I thought that the use of the concepts might be useful in helping people think critically. So much is lost in the focus of symbol manipulation of symbolic logic, predicate logic and mathematical logic. I thought it would help to put things in the proper perspective for those who want to improve their rational skills. One way to do so is to go back to the concepts of Aristotelian logic and work up to modern logic.
The point of logic as put out by Aristotle was a method of truth preservation. Note I did not say VALIDITY nor did I say preserve validity. Aristotle typically used propositions where he already knew the truth value. The flow of thought would be to move from truthful propositions to another truthful proposition (the conclusion). For Aristotle we can reason from what we already know to the things we may not currently know. That is, we can GAIN new knowledge from deduction. Mathematics suggests that deductive logic only gives us what we already know. Notice this is at odds with Aristotle.
I would like to go over some major points most people today may not be aware of because most people think classical logic is outdated. Hopefully people will read this and participate and think otherwise after the topic is discussed in detail.
The intent and purpose of the Aristotelian system is to PREVENT DECEPTION in reasoning. Historically you ought to know that there was once a group of people called PHILOSOPHERS. They had a rivalry: the SOPHIST. Generally the public could not distinguish between a Philosopher and a Sophist. For even today a lot of humans think all people are Philosophers! But none of the legit Philosophers thought all people had the capability to DO Philosophy. Plato certainly did not if he stated if there is a KING that person should be a Philosopher. He did not say any body and everyone could be KING.
Anyway let me get back to LOGIC:
Here I will go over Classical logic principles and the point as I stated above my seem OCD like because the rules of CATEGORICAL SYLLOGISMS are super strict to PREVENT or minimize DECEPTIVE reasoning that some of you will have issues with them. You fail to realize the INTENT. If you get steamed about the rules please re-read the purpose of Aristotelian logic over and over again to minimize your ego and emotions.
An Argument is defined classically as a group of propositions where there are a MINIMUM of TWO premises and a conclusion. All together a typical categorical syllogism must have three propositions stated: two premises and one conclusion. Yes an argument can have more than two premises and multiple conclusions but for every two propositions there must be a conclusion (which will often be sub conclusions in a long chain argument).
A categorical syllogism is a class of arguments. Some arguments are not syllogisms. Some arguments are not deductive. The categorical syllogism class is used directly for argument evaluation--not as a language substitute as what Predicate logic tries to do. We use categorical syllogisms as a litmus test for DECEPTION only. This is not about Validity.
The categorical syllogisms are arguments that convey information. This is not to be confused with persuasion. The information for consideration is expressed through PROPOSITIONS. Propositions are CONCEPTS. They are not SENTENCES of any type. Propositions are substituted in BY DECLARATIVE SENTENCES. The same way a mathematician would use the variable x and substitute any number he likes for that x. What the proposition expresses is a message that has a truth value: either TRUE or FALSE. There is no other objective value. This is not SCIENCE where you have to be aware of something before you KNOW there is a truth value. Objectivity is NOT about YOU or your awareness. There is life on the Sun is either true or false whether you are aware of it or not. How are you supposed to know which one it is true or false is YOUR problem. Objectively there is only two possibilities: true or false. Do not talk about your awareness---that is not the field of logic. Awareness and emotions belong to that other subject that starts with the letter P.
There is no such thing as a categorical syllogism with no premises. There is no such thing as a categorical syllogism with one premise. Because you do not literally see the premise there does not mean there is one premise. The rules below will necessitate why.
A categorical syllogism has components. The first premise is called the Major Premise. The predicate term in the conclusion will come from the major premise : (the term that is not a middle term.) The second premise is called the Minor Premise. The subject term of the conclusion comes from the Minor Premise. These premises also have components: a quantifier, a subject term, a copula, and a predicate term.
The quantifier expresses how many. There are exactly FOUR quantifiers and NO MORE. The quantifiers are ALL, NO, SOME, and SOME are NOT. These quantifiers are modern terms and break the rules: MANY, MOST, MAJORITY of, etc. There is no leniency about the quantifiers because deception can creep in. so stick to the only allowed quantifiers, which means no modern terms trying to be slick.
The subject term and the predicate terms MUST be Nouns or noun Phrases. No use of adverbs or adjectives in place of nouns. This means all premises in a syllogism must END with a noun or noun phrase. This means you should not try to be slick and end with vague words which are likely adverbs and adjectives. The reason is equivocation can easily occur or other informal fallacies can occur if you violate this rule. Doing your own thing because you can is emotional and not Logical here. The aim is to prevent deception!
The copula is simply a place for a VERB. That verb ought to be IS or ARE or some variant containing those two choices--Not something you choose just because you want to.
