A fortiori An argument that usually contains the language "how much more"; based on some greater/lesser or lesser/greater premise (often unstated), it reasons that if such is the case as stated in the premise then how much greater or lesser must it be the case in the conclusion.
Ad Hoc Rescue All evidence is made to comport "to this" (ad hoc) conclusion. Relevant evidence is not taken at face value. This conclusion can never be proven wrong because all contrary evidence is incorporated into it or simply brushed aside. Significant details are overlooked in what can justifiably be called a fallacy of the closed mind, or invincible ignorance. On a large scale in scientific or philosophical theory construction, this is known as irrefutable hypothesis. It is important to distinguish this fallacy from large circle circularity.
Affirmo Latin, to affirm
Argument Structure The way the parts of an argument hang together forming, from argument to argument, various patterns that can be depicted by means of arrow diagrams, Venn diagrams, standard categorical argument forms (A, E, I, O), symbolic logic, and truth tables. The skeleton that underlies a fleshed out argument.
Argument Term Position In a categorical syllogism, there are three argument terms: major term, minor term, and middle term. The position of these terms is scattered over the six category slots; their position is fluid versus fixed in one location except in the conclusion where, given standard form, the minor term is always in the subject term position of the statement and the major term is always in the predicate term position of the statement.
Argument term position is to be distinguished from statement term position though there is obvious overlap (cf. the minor term of the argument is the subject term of the conclusion given standard form obtains; the major term of the argument is the predicate term of the conclusion given standard form obtains).
Argument Venn Diagram Three intersecting circles (two at the top one at the bottom) that picture a categorical argument by depicting the relationship between its three terms. The relation of the major term to the middle term is expressed by the overlap of the left circle with the bottom circle (this is the major premise). The relation of the minor term to the middle term is expressed by the over lap of the right circle with the bottom circle (this is the minor premise). The relation of the major term to the minor term is expressed by the overlap of the left circle with the right one (this is the concluding statement).
Argument A set of statements in which one part is used to prove or justify the other.
Arrow Diagram A graph representing an argument as a skeletal whole where various ligaments (such as the vertical arrow, the dotted or solid line, the plus sign) and bones (numbers representing premises and conclusions) depict how the parts of the argument hang together.
Autonomy (as an intellectual sin) Explicitly or implicitly asserting the independence and self-sufficiency of human reason making it the standard of truth determining such things as whether or not God exists. If it is thought of as the standard by which God's existence is determined then it must be functioning without dependence on Christ (cf. Col. 2:8f.).
Balance Rule A principle of validity for categorical syllogisms, namely, if a term is distributed in the conclusion then it must also be distributed where it occurs in the premises. Note the "if" here. Both terms of a conclusion may be undistributed. Also, note that this rule balances up from the conclusion to the premises, thus, a term distributed in the premises need not be distributed in the conclusion (the concern is to work from the conclusion up to the premises).
Balance Fallacy Violation of the balance validity rule for categorical syllogisms.
Categorical Statement A true or false information giving expression that affirms or denies membership of one category in another (particularly, of the subject term in relation to the predicate term)
Category A class or group of things.
Chain Argument A compound argument in which one conclusion becomes the premise for another.
Christian worldview How a Christian sees the world in answering the significance questions of life. Literally, the largest picture one has of the world from a presuppositional standpoint (cf. weltanschauung). Ultimately, the view of the world governed by belief in God speaking through Christ by the Spirit in Scripture versus the view of the world governed by belief in human autonomy.
Compound Argument An argument that has multiplicity on at least one side (premise side has independent premises or conclusion side has more than one conclusion).
Compound Statement An information giving expression that has more than one component. There are four types: conjunction (John is tall and Bill is short), disjunction (Either Joe will go or Tim will go), conditional (If I go to the mall, then I spend money), and negational (Clinton is not eight feet tall). Compound statements are built up from simple statements.
Conclusion The point being made or the claim being justified in an argument.
Conditional Compound Statement A compound statement formed by the use of "if...then...."
Conjunctive Compound Statement A compound statement formed by the use of "and."
