[NOTE: This article follows the article, "Epistemology, Concepts," which should be read before this one. It is not possible to understand what propositions are without understanding what concepts are.]
All knowledge is propositional. All we know is in the form of propositions.
The word, "propositions," is used throughout philosophy with many different definitions especially in relationship to logic. In this article a proposition is defined as follows: A proposition is a verbal statement or sentence that asserts something about something else.
The Simple Basic Structure Of Propositions
Very few of the sentences we use in every day speech, writing, or thinking will very closely follow the basic structure of propositions. While there are no rules for how propositions must be formed, because language is a human invention, a description of how basic propositions are formed will explain what a proposition must do to be knowledge.
Propositions are sentences or statements that assert a relationship or relationships between two or more existents. The existents and the relationships are identified by their concepts or descriptions, which are designated by the words, or phrases that designate them. The designating words in a proposition are called terms.
Every basic proposition consists of three terms, a subject, about which the assertion is being made; a predicate which is being asserted about the subject, and a copula, which specifies the exact relationship between the subject and predicate.
In the proposition, "coffee is a beverage," the terms are, "coffee," "is," and "a beverage." "Coffee," is the subject, "a beverage," is the predicate, and "is" is the copula. In basic propositions, the copula is usually a form of the verbs, "to be" or "has."
The copula, "is," in basic propositions does not mean "equal to," or, "identical with," but simply that the existent identified by the subject term, "is or has," whatever quality, relationship, action, or category is indicated by the predicate term.
A proposition does not assert a relationship between the concepts or the terms of the proposition, but between the existents the concepts or descriptions identify. In the example proposition, it is not the term, "coffee," that is the term, "beverage, and it is not the "concept coffee" that is "the concept beverage" (you cannot drink concepts) it is the "actual black liquid" identified by, "coffee" that is "something you drink" identified by the universal concept "beverage."
The terms, "subject" and "predicate" in basic propositions is not identical with the same terms in English grammar. The subject may consist of any number of words as may the predicate. In the proposition, "the last person leaving the room is responsible for turning out the lights," "the last person leaving the room," is the subject, and, "responsible for turning out the lights," is the predicate.
Knowledge and Propositions
All knowledge consists of propositions which may be actual propositions or implied. All knowledge is knowledge about things. In propositions, the things that are known about are subjects, and the things known about subjects are predicates. The subject, "thing," is whatever existent or existents are identified by the concept or description identifying what it is the predicate is about. The predicate that is "what is asserted," about the subject, is a concept or description identifying what is asserted about the subject.
In the simplest propositions, the subject and predicate consist of single terms, such as, "plants are living," and "water is liquid."
Every proposition asserts something (the predicate) about something else (the subject). The usual form of a proposition is, "the subject is the predicate," or, "the subject has the predicate."
The subject (A) of a proposition may be a concept for or description of a single existent, a combination of existents, a category of existents (universal), material or epistemological including: existents, qualities, actions (events, behavior), or relationships. The predicate (B) may be a concept for or description of a category of existents (universal), a quality, an action (events, behavior), or relationship. A relationship (x) may be any kind of relationship, material or epistemological. The following are all the possible forms of propositions:
something is a referent of a universal. (A is a B)
something has a specific quality (A has quality B)
something is doing (or does) some action (A does B)
something has a specific relationship to something else (A has relationship x to B)
[NOTE: Those propositions using the copula, "has, or, "have," mean the same as, "is," or, "are" in the sense that "A has the quality 'red'," means the same as, "A is red," and "A has the relationship 'above' to B," means the same as "A is above B."]
[NOTE: Since the subject term can identify a collection of existents all propositions may also have a plural form as, "some things are ...," or, "some things have ...."]
A proposition may assert the negative of any proposition:
something is not a referent of a universal. (A is not a B)
something does not have a specific quality (A has no quality B)
something is not doing (or does not do) some action (A does not do B)
something does not have a specific relationship to something else (A has no relationship x to B)
A proposition may assert a past version of any proposition:
something was a referent of a universal. (A was a B)
something had a specific quality (A had quality B)
something was doing (or did) some action (A did B)
something had a specific relationship to something else (A had relationship x to B)
A proposition may assert a past negative version of any proposition:
something was not a referent of a universal. (A was not a B)
something did not have a specific quality (A had no quality B)
something was not doing (or did not do) some action (A did not do B)
something did not have a specific relationship to something else (A has relationship x to B)
Since everything a human being does must be consciously chosen, the thought processes used to make choices are always about the future, whether that future is the next moment or many years later. Propositions about the future are different from all others, because they are neither true or false.
