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Philosophy 103: Introduction to Logic 
Petitio Principii

Abstract: Petitio principii (circular) argument is described and several examples are noted.

 

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I.  Petitio Principii: (circular reasoning, circular argument, begging the question) in general, the fallacy of assuming as a premiss a statement which has the same meaning as the conclusion.

  1. The least convincing kind of petitio principii is the repetition of the same words in the same order in both premiss and conclusion..  Generally, such an argument would not be misleading and would only be given in unusual circumstances, e.g., the speaker is very tired, talking to a child, or talking to a subordinate.  Two examples follow.


    1. "Dear Friend, a man who has studied law to its highest degree is a brilliant lawyer, for a brilliant lawyer has studied law to its highest degree."  Oscar Wilde, De Profundis.


    2. --"What a brain!  And you know how to prove things, like the big shots?
      --Yeah, I have a special method for that.  Ask me to prove something for you, something real hard.
      --All right, prove to me that giraffes go up in elevators.
      --Let's see.  Giraffes go up in elevators  ... because they go up in elevators.
      --Good, that was great! ... Suppose I asked you to prove giraffes don't go up in elevators.  
      --That's easy.  I just prove the same thing, but the other way around." Fernando Arrabal,  El Cementerio de Automoviles, el Arquitecto y El

  2. A more common kind of petitio principii is the transformation of the conclusion into a premiss using logical or grammatical principles. For example ...


    1. "You know that God is a just and loving God because God is God and cannot be unjust or unloving."
    2. "Women write the best novels because men do not write novels as well."
    3. "There are many juvenile delinquents because many juveniles break the law, and the reason so many juveniles break the law is that they are juvenile delinquents."


  3. A third kind of petitio prinicpii is the use of an intermediate step in shifting to the same meaning from the premiss to the conclusion. A linking of premisses and conclusions return to the beginning. For example ...


    1. "The soul is simple because it is immortal, and it must be immortal because it's simple."


    2. "I once overheard three brothers dividing two candy bars. The oldest one gave each of the two younger ones half of a candy bar, and kept a whole bar for himelf. When asked why he got more candy, he said he was the smartest. A few minutes later, one of the younger ones asked why he was the smartest, and in reply the oldest said \'Because I have more candy.'" Ernest J. Chave, Personality Development in Children (Univ. of Chicago, 1937), 151.


  4. The most difficult kind of petitio principii to identify is the kind where the premiss and the conclusion have the same "propositional content." I.e., the statements are suitable paraphrases of each other, and each depends upon the other for its truth.


    1. "The elemental composition of Jupiter is known to be similar to the sun... The core would be composed mainly of iron and silicates, the materials that make up most of the earth's bulk. Such a core is expected for cosmogonic reasons: If Jupiter's composition is similar to the sun's, the the planet should contain a small portion of those elements." J. Wolfe, "Jupiter," Scientific American (Vol. 230 No. 1), 119.


    2. The following example is a description of a petitio principii committed by Engel:

      "A law has been named after Engel in light of this work. Engel's law states that 'the poorer the individual, the family or a people, the greater must be the percentage of the income needed for the maintenance of physical sustenance, and of this a greater proportion must be allowed for food.' It is odd to find this as a law, since Engel had used the proportion of outgoings on food as the measure of material standard of living." Ian Hacking, The Taming of Chance, (Cambridge Univ. Press, 1990), 140.


    3. A contradiction to my theory of dream produced by another of my women patients (the cleverest of all my dreamers) was resolved more simply, but upon the same pattern: namely that the nonfulfillment of one wish meant the fulfillment of another.  One day I had been explaining to her that dreams are fulfillments of wishes. Next day she brought me a dream in which she was traveling down with her mother-in-law to the place in the country where they were to spend their holidays together.  Now I knew that she had violently rebelled against the idea of spending the summer near her mother-in-law and that a few days earlier she had successfully avoided the propinquity she dreaded by engaging rooms in a far distant resort.  And now her dream had undone the solution she had wished for;  was not this the sharpest contradiction of my theory that in dreams wishes are fulfilled? No doubt;  and it was only necessary to follow the dreams logical consequence in order to arrive at its interpretation.  The dream showed that I was wrong.  Thus it was her wish that I might be wrong, and her dream showed that wish fulfilled (italics original)" Sigmund Freud, The Interpretations of Dreams (New York: Avon, 1966), 185.


II. The informal structure of the petitio principii is usually similar to one of the following.


Statement p is true.
Statement not-p is not true.

or

Statement p is true.
Statement q is true.
Statement r is true.
Statement p is true.


III.  The reason petitio principii is considered to be a fallacy is not that the inference is invalid (because any statement is indeed equivalent to itself), but that the argument can be deceptive.  A statement cannot prove itself.  A premiss must have a different source of reason, ground or evidence for its truth  from that of the conclusion.

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