Connective A word that joins simple statements making them into compound statements (i.e. and, or, if, not).
Consistency An essential ingredient of a valid argument, namely, that it have no contradiction within or between any of its claims.
Contradiction When two claims are exactly opposite in such a way that they could neither both be true at the same time nor both be false at the same time.
Contrariness When two claims are opposed in such a way that they cannot both be true at the same time but they both could be false at the same time.
Critical Thinking CT is deliberative reasoning in pursuit of wisdom that involves the necessary components of contextual sensitivity, logical skill, open-minded humility (OMH), presuppositional awareness, and acceptance of paradox. CT is not simply a matter of being logical because wisdom is necessary in the very process of obtaining wisdom; we need wisdom to govern the process whereby we discover and use wise principles of logic It therefore includes a cluster of humble Christian graces, humble self-criticism at a presuppositional level, and a most humble acceptance of theological paradox. Humility must surround and govern logical skill so that together these components define what it means to be a critical thinker with godly wisdom for the glory of God.
Deductive A characterization of arguments that have the goal of certainty.
Dependent Premises Premises that work together in such a way that if one were false then the argument would be weakened or canceled.
Dilemma An argument form composed of two (di) propositions (lemmas) that are used to show that a belief is unacceptable because one or the other pertain to the belief and both lead to unacceptable or contradictory entailments.
Disjunctive Compound Statement A compound statement formed by the use of "or."
Distribution of Terms Applied to the membership of categories distribution means that all members in a category are being referred to; if there are 5,000 brain surgeons in the world, a distributed term makes reference to all 5,000 of them and the same term in undistributed form makes reference to some portion of that 5,000 from 1 to 4,999.
Note that distribution does not refer to how terms are spread around, thrown out, or placed within a categorical argument. Instead of telling us where each term of an argument may be found, distribution tells us how many members each term refers to. In the same argument, surgeons may be distributed in one statement and undistributed in another. Each term must be considered individually to determine its distribution.
Distribution of terms can be discovered by working with two circle Venn diagrams, by memorizing a chart of the AEIO forms indicating distribution, or by thoughtful inference using the following principles which focus on the subject and predicate terms separately:
Distribution of the Subject Term is defined by the quantifier of the term
- "All" indicates a distributed term
- "Some" indicates an undistributed term
Distribution of the Predicate Term is defined by the quality of the statement
- If the statement is an affirmation, the predicate term is undistributed
- If the statement is a denial, the predicate term is distributed.
Enthymeme Parts of an argument, specifically a premise or conclusion, that is unstated but intuitively/contextually present; its presence is implicit and thus can be inferred from the flow of thought.
Ethics The pursuit of wisdom for practical application to conduct.
Exclusion Rule A validity principle of standard categorical syllogism which states that if a denial occurs in the premises then it must also occur in the conclusion. Also, denial need not occur in the first place but if it does it must occur exactly two times, once in the premises and once in the conclusion.
Exclusion Fallacy Violation of the exclusion validity rule for categorical syllogisms.
Equivocation A change of meaning of a term within an argument. One of the terms has two different meanings and there is therefore now four terms in the argument (hence, the four-term fallacy). Here is an example: "All bears are dangerous, this animal toy is a bear, so this bear is dangerous." A contrasting term is univocal, having one meaning.
Fallacy An error of reasoning within an argument.
Figure The location of the middle term in a standard categorical syllogism. Figure only applies to the premises of an argument because the middle term is never found in the conclusion. There are four locations called figure-1 (split left), figure-2 (predicate position), figure-3 (subject position), and figure-4 (split right). MT stands for middle term and shows its four possible locations:
Figure-1 Figure-2 Figure-3 Figure-4
Subject Predicate Subject Predicate Subject Predicate Subject Predicate
Major Premise MT - - MT MT - - MT
Minor Premise - MT - MT MT - MT -
Glossary From the Greek glossa (tongue, language, utterance, word); thus a list of words with their definitions. Two goals impact the choice and definition of words in this text: 1) to remain true to historical and technical usage as much as possible, 2) to creatively adapt some terms to the Christian worldview (cf. logic in relation to theology as "the study of the principles by which God is known"). In the view of the author, this is necessary to develop a coherent and consistent worldview that seeks to do justice to Christian presuppositions.