Every future proposition is hypothetical. It is hypothetical in the sense that it is conditional, contingent on all things being what they are presently known to be. Future propositions are certain to the degree they are based on principles and whatever they are contingent on is known. A proposition that states the velocity of an object falling toward the earth is almost perfectly certain while a proposition about the tomorrow's weather is much less certain.
What Future Propositions Assert
Future propositions assert the same kind of relationships all propositions assert. All future propositions, however, imply the contingent context of what they assert, as, for example: "within the context of what is currently known," or, "all things remaining as they are currently known to be."
something will be a referent of a universal. (A will be a B)
something will have a specific quality (A will have quality B)
something will be doing (or will do) some action (A will do B)
something will have a specific relationship to something else (A will have relationship x to B)
A proposition may assert a future negative version of any proposition:
something will not be a referent of a universal. (A will not be a B)
something will not have a specific quality (A will not have quality B)
something will not be doing (or will not do) some action (A will do B)
something will not have a specific relationship to something else (A will not have relationship x to B)
Universal and conditional propositions based on principles are sometimes stated in future form but are not really future propositions. For example, "triangular braces will provide rigid support," or, "water will freeze at temperatures below minus 32 degrees F. are not future, but "timeless" propositions.
Propositions of intention may be in future form, "Tomorrow I'll see the doctor." Such propositions are not true if they are predictions, but are true if they are only intentions and really are what one intends, because they are then present propositions.
Variations Of Propositional Forms
Propositions must assert one of the above, but do not have to be in the exact form described. One of the most common forms of propositions uses the copula "equals" (=). In propositions, "equals," means, "has the specific quantitative quality." For example, "A equals B," means, "something A has the specific quantitative quality B," or, "something A has the same specific quantitative quality as B." "A equals B," may also be a relationship x, where relationship x is "has the same value as," "A = B" like the relationships, "has a greater value than," "A > B" and "has a lesser value than, "A < B." Quantitative propositions assume values are "counts" or "measurements in commensurable units."
The proposition, "something A is something B," (A is B), if A and B are both existents, the proposition is not possible, because no two things can be the same thing. Propositions of the form A is B, where A or B is a descriptive attribute (a quality, an action, or a relationship) like Bill is the "culprit" (a quality), or Fitzgerald is "the author of Gatsby" (an action), are not, as some ignorant philosophers have tried to claim, tautologies. A true tautology would be "A is B" where A and B are simply different "words" for the same concept, such as, "a home is a casa," which are just the English word and Spanish word for the same concept and is exactly the same in meaning as, "a home is a home," which might be interesting rhetoric, but is not a legitimate proposition.
The reason these twenty four basic propositions are all the possible propositions there are, is because existents, (physical entities and epistemological existents), events, attributes, and relationships are all there is. Events, attributes, and relationships exist, so are also existents, and can be identified by concepts and related to other existents in propositions. No attributes, events, or relationships, however, exists independently of the existents they are the actions of, the attributes of, or the relationships between. Any proposition that treats any attribute, action, or relationship as though it existed independently is an invalid proposition.
The basic propositions described are not some kind of law or ontological principles, they are the sum of reasoned observation. Epistemology is not dictated by some authority, it is discovered by human beings, just as all other disciplines, like the sciences, geography, or history. If some other suitable way of identifying the nature of propositions were devised, so long as it did not contradict how they are actually used and how they are actually constructed, it could be just as valid as the way they are here described and classified.
Very few of the propositions we use when thinking, writing, or speaking will be in the exact form of basic propositions, but any proposition or statement we make, if it is true, will be able to be put into the form of a basic proposition or a set of basic propositions.
[NOTE: This is not some kind of philosophical rule or principle, but a way of understanding if what we think, write, and say is true or not. It is not only possible, but very common, to say things in ways that are so complex, convoluted, and ambiguous that, whether they are true or not, or even if they actually say anything, is difficult to determine. The virtue of the formal propositions is that what they assert is always explicit and whether what they assert is true or not is much easier to determine.]
Every proposition, basic or common, is an expression of a relationship or relationships. It is a statement that asserts something about something else, or simply a relationship between two things. The "things" may be single things, groups of things, classes of things, and may be any existent or existents identified by a concept or a description.
