intellectual vanities… about close to everything

Formal and Informal Logical Fallacies

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(After reading many such, oft aberrant, lists I concocted this one. It is based on the List of common fallacies – compiled by Jim Walker 1997/2004) In general, one useful way to organize fallacies is by category. We have below fallacies of relevance, component fallacies, fallacies of ambiguity, and fallacies of omission. I will discuss each type in turn. The last point to discuss is Occam’s Razor.


You don’t need to take drugs to hallucinate; improper language can fill your world with phantoms and spooks of many kinds.


-Robert A. Wilson



whirlygig_thindouble.jpgCOMPONENT FALLACIES:

Component fallacies are errors in inductive and deductive reasoning or in syllogistic terms that fail to overlap.


  • Argumentum in circulo, also Circulus vitiosus or Petitio principii (circular reasoning): stating in one’s proposition that which one aims to prove. (e.g. God exists because the Bible says so; the Bible exists because God influenced it.) The Argumentum in circulo is in contradiction with the principal rule of logic, that every thesis cannot be proven true but by premises that are proven themselves as true. Also: loaded questions – embodies an assumption that, if answered, indicates an implied agreement. (e.g., Have you stopped beating your wife yet?)


  • dicto simpliciter (Latin: “simply speaking” – Hasty Generalization, also called Jumping to Conclusions, “Converse Accident”): Mistaken use of inductive reasoning when there are too few samples to prove a point. One common type of hasty generalization is the Fallacy of Accident. This error occurs when one applies a general rule to a particular case when accidental circumstances render the general rule inapplicable. For example, in Platos Republic, Plato finds an exception to the general rule that one should return what one has borrowed: Suppose that a friend when in his right mind has deposited arms with me and asks for them when he is not in his right mind. Ought I to give the weapons back to him? No one would say that I ought or that I should be right in doing so.. What is true in general may not be true universally and without qualification. So remember, generalizations are bad. All of them. Every single last one. Except, of course, for those that are not. The same applies to misunderstanding the nature of statistics (e.g., the majority of people in the United States die in hospitals, therefore, stay out of them.), or to the statistics of small numbers: similar to observational selection (e.g., My parents smoked all their lives and they never got cancer. Or: I don’t care what others say about Yugos, my Yugo has never had a problem.) Simply because someone can point to a few favorable numbers says nothing about the overall chances. “Statistics show that of those who contract the habit of eating, very few survive.” — Wallace Irwin


  • non sequitur: Latin for “It does not follow.” An inference or conclusion that does not follow from established premises or evidence. (e.g., there occured an increase of births during the full moon. Conclusion: full moons cause birth rates to rise.) But does a full moon actually cause more births, or did it occur for other reasons, perhaps from expected statistical variations? Similar in Non Causa Pro Causa (Literally, “Not the cause for a cause”): A general, catch-all category for mistaking a false cause of an event for the real cause.: two events serve as elements of an assumed causation, either when they are concomitant (cum hoc ergo propter hoc) or follow eachother (post hoc ergo propter hoc), from Latin for “It happened at the same time / after, so it was caused by.” As a non sequitur, but time dependent. (e.g. She got sick after she visited China, so something in China caused her sickness.) Perhaps her sickness derived from something entirely independent from China. also: confusion of correlation and causation: (e.g., More men play chess than women, therefore, men make better chess players than women. Stephen Jay Gould called the invalid assumption that correlation implies cause as “probably among the two or three most serious and common errors of human reasoning” (The Mismeasure of Man).


  • The Argumentum a fortiori is also a non sequitur. Quantitatively magnifying the premises of reasonably proven argument it concludes about their effects in a new situation. “Studies have shown a concentration of 10 mg/l of this substance are harmful to health. The victim has been exposed to higher concentrations over a longer period and as such his health damage is out of question”


  • Similarly the Argumentum ex concesso refers to a previously accepted statement: “You did concede to have been at the crime scene during the mentioned time. As the crime scene’s structure is such, that noticing the blood stain is inevitable, how do you explain that while approaching it, you did not notice anything?”