Horizontal Arrow A graph in which an arrow represents philosophy as composed of a process moving toward a goal, namely, striving after wisdom.
Human Autonomy Belief in the ultimate independence and self-sufficiency of human reason and experience, that man is the measure of all things.
Implication A conclusion thrown out or indicated by a speaker or writer.
Independent Premise Premise that can be false or omitted without weakening or canceling the impact of other premises in an argument.
Inductive A characterization of arguments that have the goal of likelihood or probability.
Inference A conclusion caught or received by a listener or reader.
Justification of Logic In a Christian worldview, the defense of the use of logic and critical thinking by Christians.
Large Circle Circularity (LCC) Refers to the fact that all reasoning is ultimately circular. When the circular relationship between premises and conclusion is necessary in order to maintain rationality itself, such reasoning cannot be deemed fallacious. Such is the case if one tries to construct a syllogism to prove proof itself. At each step principles of proof must be already assumed. On the grandest scale, it is a fundamental claim of this text that God speaking in Scripture must be presupposed in every assertion and thus in every statement within an argument, and therefore, belief in God speaking in Scripture is necessary to maintain rationality and to avoid irrationality (cf. Cornelius Van Til's "proof of proof" in Defense of the Faith 99-105).
Logic Study of argument.
In relation to philosophy it is the study of the striving process or the means by which wisdom is obtained; for short, it is the study of the principles by which wisdom is obtained. It has this function in relation to all disciplines of study whether formal or informal. Thus, in relation to auto mechanics logic is the study of the principles by which wisdom for doing auto mechanics is obtained. In relation to theology, logic is the study of the principles (of argument) by which God is known. Because the ultimate goal of the striving process is Wisdom with a capital letter, philosophy is to be defined as seeking God, seeking to know God. Understandably then, logic is a theological discipline.
Logical Operator A symbol that stands for a connective.
Major Premise The premise (support claim) of a categorical syllogism that has the major term in it.
Major Term The predicate term of the conclusion of a standard categorical syllogism. Its presence in a premise defines the premise as the major premise.
Metalogic That which goes with and underlies (meta) logic; study of the foundation upon which central notions such as consistency, validity, and proof ultimately rest.
Middle Term The argument term in a categorical syllogism that works between (in the middle of) the premises and is never found in the conclusion.
Middle Term Rule A principle of validity for categorical syllogisms, namely, the middle term must be distributed at least once.
Middle Term Fallacy Violation of the middle term validity rule for categorical syllogisms.
Minor Premise The statement in categorical syllogism that has the minor term in it.
Minor Term In a categorical syllogism, the minor term is the subject term of the conclusion (assuming standard form).
Mood Applies to standard categorical syllogisms and indicates the AEIO pattern down the argument. Thus EIO tells us that the major premise is a universal negative, the minor premise is a particular affirmation, and the conclusion is a particular negation. See statement positions in a standard categorical syllogism.
Movement An essential ingredient of a valid argument where that which is implicit in the premises become explicit in the conclusion. There is a movement or unpacking of P (premise) in C (conclusion). Violation of this principle is call small circle circularity where there is only P to P instead of P to C.
Negative Compound Statement A compound statement formed by the use of "not."
Nego Latin, to deny
Non sequitur Literally, "it does not follow." A summary way of referring to fallacies of irrelevance in which the conclusion does not follow from the premises for some reason or other. It is a non sequitur to claim that irrelevant premises strike the conclusion like an arrow hits a target; instead, the arrow misses the target.
Open-minded humility A cluster of Christian graces that are required to be a critical thinker. In a word, it is the wisdom needed in the process of bringing our thoughts into conformity with God's thoughts. Wisdom is required in the process of striving after wisdom (W/w: Wisdom personified refers to God and wisdom practiced refers to godliness, cf. Proverbs in the Old Testament). OMH summarizes an attitude of reverence to the Lord Jesus Christ that ought to come to expression in Christian argumentation.