In the proposition, "the concert begins at eight o'clock," what is being asserted is not about the concert, but at what time the concert starts. To put the proposition in formal form it might be rewritten, "the start of the concert is eight o'clock," or, "the concert's beginning is at eight o'clock." It is now clear the subject is, "the concert's beginning, and the predicate is, "at eight o'clock." Whether the proposition is true or not is determined by whether or not the scheduled time for the beginning of the concert is really eight o'clock, which can be determined by checking the concert program schedule.
Since everything has an ontological or epistemological context most of the propositions we use will either assume that context, or specify it with such terms as, "if (the context) then," which means under these conditions or within these limits.
Any of the terms of a proposition may be limited or further defined by such modifiers as "all," "every," "some," "most," "many," "few," "only," "not all," "not many," "not a few," "always," "often," "before," "after," and "during."
Terms of propositions can be combined using "or," "either...or," "not," "neither...nor," "and," "both...and," "not both," "if...then," and, "if and only if."
["A and X are B," "A has both qualities B and C," "A has neither relationship x or y to B"]
Propositions can also be combined using "or," "either...or," "not," "neither...nor," "and," "both...and," "not both," "if...then," and, "if and only if."
["A is X or B is K," "Either A is X or A is K," "If A is X, then B is K."]
When propositions are combined, the combined propositions are only true if each individual proposition is true. See, "The Meaning of Propositions" and the only conditions in which they are true, below.
Propositions Only Epistemological
Propositions, like concepts, have no ontological or material existence. They only exist as the creation of and within the consciousness of human minds. Such arguments as, "since rocks actually exist, the proposition, 'rocks exist,' is true, independent of any mind," ignores the fact that propositions do not exist independent of any mind. Rocks, like all material existents exist and are what they are whether anyone is conscious of them or knows what they are, but that they exist and are what they are can only be known and stated by a conscious mind.
A similar spurious argument is sometimes made about mathematical concepts and propositions. The argument is that, "two plus two equals four," is a true proposition whether anyone knows it or not and is therefore, "mind independent." Actually 2+2=4 means nothing. 2, 4, +, and = are symbols, like words, for concepts, specifically for the two numbers, 2, which is how far a count gets if counting only two things, and 4, which is how far count gets if counting four things, and +, which is the symbol for adding things together and counting them, and =, which is the symbol meaning the same numeric value. There are no wild 2s, 4s, +s, or =s running around, they only exist in human minds. Valid propositions must be about existents, they are not about the concepts that identify the existents. 2+2=4 means, any existents of which there are two, added to two other existents, when counted will be four existents. 2+2=4 sans existents means nothing. (This is perhaps the biggest mistake in math theory.)
All Knowledge Propositional
Some attribute the human intellect to the ability to form concepts, and it is true, without that ability the intellect would be impossible. But philosophically, concepts are not knowledge, and concepts alone are not language.
All human knowledge is made possible by language and consists of propositions. Knowledge is about things: about existence itself, about the existents that are existence, and about their nature, their attributes, their actions, and their relationships to each other. It is by means of propositions that state what the nature of existents, attributes, actions, and relationships to each other are that all knowledge is expressed and held.
Though most philosophers consider concepts knowledge, and even though no knowledge is possible without concepts, concepts alone are not knowledge.
All supposed knowledge must be either true or false, and is only knowledge if it is true. Except by implication, no concept is either true or false. Concepts can be good or bad, that is, they may identify confused ideas, or be vague and poorly defined, or may identify what does not materially exist, (as though it did), as most mystic concepts do. What those concepts identify are fictions, but the concepts are neither true nor false. A concept only identifies things, and is just as valid when identifying fictional things as when identifying actual things.
Only propositions can be true or false. A proposition is a statement that asserts something about an existent or class of existents. For example, "Zeus is a god worshiped by the ancient Greeks," asserts something about Zeus. If what is being asserted is correct, the proposition is true; if what is being asserted is incorrect, the proposition is false. The assertion, in this case, and therefore the proposition, is true, even though the concept "Zeus" identifies a fictional existent. The same concept can be use in both true and false propositions. "The phoenix is a common bird found in the forests of Colorado," is false, but, "the phoenix is a mythical bird of ancient Egypt," is true.
Since only propositions can be true or false, knowledge consists entirely of propositions; but all propositions are constructed of concepts, without which no knowledge would be possible. Concepts identify the existents all our knowledge is about. Technically, concepts are not knowledge, but a definition, if correct, is knowledge because it is stated as a proposition.
