Basic Logic, Principles of Reasoning, and Mind

  Larry Fike speaks his mind while Aristotle patiently listens.  August, 2017.  Photo by Aaron B. Fike.

Larry Fike speaks his mind while Aristotle patiently listens.  August, 2017.  Photo by Aaron B. Fike.

 
 

Argument Evaluation Flowchart to help you along

Exercise Sheet for Standard Logical Form, Validity, Soundness, and Beyond

Symbolic Logic Basics Handout


This page is designed to help you solidify your understanding of a few logical terms and the concepts they denote, but only as these terms are stipulatively defined by Lawrence Udell Fike, Jr. in his introductory level philosophy courses. 

This ten-minute video may be of use to some students.  Although it's not terribly exciting, the narrator does accurately describe the relationships that hold among validity, truth, soundness, strength and cogency.

DEFINITION OF A CLAIM (STATEMENT): A claim (statement) is that which can and must be either true or false. Nothing else in the universe possesses this feature.

DEFINITION OF VALIDITY: Validity is a feature possessed by all and only those arguments in which if we assume that the premises are all true, the conclusion cannot be false.

WHAT DETERMINES WHETHER A CLAIM IS TRUE OR FALSE? The universe (that which is. the "world"). More specifically, a claim is true if the (aspect(s) of the) universe is (are) the way a claim pronounces it (them) to be. For example, 'The earth is flat' is a false claim because the earth is not flat (i.e., the universe is not the way that claim purports it to be).

THE WORLD:  The totality of facts.

FACTS:  All and only those things which are the case.

An ARGUMENT is a series of claims, precisely one of which is designated as the conclusion, and (all) the other(s) of which is (are) the premise(s).

An ARGUMENT always has precisely one conclusion, but may have any number of premises as long as it is greater than zero.

A SOUND ARGUMENT is a valid argument with all true premises.

DEDUCTIVE ARGUMENTS are arguments that aim at being valid and sound.

INDUCTIVE ARGUMENTS are arguments in which, when we assume the premise(s) is (are all) true, the conclusion follows - at best - only highly probabilistically.

INDUCTIVE ARGUMENTS may be weak or strong, and their being so is a relative matter. What determines whether they are relatively weak or strong is the amount of support for the conclusion that is offered by the premises.

COGENT ARGUMENTS are strong inductive arguments with all true premises.

 

A number of implications follow immediately from the above definitions and other specifications. Some of these are merely re-statements of the foregoing. Working through these slowly by trying to say why each statement is true, may be a good way to increase your understanding of the logical concepts that we have surveyed:

  1. All sound arguments are valid, but not all valid arguments are sound.
  2. All and only arguments are valid or invalid.
  3. All and only claims are true or false.
  4. If something is a claim, it must be true or false.
  5. If something is an argument, it must be valid or invalid.
  6. Validity and invalidity, like truth and falsity, is an all-or-nothing matter; i.e., if something is valid, it cannot be invalid (in any degree), and if something is true, it cannot be false (in any degree).
  7. Likewise, if something is valid, it cannot be invalid (in any degree); and if something is false, it cannot be true (in any degree).
  8. Premises must be claims.
  9. Conclusions must be claims.
  10. Claims need not be conclusions.
  11. Claims need not be premises.
  12. What makes a claim true is not our believing it to be true.
  13. What makes a claim false is not our believing it to be false.
  14. No inductive arguments are valid.
  15. No inductive arguments are sound.
  16. No claims are valid or invalid.
  17. No arguments are true, and no arguments are false.

 

SOME BASIC PRINCIPLES OF MIND

Beliefs are one variety of cognitive states, and their objects (or contents) are claims.  Cognitive states are mental states, and they are very often directed toward something other than themselves. When they are directed toward something, they are often referred to as intentional states. Here are some types of cognitive (or intentional) states: believing, knowing, opining, wanting, wishing, hoping, conjecturing, intending, trying, thinking, intending, perceiving. Notice that these are directed toward something, and what they are directed toward is usually captured in English by something we refer to as a "that-clause": I believe that 2 + 2 = 4; I hope that the sun shines today; I wish that all people would spend more time studying philosophy; they want to go to the park; and so on.

Notice that beliefs themselves are not claims. As stated above, what makes a claim true is not our believing it to be true, and what makes a claim false is not our believing it to be false. Notice that in our way of defining things, it does not make sense to speak of "true beliefs" or "false beliefs," because only claims are true or false, and we now see that beliefs are not claims.

Notice also that what follows a "that-clause" is typically a claim (statement). So we can say that the content of our intentional states is specified by a that-clause which is itself a claim (statement). Although our beliefs and other intentional states are neither true nor false, then, the contents of them are. And what we typically hope for is that the contents of them give accurate reports of the way the world is. That way we can say that our mental content gives a true report (at least some of the time!) of the way the world actually is. In very loose and casual terms, what we are claiming is simply that our minds put us in touch with reality, or with what exists outside of us.

© 1997-2018 Lawrence Udell Fike, Jr.