Which of the following statements people assume to be true but is not necessarily so?

 

Types of Statements
Some Useful Definitions

Inhaltsverzeichnis Show

• Which of the following is a statement that is assumed to be true but not yet proven?
• Which is the statement that we assume is true?
• Which of the following refers to the statement that is either true or false?
• When someone makes you believe something that isn't true?

In analyzing arguments philosophers have found it useful to categorize statements in various ways. Though the terminology introduced by this analysis may seem confusing at first, the basic concepts involved are relatively simple and should be learned early in the student's approach to philosophy.

The claims made in either an argument or in simply stating a position without argument are generally called "statements" or
"propositions".

Statement (proposition): the meaning intended by any sentence which can be said to be true or false.

Note that a "sentence" is not the same as a "statement"; it is, rather, the vehicle by which the statement is communicated. Thus two different sentences may make the same statement. "Mary loves John." and "John is loved by Mary," are two ways of communicating the same statement.  Moreover, a sentence can be ambiguous allowing more than one equally reasonable interpretation of its meaning; each distinct meaning attributed to an ambiguous sentence is considered a distinct statement.

Note also that the truth or falsity of a statement need not be known or agreed upon. All that is required is that it is meaningful to say that (or ask whether) the statement is true or false. Thus, for example, the sentences, "There is life after death." or "Julius Ceasar had fried eggs for breakfast on March 15, 33 B.C." make statements, though their actual truth or falsity is unknown.

The actual truth value of a statement is a function of the way the world is, or as philosophers say, "of the nature of reality."  Since claims about the nature of reality are metaphysicalclaims, "truth" is considered a metaphysical concept.  However whether or not any human (or non-human) subject knows the truth value of a statement is a claim about the nature of knowledge, the subject matter of epistemology.  Therefore, while questions about what is true are metaphysical, questions about what one knows is true are epistemological questions.

 
Truth Value: the property of a statement of being either true or false. All statements (by definition of "statements") have truth value; we are often interested in determining truth value, in other words in determining whether a statement is true or false. Statements all have truth value, whether or not any one actually knows what that truth value is. [A sentence which cannot be said to be true or false is without truth value, and therefore does not assert a "statement."  Questions and commands, for example are genuine sentences, but do not assert statements and thushave no truth value.]

Remember that sine a statement is defined as what a sentence means, when we talk about a statement we mean that the meanings of the terms in that statement remain fixed.  If we change the meaning or redefine any of the terms of the statement, then we are in effect constructing a new statment.

Statements are divided with respect to why they are true or false into "analytic statements" and   "synthetic statements."

Analytic Statement: a statement the truth value of which is determined by the meanings of its terms;e.g., "All squares are four-sided." It is sometimes said (e.g. by Kant), when a statement is in simple subject-predicate form, that an analytic statement is one in which the predicate (e.g., the property of being four-sided) is-"contained within" the subject (the concept of a square).

Closely related to "analytic statements" is the term "tautology":

Tautology (tautologous statement) a statement which is necessarily true on the basis of its logical syntactical structure.

The term "tautology" is sometimes used as a synonym for "analytically true statement," but more properly  it is restricted to only that subclass of analytically true statements which are true on the basis of syntax (formal logical structure) alone; e.g., "A rose is a rose." or "Either Plato was a Greek or Plato was not a Greek."

The opposite of a tautology which is a statement which is always false:

Self-contradiction (self contradictory statement) a statement which is necessarily false on the basis of its logical structure.  A self contradictory statement both asserts and denies the same predicate of the subject, e.g., "This is a rose and it is not a rose." or "New Orleans is the largest City in Louisiana and New Orleans is not the largest city in Louisiana."

Both tutologies and self-contradiction make use of the concepts of "necessity" applied to truth value:

Necessary truth: logically impossible to be other than true.

Descartes formulated the concept of necessary truth such that a statement is said to be "necessarily true" if it is logically impossible to deny it (i.e., believe it to be false). Note that what is required is logical impossibility (not physical or psychological impossibility). Thus for example the analytic statement, "All triangles are three sided." is necessarily true because it is logically impossible to conceive of what it would take to deny this claim, namely a "non-three-sided triangle." What would such a thing be?

It is not necessary to express this concept of necessarry truth in the mentalistic vocabulary of traditional Enlightenment philosophy, i.e. about what we can conceive of.  One can also say that a statement is necessarily true if its denial is logically self contradictory, i.e. necessarily false.  To try to show "All triangles are three sided." is false one would have to assert "At least one triangle is not three sided." But since "triangle" is defined as a three sided figure, this statement would become "At least one three sided figure is not three sided." which would be commonly taken as logically necessarily false.

Analytically true statements or tautologies are all necessarily true. However, because their truth is the result of the meanings of their terms (their semantics) or their logical structure (their syntax), they are informative only of linguistic conventions,  not about matters of fact that logically could be otherwise. For this reason it is generally agreed that analytic statements cannot convey information about the way the world is; they are said to be "vacuous" or "uninformative" or "empty of empirical content."
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Synthetic Statement: a statement the truth value of which depends on'the way-the world is; e.g., "New Orleans is the largest city in Louisiana."

Synthetic statements are all those statements which are not analytic, or in other words, any statement the truth of which cannot be determined by linguistic meaning alone.

Contingent Statement a statement which could logically be either true or false.

All true statements which are not necessarily true (logically could not be other than true) are contingently true. Their truth is said to be contingent upon (depends on) the facts concerning the way the world is. Thus all contingent statements are synthetic statements.

Statements can also be categorized according to how their truth can be determined: here again there are two possibilities:
 

A Priori known independently of any particular experience (observation) of the way the world is.

A statement is said to be "known a priori" if we can determine its truth value without any appeal to the facts of experience.

A Posteriori (empirical) known only on the basis of experience of the world.

All claims made on the basis of observation are "known a posteriori," they are said to be "empirical" claims. (in actual practice the word "empirical" has almost totally replaced the use of the expression "known a posteriori").

NOTE: It should be clear from these definitions that any analytic statement can be known a priori and that any statement the truth of which can be knowm only empirically will be a synthetic statement. Whether or not some synthetic statements can be known a priori; i.e., whether or not some truths about the world can be known independently of any experience of the world) remains an unsettled philosophical questions, though most philosophers today would deny that any synthetic statement can be known a priori.

The fact that the distinctions drawn above are basic to the appreciation of Western epistemology does mean that some of the concepts involved in the definitions given above are entirely unproblematic. Indeed the proper way to categorize statements remains a continued topic for intense philosophical debate.  In particular the late twentieth century has witnessed  continuing debates over whether the analytic/synthetic distinction can be clearly drawn or whether some synthetic statements can be known to be necessarily true.

Which of the following is a statement that is assumed to be true but not yet proven?

Which is the statement that we assume is true?

Which of the following refers to the statement that is either true or false?

When someone makes you believe something that isn't true?