What exaclty is ‘Logic’? Unit 2
WHAT EXACTLY IS ‘LOGIC’?
How To Use It
In the first unit, we began to discuss the comparative application of reason and logic to determine the true nature of what we percieve. There, you saw a diagram of a comparator as it related to logic circuits in computers. Let us now examine how that same comparison is made in the human mind.
The rational decision-making process can be broken down to three integral parts:
Below is the same diagram we looked at in Unit 1, but instead of the language of circuitry, we have inserted language that applies to the human decision-making process:
You will remember that in the digital circuitry a pure reference was needed to determine whether or not the input signal was valid. It is also necessary in the mental decision-making process.
It is in this cognitive process that logic is applied. In order to use logic, we have to first understand what ‘logic’ is.
The following is a lesson excerpt from a class conducted at well-recognized School of rational thought, that describes exactly what logic is.
Dr. Joe Lau
Department of Philosophy, University of Hong Kong
Dr. Jonathan Chan
Department of Religion and Philosophy, Baptist University of Hong Kong
[L01] What is logic?
The term “logic” came from the Greek word logos, which is sometimes translated as “sentence”, “discourse”, “reason”, “rule”, and “ratio”. Of course, these translations are not enough to help us understand the more specialized meaning of “logic” as it is used today.
So what is logic? Briefly speaking, we might define logic as the study of the principles of correct reasoning. This is a rough definition, because how logic should be properly defined is actually quite a controversial matter. However, for the purpose of this tour, we thought it would be useful to give you at least some rough idea as to the subject matter that you will be studying. So this is what we shall try to do on this page.
§1. Logic is not the psychology of reasoning
One thing you should note about this definition is that logic is concerned with the principles of correct reasoning. Studying the correct principles of reasoning is not the same as studying the psychology of reasoning. Logic is the former discipline, and it tells us how we ought to reason if we want to reason correctly. Whether people actually follow these rules of correct reasoning is an empirical matter, something that is not the concern of logic.
The psychology of reasoning, on the other hand, is an empirical science. It tells us about the actual reasoning habits of people, including their mistakes. A psychologist studying reasoning might be interested in how people’s ability to reason varies with age. But such empirical facts are of no concern to the logician.
§2. The principles of logic
So what are these principles of reasoning that are part of logic? There are many such principles, but the main (not the only) thing that we study in logic are principles governing the validity of arguments – whether certain conclusions follow from some given assumptions. For example, consider the following three arguments :
If Tom is a philosopher, then Tom is poor.
Tom is a philosopher.
Therefore, Tom is poor.
If K>10, then K>2.
If Tarragona is in Europe, then Tarragona is not in China.
Tarragona is in Europe.
Therefore, Tarragona is not in China.
These three arguments* (see below) here are obviously good arguments in the sense that their conclusions follow from the assumptions. If the assumptions of the argument are true, the conclusion of the argument must also be true. A logician will tell us that they are all cases of a particular form of argument known as “modus ponens“:
If P, then Q. P. Therefore, Q.
We shall be discussing validity again later on. It should be pointed out that logic is not just concerned with the validity of arguments. Logic also studies consistency, and logical truths, and properties of logical systems such as completeness and soundness. But we shall see that these other concepts are also very much related to the concept of validity.
It is of note that Jesus Christ is referred to in Scripture as the Logos. The word logos is of Greek origin and it’s root means “persuading by the use of reasoning’.
The Math Behind Logic
George Boole, an Engligh mathematician and philosopher, wrote a book first published in 1854 that would set the scene for the introduction of the computer over 100 years later. In his book, “The Laws of Thought”, Boole introduced a concept to express the combination of ideas using the key words ‘AND’, ‘OR’, and ‘NOT”. He wanted his ‘algebra’ to encompass all of Aristotle’s insights into human reasoning. Aristole developed a concept he described as the “logic of propositions“.
Boole created a mathematical model of the logical thought process. A statement or proposition can only be ‘tue’ in a specific set of conditions. It seems ‘bold’ to think a mathematical equation could described how we think and reach accurate conclusions.
His philosopher’s background played a key role in his making a correlation between ‘thinking’ and mathematics. Philosophy is the study of ideads about knowledge, truth, nature, and the meaning of life. So, his thoughts had been already focused on understanding the thoughts of the human mind. This led him to search for the “why” and the “how come” of things.
The accuracy of his conclusions are validated by the successful use of his model. Computers work almost flawlessly with strick adherence to the concepts he discovered and its mathematical correlations. Imagine the dysfunction of your computer or mobile phone if these rules of logic were ignored.
The application of the logical process begins with a ‘proposition‘ that is the subject of consideration. A proposition is a declaration that ‘something’ is a fact of truth. A statement in propositional logic which may be either true or false.
The Linearity of Logic
Linear Thinking is defined as:
a process of thought following known cycles or step-by-step progression where a response to a step must be elicited before another step is taken.
If a = b, and b = c, then a = c. The application of linear thinking can be found in the well known Socratic Method:
a form of inquiry and debate between individuals with opposing viewpoints based on asking and answering questions to stimulate rational thinking and to illuminate ideas.
Example: Here is a stated proposition, “All American’s are virtuous people!”
Is this TRUE or is it FALSE?
There is a logical methodology to determine the veracity of the above stated proposition.
Next, is a brief video that demonstrates the application of George Boole’s concept (Boolean Algrebra).
While it is not necessary to understand the math complexities, it is important to grasp the concept that there is a mathematical progression and order to reasonable/logical conclusions of thought.