Paradox An apparent but not an actual contradiction; a state of affairs wherein distinct threads of biblical truth are difficult to harmonize; thus, they press human thought to its limits and call for the submission of the reasoning self to Christ speaking in Scripture. For a summary see the brief on the paradoxical method in theology and also the discussion of paradox in the section on the philosophy of logic.
Philosophy of logic Wise principles pertaining to the use of logic.
Philosophy Literally striving after wisdom including both a process and a goal. The process is the means by which the goal of wisdom is obtained.
Premise The support, basis, or evidence statement in an argument.
Presupposition A belief that takes precedence over other beliefs in such a way that without the former these other beliefs have no ground, basis, or foundation (cf. comparative strengths of weak and strong).
Quality A feature of a categorical statement designating that it is either an affirmation or a denial.
Quantifier A word in a sentence that indicates scope whether universal or particular; specifically all (universal) and some (particular). These quantifiers are necessary to have standard categorical form. They also define the distribution of the subject term in a standard categorical statement.
Reasoning indicators Words within an argument that signal the presence of premises and conclusions. An argument because points to a premise whereas an argument therefore points to a conclusion. They are like road signs that say, "here comes x or y."
Reductio An argument form that seeks to reduce the opponents position to an absurdity; hence reductio ad absurdum; the goal is to point out the impossibility of the opposing view because of the contradiction that embracing it entails.
Region On a Venn diagram, the distinct areas formed by the lines of the intersecting circles; these areas represent sub-categories formed when categories are interrelated.
Relevance An essential ingredient of a valid argument that means premises hit the targeted conclusion justifying the conclusion to the degree of validity claimed for it in the premises.
Science Any discipline of study but especially systematic and technical theory development in the explanation of things.
Sciences Cube A model in the shape of a three-dimensional cube that represents all conceivable disciplines of study whether formal or informal. It shows them as a unit that can be viewed from different angles and sub-divided into various slices of a single whole.
Scope A feature of a categorical statement designating that it is either universal or particular. It is synonymous with quantity.
Simple Argument An argument that has singularity or oneness on both premise and conclusion sides; on the conclusion side singularity means that there is only one conclusion and on the premise side it means that there is either one premise or if there is more than one these premises need each other to function properly in the argument (they are dependent premises).
Simple Statement An information giving expression (T or F) that has one positive component (a single component, which is necessarily positive; it expresses a single thought, i.e. Tricia loves her husband). Simple statements are root or foundational because compound statements can be said to grow out of them or to be built up from them.
Small Circle Circularity SCC occurs when an argument lacks movement, when there is no unfolding in the conclusion of what is implicit in the premises. The conclusion simply restates or repeats the premises. Some typical fallacies of this type are veiled circularity, ad hoc rescue, and irrefutable hypothesis. Contrasts with large circle circularity (LCC).
Soundness Applies to arguments that have true premises and validity.
Standard Categorical Statement A true or false information giving expression that affirms or denies membership of one category in another using required form. Required categorical form consists of explicit use of quantifiers, the copula (preceded by the subject term and followed by the predicate term), categorization throughout (i.e., naming a category), and negation expressed by "no" preceding the subject term or "not" following the copula.
Standard Categorical Syllogism A three part argument in which each statement relates categories to one another by means of required form. Required categorical form consists of explicit use of quantifiers, the copula, categorization throughout (i.e., naming a category), and negation expressed by no preceding the subject term or not following the copula. Standardization of syllogism includes proper statement position coming down the argument (1st, 2nd, 3rd positions). A standard categorical syllogism will thus have required AIEO form and proper statement position. Mood is based on proper statement position.
Statement Position Each statement in a categorical syllogism has an assigned position for standard form. Coming down the argument, position one (or the first statement position) is the major term position, position two (or the second statement position) is the minor term position, and position three (or the third statement position) is the conclusion position. Thus, in EAO mood, the major premise has the E-form, the minor premise has the A-form and the conclusion has the O-form.
Statement Term Position Each term of a categorical statement has required order for standard form. The subject term has the first position (also called the subject position) coming before the copula an the predicate term has the second position (also called the predicate position) coming after the copula.