One might say, all correctly defined concepts constitute a kind of knowledge, but notice, it is really only the definitions that are the knowledge, not concepts as identifiers, which is their only function. Concepts imply knowledge, and most concepts would be impossible without knowledge, but attributing knowledge to concepts themselves is an epistemological mistake. It is that mistake that is the source of such confused ideas as those that suggest knowledge somehow changes the meaning of concepts, so that what a child means by an apple, and what a botanist means by an apple are different things.
Our knowledge, then, consists of all the propositions we understand and have stored in our memory that are true statements about any aspect of existence. By the time we are adults we have learned and stored thousands, possibly millions of propositions in memory.
Conceptual Relationships to Knowledge
A concept itself only identifies existents. It is the existents all our knowledge is about, not the concepts that identify those existents. Nevertheless, because a concept identifies existents and means those existents with all their attributes and all that can be known about them, the concept acts like a reference to all that we know about those existents.
The concept itself does not hold any of that knowledge or actually do the referencing, but our ability to ask and answer the question, "what do I know about the existents this concept identifies?" is made possible by the concept. In that sense every concept can be used like a key-word in a search engine that will find all the propositions we have in memory that begin, "this existent is ..." where the predicate of the proposition is something known about the concept's referents.
[NOTE: The key-word/search-engine explanation is only an analogy for the relationship between consciousness and memory. It is always what we are conscious of that prompts recall from memory. It is when we are consciously considering a concept that propositions we have in memory will be recalled, in most cases the ones we use or consider most often first followed by lesser used ones. Some propositions are very difficult to recall if not often used. An example is that case of thinking, "I'm sure there is something else I know about this but can't remember it."]
Using the concept "dog" for example, the answer to the question, "what do I know about dogs," can call up every proposition we can remembered that begins, "a dog is ..." where the predicate is some concept that is true about dogs in general, or any dog in particular.
Some of the propositions regarding dogs might be, "a dog is a mammal," "some dogs are dangerous," "some dogs are used to help people," "some dogs are pets," "dogs are not allowed in this building," "that dog bites." As each proposition is recalled, the concepts from which the propositions are constructed can begin a new series of recalled propositions. The concept "mammal" in the proposition, "a dog is a mammal," may act as a key-word to search for all that is known about "mammal" by means of the propositions, "a mammal is ...." Since there will be an indefinite number of possible such propositions for every concept indicating what is known about them in terms of other propositions, the interrelationships between concepts and propositions in this manner is indefinitely complex.
It is neither necessary or possible to identify or "unscramble" the nearly infinite complexity of the cognitive relationships between concepts and propositions, however, because concepts themselves are the means of maintaining the order and understanding those relationships. It is because all our propositional knowledge is only recalled in relation to concepts we are currently conscious of that propositional ideas always relate to what is currently important to our own thinking.
The Meaning of Propositions
What concepts mean are the existents they identify which are called their units, referents, or particulars. Since propositions assert something about something else, which specifically attributes the predicate of the proposition to the subject, the proposition means: "whatever is specified by the predicate concept is true of the existents identified by the subject concept."
A proposition is a "logical connection" between the existent or existents that are the referents of the subject concept and the existent or existents that are the referents of the predicate concept. A proposition is true if and only if the relationship described by the proposition is the actual case.
A proposition is true if:
- ... the predicate is a universal concept, and the existent or existents identified by the subject concept really are referents of that concept.
- ... the predicate is a concept of a quality or qualities, and the existent or existents identified by the subject concept really have that quality or those qualities.
- ... the predicate is a concept of action, actions, behavior, or behaviors, and the existent or existents identified by the subject concept really exhibit the action, actions, behavior, or behaviors.
- ... the predicate is a concept for a specified relationship or relationships, and the existent or existents identified by the subject concept really have the specified relationship or relationships.
These, of course, apply to all the negative, past, and future forms as well.]
In most general terms, therefore, a proposition means the actual connection between the existents identified, and that the predicate is true of the subject. A concept identifies existents. A proposition specifies a connection between existents.
[NOTE: It would not be incorrect to say a proposition "identifies" a "relationship" between existents, but I prefer "specify" to distinguish the operation from the function of concepts to "identify" existents, and I also prefer "connection" to "relationship" because one of the possible connections is relationship.]