  • Ignorantia Elenchi (Irrelevant Conclusion): This fallacy occurs when a rhetorician adapts an argument purporting to establish a particular conclusion and directs it to prove a different conclusion. (e.g. when a particular proposal for housing legislation is under consideration, a legislator may argue that decent housing for all people is desirable. Everyone, presumably, will agree. However, the question at hand concerns a particular measure. The question really isn’t, “Is it good to have decent housing?” The question really is, “Will this particular measure actually provide it or is there a better alternative?”) This type of fallacy is a common one in student papers when students use a shared assumption–such as the fact that decent housing is a desirable thing to have–and then spend the bulk of their essays focused on that fact rather than the real question at issue. It’s similar to begging the question, above.


  • One of the most common forms of Ignorantia Elenchi is the “Red Herring.” A red herring is a deliberate attempt to change the subject or divert the argument from the real question at issue to some side-point; for instance, Senator Jones should not be held accountable for cheating on his income tax. After all, there are other senators who have done far worse things. Another example: I should not pay a fine for reckless driving. There are many other people on the street who are dangerous criminals and rapists, and the police should be chasing them, not harassing a decent tax-paying citizen like me. Certainly, worse criminals do exist, but that it is another issue! The questions at hand are (1) did the speaker drive recklessly and (2) should he pay a fine for it? Another similar example of the red herring is the fallacy known as Tu Quoque (Latin for “And you too!”), which asserts that the advice or argument must be false simply because the person presenting the advice doesn’t follow it herself. “Reverend Jeremias claims that theft is wrong, but how can theft be wrong if Jeremias himself admits he stole objects when he was a child?” Straw Man Argument: A subtype of the red herring, this fallacy includes any lame attempt to “prove” an argument by overstating, exaggerating, or over-simplifying the arguments of the opposing side. Such an approach is building a straw man argument. The name comes from the idea of a boxer or fighter who meticulously fashions a false opponent out of straw, like a scarecrow, and then easily knocks it over in the ring before his admiring audience. His “victory” is a hollow mockery, of course, because the straw-stuffed opponent is incapable of fighting back. When a writer makes a cartoon-like caricature of the opposing argument, ignoring the real or subtle points of contention, and then proceeds to knock down each “fake” point one-by-one, he has created a straw man argument. (e.g., one speaker might be engaged in a debate concerning welfare. The opponent argues, “Tennessee should increase funding to unemployed single mothers during the first year after childbirth because they need sufficient money to provide medical care for their newborn children.” The second speaker retorts, “My opponent believes that some parasites who don’t work should get a free ride from the tax money of hard-working honest citizens. I’ll show you why he’s wrong . . .”) In this example, the second speaker is engaging in a straw man strategy, distorting the opposition’s statement about medical care for newborn children into an oversimplified form so he can more easily appear to “win.” However, the second speaker is only defeating a dummy-argument rather than honestly engaging in the real nuances of the debate.


  • Argumentum ad temperantiam (argument of the golden middle) positions itself between two extremes ignoring eventual evidence for the two of them. “As the trade unions demand 10% increase of income and employers do offer 2%, we should agree upon 6%”. Although extreme positions are often less reasonable than a compromise, the argumentum ad temperantiam is no evidence of truth. As in opposition, the Tertium non datur (excluded middle or false dichotomy) is considering only the extremes. Many people use Aristotelian either/or logic tending to describe in terms of up/down, black/white, true/false, love/hate, etc. (e.g., You either like it or you don’t. He either stands guilty or not guilty.) Many times, a continuum occurs between the extremes that people fail to see. The universe also contains many “maybes.” Undistributed Middle Term: A specific type of error in deductive reasoning in which the minor premise and the major premise of a syllogism might or might not overlap. Consider these two examples: (1) All reptiles are cold-blooded. All snakes are reptiles. All snakes are cold-blooded. In the first example, the middle term snakes fits in the categories of both reptile and things-that-are-cold-blooded. It is what logicians call a distributed middle term. (2) All snails are cold-blooded. All snakes are cold-blooded. All snails are snakes. In the second example, the middle term of snakes does not fit into the categories of both things-that-are-cold-blooded and snails. It is an undistributed middle term. Sometimes, equivocation (see below) leads to an undistributed middle term.



These errors occur with ambiguous words or phrases, the meanings of which shift and change in the course of discussion. Such more or less subtle changes can render arguments fallacious.