Then there is the RELATIONSHIP part called the MIDDLE TERM. The Middle term relates the propositions to each other. With no middle term you have NO ARGUMENT. The middle term can be either a Subject term or a Predicate term. The way to identify the Middle term is that the Middle term repeats in the premises and DOES NOT appear in the conclusion. Again with NO Middle term you have three random sentences.
So now you should see why arguments must have a minimum of TWO premises. The middle term has to be there. The conclusion cannot have a middle term. Because you do not see two premises indicates a premise is HIDDEN. This is a kind of dishonest intention objectively to hide a premise because if you are evaluating an argument all components need to be there which makes your job EASIER. With missing premises YOU have to figure out what is missing! In class this is done on purpose as an exercise. In reality why should someone make you work harder? In math I cannot simply put a solution to a complex equation and hint for the professor to figure out how I arrived at the answer! That will not fly! It should not fly in logic either objectively, but rank has its privileges. Historically the answer for hidden premises is not to deceive but the initiated understand what is missing so it is not a problem. It is a given or well known so it is not stated for the initiated.
A sorities is a chain argument that has categorical form. That is, it has MORE THAN three propositions and more than one conclusion. Some of the premises or sub conclusions may be hidden.
An Enthymeme is an argument with hidden material such as an unstated premise or an unstated conclusion. Still there are at least two propositions whether you SEE them or not.
An Epicheirema is a casual argument where at least one premise expresses a reason for believing the proposition to be true. Usually this is done all in the same sentence:
All M is P BECAUSE of R.
All S is M .
Therefore, S is a P.
this is commonly written today in the form of IF . . . THEN statements. This is likely the reason why math calls the first part the hypothesis and the part that comes after THEN is called the Conclusion. Notice the hidden premise!
This does not make all IF. . . THEN statements arguments automatically. These types of statements are called conditionals technically. A large number of IF . . . THEN statements can be made into syllogisms as above.
What you really see in an Epicheirema is TWO syllogisms! The first premise is a syllogism by itself. The initial premise you read states the conclusion first and the BECAUSE portion indicates one of the premises; and the second premise is hidden all in that ONE sentence. Then after that syllogism in the first premise is stated the second premise of the MAIN syllogism is stated and finally the conclusion.
There are three forms of Epicheirema. One where the casual premise is in the major premise, one where the casual premise is in the minor premise; and finally both the major premise and the minor premises have a casual premise in them.
There is a lot of technical material above. I will end here because of time. Your thoughts and questions will be appreciated. I hope this will be a blessing for someone.
The point of logic as put out by Aristotle was a method of truth preservation. Note I did not say VALIDITY nor did I say preserve validity. Aristotle typically used propositions where he already knew the truth value. The flow of thought would be to move from truthful propositions to another truthful proposition (the conclusion). For Aristotle we can reason from what we already know to the things we may not currently know. That is, we can GAIN new knowledge from deduction. Mathematics suggests that deductive logic only gives us what we already know. Notice this is at odds with Aristotle.
I would like to go over some major points most people today may not be aware of because most people think classical logic is outdated. Hopefully people will read this and participate and think otherwise after the topic is discussed in detail.
The intent and purpose of the Aristotelian system is to PREVENT DECEPTION in reasoning. Historically you ought to know that there was once a group of people called PHILOSOPHERS. They had a rivalry: the SOPHIST. Generally the public could not distinguish between a Philosopher and a Sophist. For even today a lot of humans think all people are Philosophers! But none of the legit Philosophers thought all people had the capability to DO Philosophy. Plato certainly did not if he stated if there is a KING that person should be a Philosopher. He did not say any body and everyone could be KING.
Anyway let me get back to LOGIC:
Here I will go over Classical logic principles and the point as I stated above my seem OCD like because the rules of CATEGORICAL SYLLOGISMS are super strict to PREVENT or minimize DECEPTIVE reasoning that some of you will have issues with them. You fail to realize the INTENT. If you get steamed about the rules please re-read the purpose of Aristotelian logic over and over again to minimize your ego and emotions.
An Argument is defined classically as a group of propositions where there are a MINIMUM of TWO premises and a conclusion. All together a typical categorical syllogism must have three propositions stated: two premises and one conclusion. Yes an argument can have more than two premises and multiple conclusions but for every two propositions there must be a conclusion (which will often be sub conclusions in a long chain argument).
A categorical syllogism is a class of arguments. Some arguments are not syllogisms. Some arguments are not deductive. The categorical syllogism class is used directly for argument evaluation--not as a language substitute as what Predicate logic tries to do. We use categorical syllogisms as a litmus test for DECEPTION only. This is not about Validity.
