Critical Thinking

Exit Standard 1. Discuss what constitutes a good argument, how arguments work and what makes some arguments better than others. (minimum 600 words)

Copi and Cohen define an argument in Logic as, “…any group of propositions of which one is claimed to follow the others, which are regarded as providing support or grounds for that one.” (Copi, 7)

An argument is any group of propositions of which one is claimed to follow from the others, which others are then regarding as providing support or grounds for the truth of the one. These propositions can all be in one sentence, or be a series of sentences. The proposition that is being ‘proved’ is called the conclusion, and the propositions that support and prove the conclusion are called premises. However there remains a question as to the validity or invalidity of arguments and this is determined by the premises. If an argument is correct both in form and with true premises, then we can say that the argument is both valid and sound.

An argument may be valid, based on its correct use of the rules of form, and yet we may have to reject the argument because one or more of its premises may be false. An argument, correct in form but with false premises is called an unsound argument. “An argument form is valid if and only it has no substitution instances with true premises and a false conclusion. And since validity is a formal notion, an argument is valid if and only if the specific form of that argument is a valid argument form.” (Copi, 336)

A good argument then is one that meets all of the logical criteria being both valid and sound. If a proposition is affirmed by other propositions and the resulting conclusion is therefore valid then the argument is better than one that can be found fallacious by either 13 fallacies of relevance, or the fallacies of ambiguity (both enumerated below.)

The simplest kind of argument consists of one premise and a conclusion that is claimed to follow from it. An example of this would be:

“Man cannot see past the horizon therefore the earth is flat.”

 Most arguments are a little more complicated than the example presented above. In fact, there are arguments that contain compound propositions with their several components related intricately. The fact remains that every argument, whether it is simple or compound, consists of a conclusion and a premise or premises offered to support it.

Another crucial area of arguments is fallacies. A fallacy is a type of argument that may seem to be correct, but in actuality contains a mistake in the reasoning thus making it not to be so. In relation to logic Copi and Cohen state, “…it designates not any errors in reasoning, but typical errors – mistakes in reasoning whose common patter can be detected.” (Copi, 125) There are two types of fallacy, informal and formal. Informal fallacies usually involve valid arguments that nonetheless have unacceptable premises, making them unsound. A formal fallacy is usually a result of an invalid argument.

There considered to be thirteen (13) fallacies of relevance that have bearing on whether an argument is considered  sound or unsound. These fallacies are:

*        Genetic Appeal

*        The Appeal to Emotion Argumentum ad Populum)

*       Appeal to Tradition (Argumentum ad Traditio)

*        The Appeal to Pity

*       The Appeal to Force (Argumentum ad Baculum)

*        Personal Attack (Argumentum ad Hominem)

*        Appeal to Improper Authority (Argumentum ad Verecundium)

*        Argument from Personal Incredulity

*       Argument from Adverse Consequences

*        Abusive Appeal

*        Circumstantial Appeal

There are also fallacies of ambiguity that influence an argument. These are:

*        Equivocation: Using a word in a different way than the author used it in the original premise, or changing definitions halfway through a discussion.

*        Amphiboly: A statement may be true according to one interpretation of how each word functions in a sentence and false according to another.

*        Composition: This fallacy is a result of reasoning from the properties of the parts of the whole to the properties of the whole itself–it is an inductive error.

*        Division: This fallacy is the misapplication of deductive reasoning wherein one fallacy of division argues falsely that what is true of the whole must be true of individual parts.

*        Fallacy of Reification (Also called “Fallacy of Misplaced Concreteness” by Alfred North Whitehead): The fallacy of treating a word or an idea as equivalent to the actual thing represented by that word or idea, or the fallacy of treating an abstraction or process as equivalent to a concrete object or thing.


Exit Standard 2. What is the difference between inference and deduction? (minimum 100 words)

All arguments begin with the assertion that its premises provide grounds for the truth of its conclusion. (Copi, 12) However there are two distinct manners in which the conclusion may be supported by the premises, namely induction (inductive) or deduction (deductive) reasoning.

Deduction arguments maintain that their conclusion is necessarily true if all of the premises are true and it is a valid argument. The argument fails (is invalid) though if the premises do not provide the logical necessity that is claimed. “Since every deductive argument either does what it claims or does not, every deductive argument is rendered either valid or invalid.” (Copi, 13) Deductive theory also aims to explain the relations of premises and conclusions in valid arguments. An example of this would be:

Rain falls to the ground.

The ground soaks up the rain.

Plants grow better when they have rain or water.

Therefore, rain or water is necessary for plants to grow.