False Dichotomies Of Propositions
There is a very bad idea in much of philosophy that is an assault on the nature of propositions by that class of philosophers who are the enemies of knowledge and truth. It is an attempt to invalidate propositions by dividing them into two classes, both wrong and both intellectually destructive. I'll call the two classes certain and unknowable. Each class contains three subclasses of propositions, as follows:
Certain: Analytic, A Priori, and Necessary
Unknowable: Synthetic, A Posteriori, and Contingent
These supposed subclasses of propositions are usually paired as, "certain vs. unknowable," as follows: Analytic (certain) vs. Synthetic (unknowable), A Priori (certain) vs. A Posteriori (unknowable), and Necessary (certain) vs. Contingent (unknowable).
These three false dichotomies of propositions may be briefly described as follows:
Pertaining to language and the meaning of concepts:
Analytic propositions are those it is supposed must be true (certain) because the predicate is contained in the subject. Such propositions are true, it is claimed, "by definition." One frequent example is, "all bachelors are single" must be true because the predicate (single) is contained in the definition of the subject (bachelor). Such propositions are called, "analytic," because they can be known to be true simply by analyzing the definitions of the words.
Synthetic propositions, it is claimed, cannot be known to be true (unknowable) because they depend on experience, which is never certain. Examples are "Americans eat less rice than Asians," "The cat is sick," and, "the light is red," which of course can only be true if correctly observe, so could be false (mistaken).
Pertaining to logic and knowledge (epistemology):
A priori propositions are those one can know are true (certain) independent of experience. The propositions, "The sum of the interior angles of a triangle is 180 degrees," and, "two plus two is four," are known to be true without measuring every triangle or observing actual addition. These are supposedly known independently of, or prior to, any experience.
A posteriori propositions cannot be known to be true (unknowable) because they depend again on experience. Examples are, "The light is yellow," "Tom is heavier than Sue," "The car has crashed," which can only be known if those facts are observed without error.
Pertaining to the nature of existence (ontology):
Necessary truths cannot be false (certain), it is supposed, because to deny them leads to a contradiction. Examples are, "It is either night or day," "Cows are mammals," and "Ice is solid." These propositions are true, it is said, because they're not being true cannot be imagined and they are true "in all possible worlds."
Contingent truths are those that are not necessary and whose opposites or contradictions are possible, so are unknowable. Examples are, "I ate a burger for lunch," "Today is the hottest day on record," and, "The cat is in cupboard." while any of these may be true, they are contingent, it is argued, because their opposite can be imagined and could have been different, in another universe, for example.
All these false dichotomies contradict all sound philosophical principles of epistemology and ontology:
The Analytic vs Synthetic dichotomy evades the epistemological fact that a "word" is not a concept and a concept does not mean its definition. A proposition, like, "all bachelors are single," cannot be known to be true because the word, "bachelor," is defined as, "a never married man." The definition may be wrong, and unless one knows what a man is (a male human being), and what, "married," and, "single," mean, whether or not the proposition is true cannot be known. According to the, "analytic," perversion of propositions, if the definition of "duck," was, "a four-footed snake," the proposition, "all ducks are four-footed," would be true.
Synthetic propositions supposedly cannot be known with certainty because they depend on unreliable observation. This absurd idea would mean the proposition, "the man is dead," is doubtful, even though the man is lying there beheaded, with his head lying on his chest.
The A Priori vs A Posteriori false dichotomy confuses the epistemological with the ontological. That propositions, "The sum of the interior angles of a triangle is 180 degrees," and, "two plus two is four," are statements based on human developed knowledge methods of geometry and mathematics. None of the concepts, sum, angle, triangle, degrees, two, plus, or, four exist outside human minds. The propositions are known to be true because they are epistemologically correct descriptions of a human method. Note, that the interior angles of a triangle are only 180 degrees, because the human convention for subdividing a circle is 360 degrees. If the convention were 100 degrees, the interior angles of a triangle would be 50 degrees, or if 800 degrees, the interior angles of a triangle would be 400 degrees. None of these things could have been known a priori, because they could not be known until some human being invented them.
A posteriori propositions are those that depend on the actual observation of ontological facts, not epistemological methods. If either a priori or a posteriori proportions were doubtful, it would be a priori propositions which are dependent on the arbitrary invention of human beings, while a posteriori propositions depend only the actual facts of existence.
The Necessary vs Contingent, false dichotomy confuses the ontological with imaginary or fictional as well as what actually is with what supposedly could or might have been. Ontological (material) existence is not contingent on anything and cannot be anything other than what it is. The idea of a contingent universe is a fairy tale, the invention of superstition and the supernatural.
The only contingencies in this world are future and only those things that depend on human choice, because everything else is determined by the nature of reality itself. All past events and all currently existing entities could not be anything other than what they are.