Reason is the tool in philosophy’s search for truth, and logic is the study of correct reasoning. Here one brings evidence in support of a conclusion by using a philosophical argument. It boils down to essentially two modes, commandments of thought as it were: deduction and induction.
Of necessity, if the premises of a deductive argument are true then the conclusion must be true. It is then termed valid. Deduction investigates the necessary conclusions of individual assumptions.
1a. Law of Identity aka The Golden Rule of Thought deals with “Either/Or” statements. It is essentially the bedrock upon which all reasoning is based and cannot be violated without being irrational: Simultaneously either P or Not-P is true, i.e. either p or not-p describes all truth at any given point in time. Everything that exists has a specific nature with its particular characteristics that are a part of what it is and that make it distinguishable from all else. To have an identity means to have a single identity; an object cannot have two identities simultaneously; an entity can have more than one characteristic, but any characteristic it has is a part of its single identity. A house can be both blue and red, but not at the same time or not in the same respect. Whatever portion is blue cannot be red at the same time, in the same way. Half the house can be red, and the other half blue. However, the whole house can’t be both red and blue. These two traits, blue and red, each have single, particular identities. The concept of identity is important because it makes explicit that reality has a definite nature. Since reality has an identity, it is knowable, since it exists in a particular way, it has no contradictions, and there is no middle ground between these two identities.
1b. The Categorical Syllogism is the major form of deduction and entails All, No, or Some statements.
1) A categorical syllogism consists of two (2) premises and a conclusion.
2) A categorical syllogism is one in which every statement has one of four (4) forms: a) All A are B; however this does not imply that All B are A! b) No A are B c) Some A are B and d) Some A are not B.
3) A categorical syllogism must have exactly three (3) terms.
4) In a categorical syllogism the term that occurs in both premises must be modified by All or No at least once.
5) In a categorical syllogism, there must be the same number of negative conclusions as negative premises.
6) In a categorical syllogism a term that is modified by All or No in the conclusion must be modified by All or No in one of the premises.
1c. Propositional logic deals with if-then statements. In propositional logic, only the following forms are valid:
1) If p then q, p, therefore q.
2) If p then q, not q, therefore not p.
3) If p and q, then r and s, p and q, therefore r and s.
4) If p then q, if q then r, therefore if p then r.
5) If p then q, if not p then r, therefore q or r.
6) The term fuzzy logic is a branch of propositional logic in which the terms are not 100% true or false i.e. there’s a degree of imprecision in each term e.g. if p then there’s a 50% chance of q.
Induction takes particular evidence and proceeds to form generalizations that are more or less probable such that the premises serve as evidence for the conclusion. Its great value lies in its predictive ability based on previous observations. It follows the legal “preponderance of evidence” test. Evidence (information that tends to prove or disprove a fact in question) is required to build theories not the other way around! One fact trumps a thousand theories.
2a. Observable Sensory Evidence is a necessity in guiding our thinking—correct evidence as opposed to pseudo-evidence; this is the heart of Inductive logic. How can we best gather evidence and thereby determine the facts? Simply answered: try to “think” like a police detective in your search for “What is the truth?” A police officer first tries to establish the timeline of an act; he/she gathers physical evidence for clues; interviews possible witnesses; compares witnesses’ statements and investigates for garbled or false information that contradicts the physical evidence. He/she might then assemble a list of “persons of interest” who might have a reason for committing the act and then checks their alibis and backgrounds to eliminate them as suspects; finally, he/she establishes the “motive” for the act. This procedure invariably leads to establishing the correct set of facts. We must avoid theories without facts, or twisted facts*
2b. Ockham’s razor deals with the necessity of economizing our assumptions and postulates to arrive at the truth. It handles “Is/Is Not” statements/assumptions, and that which is impossible is weeded out. All theories are based on assumptions/presuppositions/postulates that, as Kurt Gödel proved, can never both be consistent (i.e. rational) and simultaneously complete. If we want rationality, we must give up completeness and accept some assumptions that can never be proven within the system.