With an induction argument on the other hand, logical necessity is not necessary and is not claimed either. There are a great many arguments that have conclusions which cannot be established with certainty, even when their premises are known to be true. Unlike the deductive argument though, an inductive argument only claims that the premises support the conclusion with probability, thus the terms validity and invalidity do not apply to induction because there is only probability, not certainty, in the conclusion being true based on the premises. (Copi 13) An example of this would be:

Most members of the NRA are conservatives.

Most conservatives are Republican.

Therefore it is probable that most NRA members are Republicans.


Exit Standard 3. What is a fallacy? (minimum 100 words)

A “fallacy” is a mistake, and a “logical” fallacy is a mistake in reasoning. In logic a fallacy is a type of argument that may seem to be correct, but in actuality contains a mistake in the reasoning thus making it not to be so. In relation to logic Copi and Cohen state, “…it designates not any errors in reasoning, but typical errors – mistakes in reasoning whose common pattern can be detected.” (Copi, 125)  There are two types of fallacy, informal and formal. Informal fallacies usually involve valid arguments that nonetheless have unacceptable premises, making them unsound. A formal fallacy is usually a result of an invalid argument. The fallacies of relevance and ambiguity are numerated above in Exit Standard 1.

However, not just any type of mistake in reasoning counts as a logical fallacy. To be a fallacy, a type of reasoning must be potentially deceptive, it must be likely to fool at least some of the people some of the time. Moreover, in order for a fallacy to be worth identifying and naming, it must be a common type of logical error.

Exit Standard 4. What is the difference between an inference and a premise? (minimum 100 words)

Inference is the act or process of deriving a conclusion based on what one already knows or on what one assumes. The statement(s) given as evidence for or that supposedly lead to the conclusion are known as premise(s). Deductive inferences are either valid or invalid, but not both. Philosophical logic has attempted to define the rules of proper inference, i.e., the formal rules that, when correctly applied to true premises, lead to true conclusions. Strict validity and soundness are applicable to (or properties of) only deductive inferences, because deductive inferences are the only kind that can guarantee that if the premises are true, then the conclusion must be true. (West, Vol 5, 217)

In all other nondeductive forms of inference — induction, abduction, etc. — it is always possible, even in the best or strongest of such nondeductive inferences, for the premises all to be true but the conclusion nevertheless be false. So, strictly speaking, all nondeductive inferences are invalid.

A premise is a statement or proposition that an argument claims will provide support for some other proposition and which will induce or justify a conclusion. In an argument there may be simple, compound, conditional or disjunctive premises but in their own manner each will still fortify the conclusion that is expected. (Copi, 7)

Exit Standard 5. Discuss the effect of bias on thought and moral reasoning. (minimum 100 words)

Bias is a preconceived idea or belief that specific conclusions are correct and from that stance premises are created utilizing the bias to prove the conclusion. (West, Vol 1, 173) This type of reasoning can be full of fallacy because the conclusion itself invariably fallacious. History is replete with instances of bias influencing moral reasoning and thought. One of the prime examples is that of Hitler and the Nazi party using their bias to influence citizen outrage against Jews, gypsies, homosexuals, blacks and a plethora of other phobias. They produced sound arguments based on their bias that when analyzed in retrospect showed obvious fallacy in thought and reasoning. All the ills and problems of post World War 1 Germany were blamed on the financial power of the Jews. The Nazi belief in a pure Aryan race (Nordic basically) excluded any mixing of black, Jew, or gypsy blood within 10 generations according to the research performed by the SS when executing background checks on potential Schutzstaffel (SS) candidates. The SS was to be a racial elite chosen on the basis of “pure” Nordic qualities. (Hale, 74–87) Jews and gypsies who were both eventually deemed to be “Lebensunwertes Leben (“Life unworthy of life”) were executed to rid the Reich of impure blood. (Cook, 157) By thus emphasizing through bias the “sub-human” species as being the progenitors of their ills, Hitler was able to sway much of Germany into following blindly along the Nationalsozialismus (Nazi) ideological path.

This is true of the majority of politicians, albeit not to the same extent gratefully. The effect is of such potential for influence that it is one of the prime instruments of propagandists and advertising companies. Bias is a potent weapon that can affect people from childhood memories through adult prejudices that are inherited or learned from exposure to bias.

Religion is an area in which bias can be extremely replete with bias affecting thought and moral reasoning. The whole argument of abortion seems based on an individual’s religious thoughts and biases preached from the pulpit. It might even be said that like the speeches of Hitler some religious leaders inspire or convince their ‘flock’ to follow their line of reasoning and belief.

It would behoove every individual to evaluate statements that are propounded for such evident biases of the speaker which would render their conclusion as fallacious instantly. This sounds like a relatively easy task but in actuality the followers of hate monger already have a bias in the direction to which they are being led and thus accept at face value any premise that supports that belief.

