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Help with Thomas Aquinas and Fallacy of Equivocation

  1. Mar 24, 2005 #1


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    I am taking a philosphy class and happened to miss a day of class. I have a test and am trying to learn some material I missed.

    My professor went over a piece of literature written by Thomas Aquinas. I cant think of the exact name of the piece, but I know its around 5 arguments for the existence of God.

    Anyway she talks about the question will deal with subarguments of the 3rd premise. I believe its talked about somewhere in the first or second argument of Aquinas' literature but could be wrong.

    The subarguments deal with Fallacy of Equivocation.

    Can anyone give me some insight on this? As far as the premises go, you may not know of the one I speak of. I think it might deal with something like the creation of objects can not be infite. I could be wrong on that. However, I can probably look in my notes when I get home if that is needed.

    Does anyone have any idea about this? If you need more info I can get a little more if you tell me what you need.

    Thanks all.

  2. jcsd
  3. Mar 24, 2005 #2


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    The work you are speaking of is Summa Theologica. It is a long work and you probably are only studying his five proofs for the existence of God. The first two are cosmological arguments (first mover and first cause), the 3rd and 4th are ontological arguments (necessary existence and most perfect being) and the 5th is a teleological argument. You seem to be asking about the third argument, which states:

    • The third way is based on possibility and necessity. We find that some things can either exist or not exist, for we find them springing up and then disappearing, thus sometimes existing and sometimes not. It is impossible, however, that everything should be such, for what can possibly not exist does not do so at some time. If it is possible for every particular thing not to exist, there must have been a time when nothing at all existed. If this were true, however, then nothing would exist now, for something that does not exist can begin to do so only through something that already exists. If, therefore, there had been a time when nothing existed, then nothing could ever have begun to exist, and thus there would be nothing now, which is clearly false. Therefore all beings cannot be merely possible. There must be one being which is necessary. Any necessary being, however, either has or does not have something else as the cause of its necessity. If the former, then there cannot be an infinite series of such causes, any more than there can be an infinite series of efficient causes, as we have seen. Thus we must to posit the existence of something which is necessary and owes its necessity to no cause outside itself. That is what everyone calls "God."

    Medieval Sourcebook

    The Fallacy of Equivocation is an informal logical fallacy that occurs when an ambiguous word (a word with at least two unrelated meanings) is used twice in the same argument in two different ways to produce a conclusion that is valid for only one meaning of the word. The example given by the fallacy files is this:

    • All banks are beside rivers.
      Therefore, the financial institution where I deposit my money is beside a river.

    There are several problems I can see with his argument right off the top of my head. First, I'll rewrite his argument is a way that is easier to analyze:

    1. Some things can either exist or not exist.
    2. Anything that can not exist does not exist at some time.
    3. If it is possible for everything not to exist, then there must have been a time when nothing existed.
    4. If there were a time when nothing existed, then nothing would today exist.
    5. Things do exist today.
    Therefore, there must be at least one thing whose existence is necessary; that is, it must exist at all times.

    Premises 1 and 2 are not actually necessary to establish a valid argument here, but they do give some background information that Aquinas' feels is important, so I'll retain them. The first issue I have is with the truth of 3. Given an infinite amount of time, all probabilities that are not 0 become infinitesimally close to 1, so perhaps this claim would have some truth to it if we could grant an infinite amount of time. In fact, however, I do not believe that we can do this. Modern cosmology establishes a clear beginning to the passage of time, and given this finite amount of time, the probability of all things blinking out of existence at exactly the same time seems prima facie to not be very high.

    I also have a problem with 2 itself, and this may be where a fallacy of equivocation comes in. In 1, Aquinas says that it is possible for some things to not exist. He seems to be referring to logical possibility here. For instance, no contradiction would result if my hat didn't exist, and so it is logically possible for my hat not to exist. In order to move from 1 to 2, however, he must contend that it is not only logically possible for some things not to exist, but that it is also empirically possible for those same things not to exist. What that means is that not only can be imagine a possible world in which my hat does not exist without contradiction, it must also be possible for my hat not to exist in this world. While it might seem uncontentious to say that my hat could not exist in this world, this strongly depends on what we mean by "exist," hence the equivocation fallacy. It is possible in this world for my hat not to exist as a hat; that is, I can set it on fire, in which case it will cease to be a hat. The material from which the hat is made, however, cannot be blinked out of existence according to the persistence laws of physics. In this sense, it is not empirically possible for anything that exists in this universe to cease to exist.

    Again, 1 and 2 are not necessary to establish the validity of the argument from 3, 4, and 5 to his conclusion, but they are necessary to establish the truth of 3. If 3 is untrue, which I hope I have just demonstrated, then his argument, though valid, is unsound and ultimately meaningless.

    Edit: There are a couple of minor things wrong with my analysis here, but I'm going to just leave them for now, as they don't affect the equivocation fallacy that I think Aquinas makes, so hopefully this is enough for you. If you notice the mistakes I made (there are two that I can see right now), go ahead and point them out. I will then correct them.
    Last edited: Mar 24, 2005
  4. Mar 25, 2005 #3


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    If you dont mind, could you please make those corrections. I havent seen them yet, but then again this is the material I missed in class.

    I have a test question on this so I would like it to be as correct as possible.

    Thank you for responding in depth.
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