3

2

I am not asking for a defense of or pro/con of the existence of an omnipotent (or multiple omni-x) being, or for the existence of square-circles or any other similar thing. These arguments are well documented within this site, for example Is the definition of God consistent?

My question concerns the terminology associated with a logically inconsistent definition or an argument flowing from it, and whether or not assigning a truth value to the conclusion of such argument is a named logical fallacy.v

The basic laws of logic indicate:

- a valid argument is one such that if all propositions are true, then the conclusion is true.
- if any proposition to a valid argument is false, then we cannot determine whether the conclusion is true or false. It may remain true even though a proposition is false.
- with an invalid argument, it doesn't matter whether the propositions are true or false - we can never determine the truth of the conclusion.

## Questions

**Given the above, what happens if I define something in a way which is logically inconsistent and use that definition in an initial premise/proposition for an argument?**

An illogical/incoherent thing is not able to be addressed by logic, other than perhaps to assign it to the set of objects which are incoherent. So how does an incoherent definition flow in an argument?

**If a definition used in a premise/axiom/proposition of a logical argument is illogical/incoherent/paradoxical, then do we say that the proposition itself is incoherent or paradoxical as a result?**Continuing on to the logical argument that flows out of such a proposition,**

**Do we say that such an argument is also incoherent or paradoxical because one of its propositions is?****Or is it more correct to say that such an argument is simply invalid?**Which is to say we cannot establish the validity of such an argument (it is outside the realm of logic to determine it's validity)**Or something else?**

**Is there a name for the fallacy of attempting to determine the logical truth value for the conclusion of such an argument?**

*Note:**One may also be able to discuss this in mathematical terms, with the concept of infinity, division by zero and similar concepts which can be used to show impossible things (i.e. 2 + 2 = 5, etc.) by using improper or illogical definitions at the start of the proof*

*Note 2:**I don't think this requires going to a formal system of symbolic logic - if it does, please help me understand why*

Does this mean that proofs by contradiction equivocate when they reason about things like rational number with square 2? – Conifold – 2017-02-09T02:01:37.663

I'm not seeing the connection between proof by contradiction and equivocation. Maybe you could spell it our more? – virmaior – 2017-02-09T02:37:49.703

If inconsistent definition is guilty of equivocation then "rational number with square 2" is guilty of equivocation. This seems to mean that Euclid's proof of irrationality of the square root of 2 equivocates when it defines such a number and then derives a contradiction by reasoning about it. If the equivocation is in using rationality in some parts of the proof and square 2 in others (although, frankly, they mix in this case) then any conjunctive definition can be said to equivocate. – Conifold – 2017-02-09T02:52:51.617

I don't think that's an accurate description of what's happening there. Or may be to add something, an equivocation is when you accomplish your conclusion by changing the definition of the term. The proof of the existence of irraitonal numbers does not depend on that. – virmaior – 2017-02-09T03:30:43.777

We may disagree on that, but why does it matter if it is an accurate description of what Euclid does, or whether the proof depends on it? The point is that it can be (and often is) described in this manner, along with many other contradiction proofs. Where then is the definition of the term changed? It seems the same (inconsistent) conjunction is used throughout. – Conifold – 2017-02-09T03:59:22.730

I'm rather lost as to what we're talking about or why. The question is about whether the inconsistent use of terms can be fallacious. Neither the question nor my answer refers to Euclid or the proof of the irrationality of the square root of two. Moreover, at least on my memory (and interpretation) of the proof, there's no equivocation going on. There's an assumption made specifically to produce a contradiction and negate the assumption. That's not at all the same thing as equivocation. – virmaior – 2017-02-09T04:15:13.250

I am not saying there is an equivocation,

youare. Euclid's proof can be easily rephrased (accepting your view that Euclid himself does not phrase it that way) into manipulating an inconsistent term, "rational number with square 2". You say that involves equivocation, I do not see what it might be. Frankly, I generally do not see how use of inconsistent terms necessarily involves equivocation, that would seem to classify all Meinongian logics as equivocative. Why would talk about round squares be equivocative? What was the example you had in mind? – Conifold – 2017-02-09T04:28:51.143I'm positive I'm not saying Euclid equivocates. If you want to suggest Euclid equivocates, I would say either (a) we are using the term in differing ways or (b) you're wrong. If you have a different answer, provide it in the answer box (as you have). If you dislike my answer, downvote it as you may. I don't see any necessity to change it vis-a-vis the question. – virmaior – 2017-02-09T04:34:21.293

Regardless of Euclid "an argument that contains an inconsistent definition is guilty of "equivocation"" is not explained generally, or by example in the post. I was not asking you to change it, or saying that it is wrong, only asking to explain what you meant, and later trying to say why it puzzled me. I imagined a response in a couple of lines after the first comment. I don't understand what happened here, but ok, back to silence. – Conifold – 2017-02-10T02:58:52.387

my favorite example of this is "God is love. Love is Blind. Ray Charles is Blind. Therefore, Ray Charles is God." – shieldgenerator7 – 2019-02-04T03:27:16.000