  • Argumentum ambiguum, (ambiguous argument): leaves the exact meaning undetermined and allows for a retreat on a different meaning. Bill Clinton about Monica Lewinsky: “I did not have sexual relations with that woman” (Correct appealing to the connotation of sexual intercourse, less correct appealing to everyday language or juridic understanding of “sexual relation”.)


  • Amphiboly (from the Greek word “indeterminate”): This fallacy is similar to the equivocation above. Here, the ambiguity results from grammatical construction. A statement may be true according to one interpretation of how each word functions in a sentence and false according to another. When a premise works with an interpretation that is true, but the conclusion uses the secondary “false” interpretation, we have the fallacy of amphiboly on our hands. In the command, “Save soap and waste paper,” the amphibolous use of “waste” results in the problem of determining whether “waste” functions as a verb or as an adjective.


  • 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. Such an argument might hold that, because every individual part of a large tractor is lightweight, the entire machine also must be lightweight. This fallacy is similar to Hasty Generalization (see there), but it focuses on parts of a single whole rather than using too few examples to create a categorical generalization. Also compare it with Division (see below).


  • Division: This fallacy is the reverse of composition. It is the misapplication of deductive reasoning. One fallacy of division argues falsely that what is true of the whole must be true of individual parts. Such an argument notes that, “Microtech is a company with great influence in the California legislature. Egbert Smith works at Microtech. He must have great influence in the California legislature.” This is not necessarily true. Egbert might work as a graveyard shift security guard or as the copy-machine repairman at Microtech–positions requiring little interaction with the California legislature. Another fallacy of division attributes the properties of the whole to the individual member of the whole: “Sunsurf is a company that sells environmentally safe products. Susan Jones is a worker at Sunsurf. She must be an environmentally minded individual.” (Perhaps she is motivated by money alone?)



These errors occur because the logician leaves out necessary material in an argument or misdirects others from missing information.


  • Argumentum ad ignorantiam (appeal to a lack of evidence) appeals to ignorance as a proof of something. Ignorance about something says nothing about its existence or non-existence. Neither is an assumption true because it has not been falsified or vice versa. “Nobody did prove that there was no god, hence there has to exist one.”Nobody did ever eye an UFO, hence UFOs don’t exist.” Also, although one may prove non-existence in special limitations, such as showing that a box does not contain certain items, one cannot prove universal or absolute non-existence, or non-existence out of ignorance. One cannot prove something that does not exist. The proof of existence must come from those who make the claims. Or, as Argumentum e silentio, silencing certain informations is used to convince: “After proving wrong several of mr. X’s arguments, it is all obvious how sound his theory is.”


  • Confirmation bias (similar to observational selection): This refers to a form of selective thinking that focuses on evidence that supports what believers already believe while ignoring evidence that refutes their beliefs. Confirmation bias plays a stronger role when people base their beliefs upon faith, tradition and prejudice. For example, if someone believes in the power of prayer, the believer will notice the few “answered” prayers while ignoring the majority of unanswered prayers (which would indicate that prayer has no more value than random chance at worst or a placebo effect, when applied to health effects, at best). Also: half truths (suppressed evidence): A statement usually intended to deceive that omits some of the facts necessary for an accurate description. Similarly observational selection points out favorable circumstances while ignoring the unfavourable. Anyone who goes to Las Vegas gambling casinos will see people winning at the tables and slots. The casino managers make sure to install bells and whistles to announce the victors, while the losers never get mentioned. This may lead one to conclude that the chances of winning appear good while in actually just the reverse holds true. These fallacies are closely related to hasty generalization, but the term usually implies deliberate deception rather than an accidental logical error. Contrast it with the straw man argument.