As a corollary to this, we rely upon Ockham’s razor here to arrive at the best theory: If competing theories are equal in other respects, then select the theory that introduces the fewest assumptions and the fewest entities while still sufficiently answering the question at hand i.e. the simplest explanation is the one closest to the truth. To arrive at this scientists utilize a hierarchical constraint satisfaction procedure which can best be exemplified by a simple quote from Sir Arthur Conan Doyle’s fictional Sherlock Holmes whose pithy summation on theory selection states: When you have eliminated the impossible, (i.e. any theory that doesn’t account for all of the facts) whatever remains, however improbable, must be the truth.
Rules 2a and b work hand in hand. An assumption that we had hitherto believed may be disproven by the evidence in which case we must modify it or start anew. A theory forms relatively easily once the facts are established; we can then deduce new facts, which must continue to support the theory or we have to modify it, or throw it out and start all over again.Deduction and induction work together like a Swiss army knife: each one can be used alone or in combination to slice through falsehood in order to arrive at the truth!
* See the list of inductive fallacies below for more pitfalls to avoid whilst using inductive logic.
Some Informal Fallacies to Avoid and their Latin terminologies!
A fallacy is, very generally, an error in reasoning. Formal fallacies are arguments that are fallacious due to an error in their form or technical structure. Following Rules 1-5 above should prevent any formal fallacies. However, Informal fallacies are directly related to an argument's content rather than its form. Below are some of the more common ones to avoid in all thinking.
1. Inductive Fallacies aka Fallacies of Relevance are based on the failure of a conclusion to be more or less probably acceptable relative to its premises. For example, Special Pleading occurs when a proponent of a position attempts to cite something as an exemption to a generally accepted rule or principle without justifying the exemption; or when someone instead of presenting all the evidence or information one has about some view, one presents only a special part of it. A form of this includes the "double standard." Evidence that supports a theory when gathered from an appropriate source as well as evidence that contradicts a theory must be accepted regardless. Never use a criterion to accept a fact because it agrees with a presupposed theory and then reject another fact gathered using the same criterion because it does not support the pre-held theory. The theory gets thrown out never the facts!
The Fallacy of Hasty Generalizations aka Leaping to a Conclusion aka Cherry Picking results when generalizations are not made using correct statistical analysis on a data set or by using a "hunch" or guess that it looks right. The act of pointing at individual cases or data that seem to confirm a particular position, while ignoring a significant portion of related cases or data that may contradict that position all fall within the scope of this fallacy.
A fallacy of False Cause aka Post hoc, ergo prompter hoc or Cum hoc ergo prompter hoc is defined as coincidental correlation or when some event is erroneously considered the cause of another event.
The Gambler's Fallacy occurs when someone argues that because a chance event has had a certain run in the past, the probability of its occurrence in the future is significantly altered.
Similarly, the Fallacy of Conjunction occurs when it is assumed that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them.
A fallacy of Faulty Analogy is committed if 1) the conclusion of an analogical argument is considered certain, or 2) the analogous things have more differences than similarities.
Finally, we come to the fallacy of Assuming Facts Not in Evidence aka Hearsay which occurs when someone's fanciful evidentially unsupported theory gets picked up by someone else as if it were "proven fact" and then gets mindlessly repeated to the detriment of truth.
2. Begging the Question, aka Circular Reasoning aka Asking Leading questions aka Petitio Principii is a fallacy in which the premises include the claim that the conclusion is true or (directly or indirectly) assume that the conclusion is true; or where the conclusion of an argument is implicitly or explicitly assumed in one of the premises. A form of this includes the Fallacy of Alleged Certainty whereby a claim in question or doubt is qualified by a phrase which has the effect of persuading (without proving) that the claim is beyond all doubt.
Also, the fallacy of Question-begging definitions is committed when some essential word(s) of a presumably factual but questionable assertion is defined in such a way that the assertion must be certain, but cannot be factual. Rather than admit of a counter instance to the assertion the definition of the word(s) keeps changing. Facts cannot shake the generalization because its truth is guaranteed by the arbitrary definition.
Similarly, the fallacy of Moving the Goalposts occurs when evidence presented in response to a specific claim is dismissed and some other (often greater) evidence is demanded; this leaves the impression that an argument had a fair hearing while actually reaching a preordained conclusion.
