic of relatives.” When a proposition declares a relationship between the subject and predicate, it may be possible to infer a new relationship once the subject and predicate are switched places.

It roughly goes from the form “S is P in X relation” to “P is S in Y relation.”
X and Y are correlatives.

“Sophroniscus is the father of Socrates.” Thus, “Socrates is the son of Sophroniscus.”
This example of converse relation obviously works because we understand the correlative (or relative) nature of the terms “father” and “son.”

“X is greater than Y.” Thus, “Y is less than X.”
“Cephalus is older than Socrates.” Thus, “Socrates is younger than Cephalus.”
“X is north-east of Y.” Thus, “Y is south-west of X.”

Informal “Immediate Inference”