The categorical syllogisms are arguments that convey information. This is not to be confused with persuasion. The information for consideration is expressed through PROPOSITIONS. Propositions are CONCEPTS. They are not SENTENCES of any type. Propositions are substituted in BY DECLARATIVE SENTENCES. The same way a mathematician would use the variable x and substitute any number he likes for that x. What the proposition expresses is a message that has a truth value: either TRUE or FALSE. There is no other objective value. This is not SCIENCE where you have to be aware of something before you KNOW there is a truth value. Objectivity is NOT about YOU or your awareness. There is life on the Sun is either true or false whether you are aware of it or not. How are you supposed to know which one it is true or false is YOUR problem. Objectively there is only two possibilities: true or false. Do not talk about your awareness---that is not the field of logic. Awareness and emotions belong to that other subject that starts with the letter P.
There is no such thing as a categorical syllogism with no premises. There is no such thing as a categorical syllogism with one premise. Because you do not literally see the premise there does not mean there is one premise. The rules below will necessitate why.
A categorical syllogism has components. The first premise is called the Major Premise. The predicate term in the conclusion will come from the major premise : (the term that is not a middle term.) The second premise is called the Minor Premise. The subject term of the conclusion comes from the Minor Premise. These premises also have components: a quantifier, a subject term, a copula, and a predicate term.
The quantifier expresses how many. There are exactly FOUR quantifiers and NO MORE. The quantifiers are ALL, NO, SOME, and SOME are NOT. These quantifiers are modern terms and break the rules: MANY, MOST, MAJORITY of, etc. There is no leniency about the quantifiers because deception can creep in. so stick to the only allowed quantifiers, which means no modern terms trying to be slick.
The subject term and the predicate terms MUST be Nouns or noun Phrases. No use of adverbs or adjectives in place of nouns. This means all premises in a syllogism must END with a noun or noun phrase. This means you should not try to be slick and end with vague words which are likely adverbs and adjectives. The reason is equivocation can easily occur or other informal fallacies can occur if you violate this rule. Doing your own thing because you can is emotional and not Logical here. The aim is to prevent deception!
The copula is simply a place for a VERB. That verb ought to be IS or ARE or some variant containing those two choices--Not something you choose just because you want to.
Then there is the RELATIONSHIP part called the MIDDLE TERM. The Middle term relates the propositions to each other. With no middle term you have NO ARGUMENT. The middle term can be either a Subject term or a Predicate term. The way to identify the Middle term is that the Middle term repeats in the premises and DOES NOT appear in the conclusion. Again with NO Middle term you have three random sentences.
So now you should see why arguments must have a minimum of TWO premises. The middle term has to be there. The conclusion cannot have a middle term. Because you do not see two premises indicates a premise is HIDDEN. This is a kind of dishonest intention objectively to hide a premise because if you are evaluating an argument all components need to be there which makes your job EASIER. With missing premises YOU have to figure out what is missing! In class this is done on purpose as an exercise. In reality why should someone make you work harder? In math I cannot simply put a solution to a complex equation and hint for the professor to figure out how I arrived at the answer! That will not fly! It should not fly in logic either objectively, but rank has its privileges. Historically the answer for hidden premises is not to deceive but the initiated understand what is missing so it is not a problem. It is a given or well known so it is not stated for the initiated.
A sorities is a chain argument that has categorical form. That is, it has MORE THAN three propositions and more than one conclusion. Some of the premises or sub conclusions may be hidden.
An Enthymeme is an argument with hidden material such as an unstated premise or an unstated conclusion. Still there are at least two propositions whether you SEE them or not.
An Epicheirema is a casual argument where at least one premise expresses a reason for believing the proposition to be true. Usually this is done all in the same sentence:
All M is P BECAUSE of R.
All S is M .
Therefore, S is a P.
this is commonly written today in the form of IF . . . THEN statements. This is likely the reason why math calls the first part the hypothesis and the part that comes after THEN is called the Conclusion. Notice the hidden premise!
This does not make all IF. . . THEN statements arguments automatically. These types of statements are called conditionals technically. A large number of IF . . . THEN statements can be made into syllogisms as above.
What you really see in an Epicheirema is TWO syllogisms! The first premise is a syllogism by itself. The initial premise you read states the conclusion first and the BECAUSE portion indicates one of the premises; and the second premise is hidden all in that ONE sentence. Then after that syllogism in the first premise is stated the second premise of the MAIN syllogism is stated and finally the conclusion.
There are three forms of Epicheirema. One where the casual premise is in the major premise, one where the casual premise is in the minor premise; and finally both the major premise and the minor premises have a casual premise in them.
There is a lot of technical material above. I will end here because of time. Your thoughts and questions will be appreciated. I hope this will be a blessing for someone.
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