It requires due diligence in effort to ascertain and understand the truth. Most people are not willing to do mentally hard work. One of my instructors put it this way, “Most people are mental misers. They want to use the least amount of mental energy necessary to function. That is why they find it easier just to over generalize things or operate on assumptions (hearsay)”.
Many fail to use reasoning logic of the failure as a matter of choice and not because of a lack of understanding of how to reason.
There is no wonder why there is so much confusion and uncertainty in the world given a general lack of desire on the part of mankind to search and sift for the truth. This is of particular importance when it comes to knowledge of the true God and His commandments.
Let’s now return to discussing Propositions and Conclusions.
Inferences and Arguments
Reasoning is a special mental activity called inferring, what can also be called making (or performing) inferences. To infer is to draw conclusions from premises.
The dictionary definition of the word inference is:
plural noun: inferences
A conclusion reached on the basis of evidence and reasoning.
synonyms: deduction, conclusion, reasoning, conjecture, speculation, guess, presumption, assumption, supposition, reckoning, extrapolation.
So, inferences are logical conclusions that are reached based on evidence and reason.
We take in sensory information and then make inferences after we have sifted the information using logical reasoning.
A Reference by Which to ‘Justify’
Some ‘Test Rod’ of Proof is Required
Inferences must be tested against some valid and reliable standard. That reference standard serves as a ‘test rod’ to determine whether or not the inference or belief we put forth is TRUE.
To test out a belief, it is necessary to be wholly objective. When a person allows their pre-formed ideas contaminate their investigation for the truth, they are conducting their search with a ‘confirmation bias’ That is that they will only look for and recognize information that confirms what they already believe.
Confirmation Bias defined:
In psychology and cognitive science, confirmation bias (or confirmatory bias) is a tendency to search for or interpret information in a way that confirms one’s preconceptions, leading to statistical errors.
Confirmation bias is a type of cognitive bias and represents an error of inductive inference toward confirmation of the hypothesis under study.
Confirmation bias is a phenomenon wherein decision makers have been shown to actively seek out and assign more weight to evidence that confirms their hypothesis, and ignore or underweigh evidence that could disconfirm their hypothesis.
As such, it can be thought of as a form of selection bias in collecting evidence.
From Science Daily
Those who enter into the field of scientific research are required to take a course titled, “The Scientific Method”. Their are trained to avoid cross-contamination of their research and findings as a result of a confirmation bias, in order that their findings yield both valid and reliable results.
It is a confirmation bias by those who hold the belief that God the Father and His only begotten son are one in the same Person, that keeps them from accepting what the Biblical context reveals about the subject. It is because this Biblical evidence disconfirms their hypothesis.
Even though there is so much clear evidence to the contrary and that the concept is illogical (a father and a son being the same person) they block out this information contained in the test rod of such matters, the Bible.
They render the test rod useless because the are unwilling to accept the test results.
In practical day-to-day affairs people likewise disregard the information that their senses gather in order to made logical decisions, rendering them ineffective. If logical thought produces a result that is in conflict with their preconceived notions, they simple disregard the factors that weigh against their position. Such a bias narrows the perceptive field of vision, disabling a person form knowing and accepting the truth.
At the output stage of the of the cognitive logic process is the point of critical analysis, subsequent decision-making, and response in the form of action.
The Analysis phase of the thought process includes consideration of rewards versus risk. Risk being described as the alternative cost of one’s actions.
Alternative cost are the cost payed in loss for a particular course of action. These are the negative effects your actions will have on you, other people, and the negative effects your actions will have on things around you.
A completely self-centered view of life omits the consideration of or minimizes the negative effects a person’s action have on others. Sociopathic personality types (ie antisocial personality disorder) are devoid of empathy or fellow-feeling. They can be quite rational, but lack a moral aspect to their character. They tend to use their knowledge in destructive ways.
Learning to think logically is a matter of using a methodical progress of thought in order to accurately interpret sensory input information. This information can come in the form of sensory information recieved by are natural senses ( sight, smell, taste, sound, sensation, etc). It can also come in the form of information presented in the form of statements heard, sight observed, text that has been read, etc. These all must be evaluated for the validty.
There are three basic functions to the process: Data Acquisition, Data Processing, and Data Analysis.
Memory plays a key role in this process as it contains all the available stored comparative information we possess. Memory is one tool we use as a truth rod to determine if something is true or false. If we are told that we are looking at an orange tree, but we see apples hanging from the trees branches, we know that that statement is false. The Lord Jesus Christ stated, “You will tell a tree by the fruit that it bears”. Recognition is based on memories.
Accurate perception requires mental focus; the ability to separate that which is relevant from that which is not.
It is necessary to discern and factor in all important variables involved and to weigh them appropriately in the process.
It is also important not to let our preconceived ideas contaminate our analysis of what it is we are considering.
The end result of the logical thought process will leave a person in a better postion to make good decisions. They will have considered not only the personal gains or rewards they themselves will receive from a particular action; but will have also considered the negative effect that will result if they choose to act or response in a certain manner.
Logic should not be thought of as something new or as a ‘technique’. The concepts of logic seek to describe what is a natural phenomenon and articulates that there is definitely a rational process of acquiring, processing, and interpreting the information that our senses receive. It describes the methodical approach to accurate interpretation of that sensory input.
Of course, the more accurate the interpretation we have of what we are to comprehend and understand, the better capable we are to continue to learn about those things.
The next and last unit of this Section, Unit 3, will present story-problems based on every day encounters we find ourselves confronted with that will give us an opportunity to apply what has been learned.