  • Argumentum Ad Speculum (hypothesis contrary to fact): Trying to prove something in the real world by using imaginary examples alone, or asserting that, if hypothetically X had occurred, Y would have been the result. For instance, suppose an individual asserts that if Einstein had been aborted in utero, the world would never have learned about relativity, or that if Monet had been trained as a butcher rather than going to college, the impressionistic movement would have never influenced modern art. Such hypotheses are misleading lines of argument because it is often possible that some other individual would have solved the relativistic equations or introduced an impressionistic art style. The speculation might make an interesting thought-experiment, but it is simply useless when it comes to actually proving anything about the real world. A common example is the idea that one “owes” her success to another individual who taught her. For instance, “You owe me part of your increased salary. If I hadn’t taught you how to recognize logical fallacies, you would be flipping hamburgers at McDonald’s for minimum wages right now instead of taking in hundreds of thousands of dollars as a lawyer.” Perhaps. But perhaps the audience would have learned about logical fallacies elsewhere, so the hypothetical situation described is meaningless. Also in reification fallacy: when people treat an abstract belief or hypothetical construct as if it represented a concrete event or physical entity. Examples: IQ tests as an actual measure of intelligence; the concept of race (even though genetic attributes exist), from the chosen combination of attributes or the labeling of a group of people, come from abstract social constructs; Astrology; god(s); Jesus; Santa Claus, etc.reification fallacy: when people treat an abstract belief or hypothetical construct as if it represented a concrete event or physical entity. Examples: IQ tests as an actual measure of intelligence; the concept of race (even though genetic attributes exist), from the chosen combination of attributes or the labeling of a group of people, come from abstract social constructs; Astrology; god(s); Jesus; Santa Claus, etc.


  • Contradictory Premises (also known as a logical paradox): Establishing a premise in such a way that it contradicts another, earlier premise. For instance, “If God can do anything, he can make a stone so heavy that he can’t lift it.” The first premise establishes a deity that has the irresistible capacity to move other objects. The second premise establishes an immovable object impervious to any movement. If the first object capable of moving anything exists, by definition, the immovable object cannot exist, and vice-versa.



These fallacies appeal to evidence or examples that are not relevant to the argument at hand.


  • Argumentum ad nauseam (repetition) describes the erroneous belief that repetition can make a statement true. – “It was not me!” – “You have been seen at the crime scene at the time.” – “”It was not me!” – “You did hold a weapon in your hand.” – “It was not me!” – “You did threaten the victim the evening before.” – “”It was not me!” etc. It might drive the opponent mad and make him want to give up. But actually the argument is a way out of rational discussion, just insisting. The same way a proponent might repeat an argument that has been proven wrong before, once he believes that the auditory did not keep that fact in mind.

  • Argumentum ad personam: Latin for “to the person.” Note: this argumentation appeals to the auditory in order to drive one’s point home. Where logical fallacies make use, if erroneously, of rational argumentative means, an arguer who uses ad hominem attacks the person instead of the argument. Whenever an arguer cannot defend his position with evidence, facts or reason, he or she may resort to attacking an opponent either through: Labeling, straw man arguments, name calling, offensive remarks and anger are, as such, no “ad homimem”. The Argumentum ad personam usually denies the opponent’s ability to argument or his factual knowledge. Killerphrases are statements nearly void of any content, used to manipulate the auditory by solidarising it about the contempt for the opponent. “That is, what we love here. Fresh from school and now turning the whole department over. What does he think, he is?”


  • Das Argumentum ad judicium appeals to common sense in general to manipulate the one of the auditory. “The theory of relativity cannot be true, as common sense can tell. If a timel lag would depend on relative velosity exclusively, then two twins – one on a space craft and one on earth – would have the same age all the time. Finally, everyone of the them could claim the other would be moving away.” (twin paradoxon) Similarly, Argumentum ad oculos tries convincing by emphasizing a critical contradiction towards the obvious, whereas there are to events corelated that in fact are not. Or, the Argumentum ad lapidem (lapis = stone) uses a seemingly simple contradiction with practical experience to falsify a sophistcated and complex thesis. Named as such by Dr. Samuel Johnson, who tried proving wrong bishop George Berkeley’s assumption, that matter connot exist independently of perception, by kicking a stone exclaiming “I refute it thus”. Paying attention to the stone or not, while kicking it, it is yet perveived sensorically, regardless of how practical or impractical a theoretical assumption is.


  • Argumentum ad baculum (Appeal to Force or the “Might-Makes-Right” Fallacy): This argument uses force, the threat of force, or some other unpleasant backlash to make the audience accept a conclusion. It commonly appears as a last resort when evidence or rational arguments fail to convince. It’s forms are various: violence, blackmail, denigration of the opposition etc.


  • Argumentum ad populum refers to real or alleged general opinion as a warrant for a claim, concluding from the number of an idea’s adherent individuals about the veridity of this idea. “During the middle age close to one hundred percent of all people believed in the sun orbiting the earth. That cannot not have been entirely wrong.” Also: the bandwagon fallacy: concluding that an idea has merit simply because many people believe it or practice it.