3. The Appeal to Pseudo-authority Fallacy aka Argumentum ad populum ("appeal to belief," "appeal to the majority", "appeal to the people" "appeal to authority") aka The Democratic Fallacy aka Fallacy of Large Numbers where a proposition is claimed to be true solely because many people believe it to be true. The Appeal to Tradition is an example of an appeal to pseudo-authority whereby a claim is argued must be true because it has been traditionally supported through the ages.
The fallacy of Misrepresenting Authority is committed if the claims of some reputable authority are substantially changed, completely fabricated, or when an advocate appeals to an irrelevant, unqualified, unidentified, biased, fabricated source in support of an argument, that often misquotes materially or takes out of context something to make an erroneous argument.
The Appeal to the Authority of Self-Interest aka argumentum ad crumenam is committed when a certain claim must be true because it is beneficial to some particular person--you! Or when we are willing to adopt any tactic, however irrational, for the sole purpose of bringing about our desired ends.
4. An Irrelevent Appeal Fallacy aka Red Herring aka Ad Hominem Attack (attacking the person instead of the argument) aka Ignoratio elenchi occurs when an argument is given in response to another argument, which does not address the original issue, moreover it is irrelevant to the original issue at hand. For example, Rationalization occurs when a more or less acceptable reason for an action is substituted for the real reason.
The Straw Man Fallacy occurs when one simply ignores a person's actual position and substitutes a distorted, exaggerated, misrepresented version, or a weak view of that position and then proceeds to tear down the "straw man."
The fallacy of Wishful Thinking is committed when it is claimed that something is the case because it ought to be the case.
An argument from silence aka argumentum ex silentio aka argument from ignorance aka argumentum ad ignorantiam ("appeal to ignorance") occurs whereby a conclusion based on silence or lack of contrary evidence is asserted. This type of "reasoning" runs along the lines that the absence of evidence proves evidence of absence. Almost always it does not.
A further example includes the Ad Hominem Tu quoque fallacy where it is stated that a certain position is false or wrong and/or should be disregarded because its proponent fails to act consistently in accordance with that position over time i.e no one can ever change their minds.
5. A Fallacy of Confusion occurs when an argument or view is presented in such a confused or ambiguous fashion that no one knows exactly what it means, or might be used to prove two or more different things. An example includes the Equivocation Fallacy aka equivocatio or homonymia or the misleading use of a term with more than one meaning (by glossing over which meaning is intended at a particular time).
More fallacies of this kind include: the fallacy of Contradictory Assumptions which is committed when the premises used in an argument are contradictory and thus lead to an unsound argument.
The fallacy of Trivial Objections occurs when someone supposes or asserts that any objection to a view or argument is sufficient to overthrow it.
An Appeal to Emotion occurs when an argument is made due to the manipulation of emotions, rather than the use of valid reasoning; the view is made more persuasive by the use of emotional language and thereby confuses the issue without increasing the supporting evidence.
6. A Fallacy of Faulty Classification is committed when one errs in classifying something in an argument. Examples include: The Fallacy of the Continuum i.e. when it is argued that because there is a continuous distribution of differences between two extremes, there is no "real" difference and/or no stopping point in between.
The Quantification of Quality fallacy occurs when we indulge in a false sense of precision resulting when we suppose we know a quality better, as a quality, because it has been quantified. Many things do not submit themsleves to quantitative assessment. Even those that do are not simply the sum of their parts. How do the parts work together and constitute a whole that is greater than the sum of their numerical parts?
The Fallacy of the Golden Mean occurs when given two extremes (or a range of values) or conflicting views, it is wise to select a position midway between them. The mean or middle view must be true because it is the mean or middle view.
A Faulty Dilemma involves erroneously assuming or arguing that one of two views or positions must be true rather than recognizing that another third position is possible.
The Fallacy of Composition aka Reductionism is committed when it is argued that a property which is affirmed or denied of every part of some whole must be affirmed or denied of the entire whole.
The fallacy of Oversimplification results when we reduce some complex series of traits to a single factor grossly distorting it.
These are just some of the fallacies that have occurred throughout the history of thinking as humans have invented new ways for bad arguments!