Exit Standard 6. Take an Indo-European topic essay of a minimum of five pages in length and analyze it for soundness, validity, fallacies, rhetorical devices and overall quality of composition. (Contact the ADF Preceptor for examples and suggestions of papers to critique.) (minimum 600 words)

Ian Corrigan’s essay Exploring Celtia: The Primary Division, tackles the topic with a definite emphasis that convinces the reader who already has tendencies to accept the conclusions drawn. It is explained at the very first, “…that many of the conclusions reached here are very speculative.” (Corrigan, 1) and the article delivers on that statement evidentially throughout. The downside to the article and the speculation that must take place due to the lack of written record and the surmising from the number of extrapolations that takes place from lore is that many of the premises could be labeled as fallacious or unsound. This is the biggest stumbling block with any serious work regarding the Celtic area. How much of the lore has been changed over time to suit the various entities that have occupied the area. Many scholars, including Corrigan in his seventh paragraph on page 5, relate the problems that have been encountered with Greek, Roman, Viking and Christian influence. With this in mind the reader must have a willing suspension of critical demands in order to accept the conclusions that are drawn in the article.

Corrigan lays each paragraph out with a premise or premises and then attempts to provide a satisfactory conclusion at the end of the same paragraph. One of the best examples of this can be found in the first paragraph on the final page in a brief three sentence paragraph there are two premises and one conclusion. The fact that the reader may not agree with the premises or conclusions would indicate that their own biases are playing a major influence because Corrigan does follow logical thought and procedure in arriving at the conclusion that he draws. It must also be remembered that at the very beginning the reader is advised that, “We must go past scholastic certainty into inspirations and intuition to synthesize these various sources into patterns that can be put to work by modern Pagans.” (Corrigan, 1)

There are some examples of rhetorical devices employed by the author such as:

hyperbation, “Still, taken together this amounts to a considerable body of information.”

distinctio, “This is reflected in stories of war between to tribes of divine beings: the gods and the Giants.”

synathroesmus,the Underworld holds the Waters of Memory, of Bounty, and of Rebirth, the Chaos of Potential,”  

sentential adverbs for example in section 3 where he uses “clearly” in the fourth paragraph.

These rhetorical devices are used quite judiciously throughout and the overall wording employed manages to avoid too repetitive amounts. The employment of short, to the point sentences, also circumvents the tendency utilized by many authors to camouflage their real intent. Corrigan’s succinct paragraphs enable the reader to grasp the line of reasoning, ponder upon it and then proceed to the next. This is relevant because the essay is a scholarly explanatory work that requires thought and acceptance (or rejection) of the propounded proposals.

Given the advanced warning by the author at the very beginning regarding the suspension of critical scholarly examination, “…for those of us attempting to build a workable modern Celtic Paganism, we must take risks that a scholar would not take.” the essay is laid out very much as one would expect from a scholarly paper. Anyone vaguely familiar with the problems inherent in Celtic research should be aware that some latitude must be extended and that extrapolations such as those used by Corrigan throughout his essay are expected.

While there are inherent problems associated with theorizing the author of this piece manages to provide plentiful examples of what lead to his deductions. While there may be some question as to the validity of the arguments from a critical review of the premises, evidence and conclusions the essay conveys a great deal of substantiation for the audience for which it was intended. This is not a work that a casual reader would pick up and read and find any degree of enlightenment but rather a student of the Druidic art would read for edification and a furthering of personal beliefs.

Explanations such as the section The War Between the Gods and the Giants provide evidence of the author’s depth of thought, knowledge and reasoning. Elucidation for the practitioner is offered with clear evidential reasoning and example. Specific tales from Celtic lore are mentioned as evidential basis for the drawn conclusions and the reader can expand upon what is written in the essay by referring to these tales. The fact that outside influences may be reflected in the actual tales is also brought to the memory of the reader by the author. Again, the author makes it very clear that his opinions are indicated as promised, and that speculation is a major factor, but the final analysis is left to the reader who though may look at the work analytically, must at some point be willing to accept the conclusions offered because they do fall in line with those of others scholars.




Cook, Stephen and Stuart Russell. Heinrich Himmler’s Camelot. Andrews, NC Kressman-Backmayer. 1999 Print

Copi, Irving R and Carl Cohen. Introduction to Logic. Upper Saddle River: Pearson, 2005. Print.

Corrigan, Ian. Exploring Celtia: The Primary Division. ADF. Web. Jan. 18. 2012

Hale, Christopher. Himmler’s Crusade. Manhattan, NY. Bantam Press. 2003 Print

West’s Encyclopedia of American Law, Vol. 2 & 5. Farmington Hills, Michigan: Thomson Gale. 1998, Print



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