  • Argumentum ad verecundiam (argument from authority): using the words of an “expert” or authority as the bases of the argument instead of using the logic or evidence that supports an argument. “Professor so-and-so believes in creation-science.“ Simply because an authority makes a claim does not necessarily mean he got it right. If an arguer presents the testimony from an expert, look to see if it accompanies reason and sources of evidence behind it.


  • Argumentum ad misericordiam uses compassion to avoid deeper probing: “Nobody did lift your wallet. You just lost it. Why would you suspicion a poor and abused individual?”


  • Also: the Argumentum e consentu / consensu gentium (moral argument, or ethical argument): refers even more attenuating to generally acknowledged ethical or social values and tries subsuming to, or excluding an allegation from them: “We should not allow for same sex marriage as the marriage is sacred.” also: argument from omniscience: e.g., “All people believe in something. Everyone knows that.” An arguer would need omniscience to know about everyone’s beliefs or disbeliefs or about their knowledge. Beware of words like “all,” “everyone,” “everything,” “absolute.”)


  • Similarly, the Argumentum ad antiquitatem is appealing to the age or traditional acceptance of a thesis: “Siderial astrology must be true. Else, it would scarcely have survived several milleniums.”


  • Ideological Argument: particular interests are veiled by referene to some extremely general values (e.g. nature, social needs, general order or tradition). Practically it is not even a fallacy, as it often takes the form of a simple statement instead of an argument: “It is just natural to want everything remaing the same.”


  • Argumentum ad crumenam tries to prove ideas by means of wealth and success. “Who cures, is right”, or: “We all have the same chance. Mr. X did get rich too.” Used often to deceive victims of fraud about an idea’s capacity to yieald material success.


  • As in opposition to the “ad crumenam” the Argumentum ad lazarum holds that poverty and simplicity could yield proof for the argumented idea. “My spiritual mentor lives of nothing but bread and water for over 20 years now. Only he who saw the light of truth could do that.” The self-denial necessary for ascetisism does not proof anything but itself.


  • Argumentum a tuto, famous, at least since Immanuel Kant’s so-called maxim of certainty in matters of faith (argumentum a tuto): “If that which I profess regarding God is true, I have hit the mark; if it is untrue, and in addition not something in itself forbidden, I have merely believed it superfluously and have burdened myself with what was indeed not necessary but was after all only an inconvenience, not a transgression.” (v. Die Religion innerhalb der Grenzen der bloßen Ver­nunft, 2. Aufl. 1794, S 292f.) In other words: “it may not be true, but at least it won’t do any harm”. This pseudo-argument might bare comfort and hope in hopeless situations, nonetheless, it does not prove any truth.


  • Argumentum ad metum: An argument based on an appeal to fear or a threat. “If you don’t believe in God, you’ll burn in hell!“ or: “Only posession of arms will hold crime at bay. Or do you want to watch your own family abused, robbed and raped by a felon one day?” Also: slippery slope: a change in procedure, law, or action, will result in adverse consequences. “If we allow doctor assisted suicide, then eventually the government will control how we die.” It does not necessarily follow that just because we make changes that a slippery slope will occur. The Argumentum ad consequentiam (argument from adverse consequences) does practically the same: ” We should judge the accused as guilty, otherwise others will commit similar crimes.” Just because a repugnant crime or act occurred, does not necessarily mean that a defendant committed the crime or that we should judge him guilty.


  • Argumentum ad invidiam, not far from the former, is appealing to envy, malice or revengefullness. „This chap claims that we need a new data bank. Look now, he is getting much more money than you do, although you do the same work. You really want to take his side?“


  • Not much better: Argumentum ad odium: the argument to hatred: “Foreigners take all our jobs. It is all their fault. How long do you want to tolerate this?“


  • Argumentum ad novitam (innovation argument) appeals to the belief that something new is necessarily better too. “The new XYZ diet helps you reducing weight without starving.” Scientific practice needs the most recent data for finding the truth. Nonetheless it keeps happening that previous hypothesis are falsified and abandoned.