Statement term position is to be distinguished from argument term position. The latter refers to the way the terms of the syllogism are scattered over the six category slots of a categorical syllogism.
Statement term position is also to be distinguished from statement position. The latter refers to statements not terms and it refers specifically to the 1st, 2nd, and 3rd positions respectively of the major premise (in the 1st position), the minor premise (in the 2nd position), and the conclusion (in the 3rd position) coming down the argument. Mood follows this prescribed order down the argument, from left to right it indicates the standard categorical form of the major premise, the minor premise, and the conclusion.
Statement Terms Words that refer to categories in a categorical statement.
Statement Venn Diagram Two overlapping circles that represent the relationship between categories in a categorical statement. The Venn diagram "speaks." By use of labeling, shading, etc., the categorical statement can be read from the visualization.
Statement An information giving expression that is true or false.
Straw man A fallacy in which a position is defeated by an argument containing a premise that misrepresents that position. It is easy to defeat a straw man because there is no substance there to endure attack or fight back.
Syllogism A three part argument consisting of two premises and a conclusion.
Theology Literally, God's speech, a divine activity; thus the speaking of God or the speech of God. As a human activity theology is the study of God or striving to know God in order to honor Him in human thoughts, words, and deeds. It is equivalent with philosophy in that both seek wisdom that must be defined by God's perfect wisdom revealed by His speech in creation and Scripture.
Truth Functional Argument An argument containing at least one compound statement (i.e. Either Joe or Pete will sing).
Truth Functional Statement Same as a compound statement: an information giving expression that has more than one component.
Truth Functional Applies to compound statements and refers to the fact that the whole compound, however formed, is true or false. Truth is determined by the nature of the components and their relation to one another.
Truth Functions The possible truth values of a compound statement in varying circumstances (i.e., regarding "A or B," what is the truth of the whole compound when A is true but not B, when B is true but not A, when both are true, when both are false?)
Truth Tables Exhaustive lists that show all the possible truth-values of an argument including each simple statement and each compound as a whole whether they occur in the premise or conclusion; used with arguments containing compound statements.
Univocal Having one meaning.
Universals Rule A validity principle of standard categorical syllogism which states that, given modern interpretation, if the premises are universal then the conclusion must also be universal.
Universals Fallacy Violation of the universals validity rule for categorical syllogisms.
Validity Good form in an argument; it has three fundamental ingredients: consistency, relevance, and movement.
Veiled Circularity A case of small circle circularity (SCC) where the circular reasoning is hidden in the language used in the argument.
Venn Diagram A visualization using circles to represent the relationship between categories. The relationship between two categories in a categorical statement is pictured by a Statement Venn Diagram made up of two intersecting circles. Since an argument contains three categories, their relationship is pictured by an Argument Venn Diagram consisting of three intersecting circles.
Vertical Arrow A representation of the line of reasoning from premise (P) to conclusion (C); the central visualization tool in arrow diagramming.
Weltanschauung Literally, a world (welt) picture (schauung). The technical use of this word historically in German philosophy of religion and theology lies behind the English notion of a worldview. It denotes "the widest view which the mind can take of things in the effort to grasp them together as a whole from the standpoint of some particular philosophy or theology" (Orr, Christian View 3).
Wisdom God-likeness, reflecting God as His image bearers by living for Him, under His authority, by His word, and in the light of His wisdom. cf. OMH, which summarizes the attitude of reverence before the Lord Jesus Christ that ought to come to expression in Christian argumentation.
Wissenschaft German term for science; any discipline of study but especially systematic and technical theory development in the explanation of things.
Worldview How one sees the world in answering the significance questions of life. Literally, the picture one has of the world from a presuppositional standpoint (cf. weltanschauung). Ultimately, the Christian worldview, the view of the world governed by belief in God speaking in Scripture versus the view of the world governed by belief in human autonomy.
X-bar Two x's connected by a line and used to indicate that members may exist in one sub-category or another without knowing which; the bar connects x's found in different regions on the Venn diagram.