  • Argumentum ad superbium (vanity argument): refutes opposing opinions from a position of pride and superiority. “The university of XYZ claims to have found a means against cancer. That is simply not possible. We did cancer research since decades and all they know would not contain anything new to us.”


  • meaningless question: (e.g., “How high is up?” “Is everything possible?”) “Up” describes a direction, not a measurable entity. If everything proved possible, then the possibility exists for the impossible, a contradiction. Although everything may not prove possible, there may occur an infinite number of possibilities as well as an infinite number of impossibilities. Many meaningless questions include empty words such as “is,” “are,” “were,” “was,” “am,” “be,” or “been.”


  • special pleading: the assertion of new or special matter to offset the opposing party’s allegations. A presentation of an argument that emphasizes only a favourable or single aspect of the question at issue. (e.g. How can God create so much suffering in the world? Answer: You have to understand that God moves in mysterious ways and we have no privilege to this knowledge. Or: Horoscopes work, but you have to understand the theory behind it.)


ockham-pict.jpg Occam’s Razor: A Useful Tool in Logic

“substantia non sunt multiplicanda praeter necessitatem.”


The term “Occam’s Razor” comes from a misspelling of the name William of Ockham. Ockham was a brilliant theologian, philosopher, and logician in the medieval period. One of his rules of thumb has become a standard guideline for thinking through issues logically. Occam’s Razor is the principle that, if two competing theories explain a single phenomenon, and they both generally reach the same conclusion, and they are both equally persuasive and convincing, and they both explain the problem or situation satisfactorily, the logician should always pick the less complex one. The one with the fewer number of moving parts, so to speak, is most likely to be correct. The idea is always to cut out extra unnecessary bits, hence the name “razor.” An example will help illustrate this.


Suppose you come home and discover that your dog has escaped from the kennel and chewed large chunks out of the couch. Two possible theories occur to you. (1) Theory number one is that you forgot to latch the kennel door, and the dog pressed against it and opened it, and then the dog was free to run around the inside of the house. This explanation requires two entities (you and the dog) and two actions (you forgetting to lock the kennel door and the dog pressing against the door). (2) Theory number two is that some unknown person skilled at picking locks managed to disable the front door, then came inside the house, set the dog free from the kennel, then snuck out again covering up any sign of his presence and then relocked the front-door, leaving the dog free inside to run amok in the house. This theory requires three entities (you, the dog, and the lockpicking intruder) and several actions (picking the lock, entering, releasing the dog, hiding evidence, relocking the front door). It also requires us to come up with a plausible motivation for the intruder–a motivation that is absent at this point.


Either theory would be an adequate and plausible explanation. Both explain the same phenomenon (the escaped dog) and both employ the same theory of how, i.e., that the latch was opened somehow, as opposed to some far-fetched theory about canine teleportation or something crazy like that.


Which theory is most likely correct? If you don’t find evidence like strange fingerprints or human footprints or missing possessions to support theory #2, William of Ockham would say that the simpler solution (#1) is most likely to be correct in this case. The first solution only involves two parts–two entities and two actions. On the other hand, the second theory requires at least five parts–you, the dog, a hypothetical unknown intruder, some plausible motivation, and various actions. It is needlessly complex. Occam’s basic rule was “Thou shalt not multiply extra entities unnecessarily,” or to phrase it in modern terms, “Don’t speculate about extra hypothetical components if you can find an explanation that is equally plausible without them.” All things being equal, the simpler theory is more likely to be correct, rather than one that relies upon many hypothetical additions to the evidence already collected. ockham_church.jpg

Written by huehueteotl

March 10, 2007 at 3:42 am

6 Responses

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  2. This page really helped me a lot on my research. I hope that more pages with almost complete explanation will be published on the internet and would help students like me.[:


    January 6, 2009 at 12:55 pm

  3. And the ancient Greek Sophists picked arguments apart with fancy words and twisted the meaning of words. Just because you can name a phrase and fit it to what is said does not make the argument wrong; it may only be wrong because YOU DON’T LIKE IT. I’m sure you are all so proud of yourselves and your fine educations. Meanwhile, what good have you done? What will they say once you have departed this mortal coil? Oh, yeah, I guess they will say that this person could REALLY argue and knew ALL the logical fallacies…yep, that’s a good one.

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    December 2, 2010 at 7:08 am

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