The arguemtentum ad hominem is an informal fallacy. It is the assertion that a given argument is valid or sound (or invalid or unsound) for no other reason than the qualities of the person making it.
It is a principle of logic that arguments are valid or invalid based only on their forms. That is to say, that a formal argument is valid if and only if (iff) for all arguments of this from, true premises can never lead to a false conclusion. Validity is a quality contingent only on form. It does not matter who formulates it, how, or why. A sound argument is a formally valid argument that has true premises, and -- by virtue of being a formally valid -- a conclusion that must therefore also be true.
Let's take 'X=2+2'. therefore 'X=4'. A very popular argument, generally considered arithmetically valid and sound (ignoring for a moment Bertrand Russell). If we accept this argument as valid and sound, it is valid and sound no matter who says it: it's true if formulated by a white male. Or a black man. Or a Jew. Or a child. Or a mass murderer. Or someone developmentally disabled. Or Lucifer himself. To assert otherwise would be to make an argument ad hominem.
Or we can take an unsound argument: 'X=2+2' and 'X=5'. This is not a valid or sound arguement, no matter who says it. Being formulated by a priest, or a politician, or a media pundit, or a doctor of philosophy, or Yeshua ben Yosef cannot make this a valid or sound argument. To assert otherwise is again, an argument ad hominem.
Now of course, this treads dangerously close to the concept of 'appeal to authority'. Appealing to an authority is also technically an informal fallacy of the form ad hominem. The only realm where appeal to authority can be a successful argument is when it can be strongly asserted that the authority in question has a specific body of knowledge, training or understanding by which such authority can make decisions about the truth or falsity of assertions that canot be made by someone lacking that knowledge, training, or understanding. That is to say, I can appeal to authority if it can be shown that if I were to undertake the training necessary in that field and gained for myself the expert knowledge and understanding in question, I would be capable of making the exact same determinations.
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Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts
Saturday, April 4, 2009
Tuesday, March 31, 2009
Confirming the Consequent
This is a relatively simple formal deductive logical fallacy. There is a valid form of propositional arguement called modus ponens. It takes the form "If p then q", and "p", therefore "q". This is logically valid, and if one precedes from true premesis, one will reach a true conclusion. An example would be "If it is raining on my front yard, the pavement of my sidewalk will be wet", "It's raining on my front yard" therefore "My sidewalk is wet".
However, there is a desire many times to make the argument "If p then q" and "q" therefore "p". This is the fallacy of confirming the antecedant. The truth of q in no way supports or denies the truth of p. If I say "If it's raining on my front yard, my sidewalk will be wet" then observe "my sidewalk is wet", I cannot assert "it is raining". My sidewalk may have gotten wet because someone sprayed it with a hose, or the snow is melting, or there's a big puddle in the street that was splashed onto the sidewalk.
However, confirming the consequent is a fallacy perpetrated commonly in the world. A more complex example would be to say "If Obama deceived the American people about his eligibilty to become president then he would run for office and win." and then to say "Obama ran for office and won." and then conclude "Obama must have deceived the American people about his eligibility."
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However, there is a desire many times to make the argument "If p then q" and "q" therefore "p". This is the fallacy of confirming the antecedant. The truth of q in no way supports or denies the truth of p. If I say "If it's raining on my front yard, my sidewalk will be wet" then observe "my sidewalk is wet", I cannot assert "it is raining". My sidewalk may have gotten wet because someone sprayed it with a hose, or the snow is melting, or there's a big puddle in the street that was splashed onto the sidewalk.
However, confirming the consequent is a fallacy perpetrated commonly in the world. A more complex example would be to say "If Obama deceived the American people about his eligibilty to become president then he would run for office and win." and then to say "Obama ran for office and won." and then conclude "Obama must have deceived the American people about his eligibility."
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Fallacy of the Temporary Name
This is a formal logical fallacy that many, many otherwise bright people fall into from time to time. In formal symbolic logic, of one has asserted or proven an existential quantifier, it is a valid line of arguement (known as E-elimination) to imagine an object that fulfills that existential quantifier.
For instance, I was riding the light rail yesterday. At that time, I could assert the premise, "Someone is driving this train." It would follow in a valid way that I could argue "Let's call the driver of this train 'Elvis'." Something similar happens in geometry: One begins (for instance) by asserting "A triangle exists", and then one can assert in a valid way "Let's call said triangle 'ABC'." So good so far.
How is E-elimination useful? Let's take a more comlex arguement. In our light rail arguement, we can accept another premise - a universal one this time - that "For all x, if x is a light rail driver, then x works for the MTCO." Taking our previous premise of "Someone is driving this train", or more formally "There is an y, such that y is a light rail driver". Then E-elimination allows us to say "We'll call y 'Elvis'. 'Elvis' is a light rail driver." This assertion then allows us to say "Since 'Elvis' is a light rail driver, and all light rail drivers work for the MTCO, then 'Elvis' must work for the MTCO." Then we wrap things up by asserting "There is an x, such that x is an employee of the MCTO" A valid arguement. If we had a more complicated arguement, we can continue to assert in a valid way that 'Elvis' is an employee of the light rail - that's a quality 'Elvis' has been proved to have working simply from already established premises. The limitation to 'E-elimination' or as it's sometimes called 'giving a temporary name' is that no other information can be asserted by the temporary name than what has already been proven from the arguement, and the choice of the temporary name should reflect that.
The fallacy of the temporary name is when that limitation is violated. Let's go back to our example. We could add another premise, "For all z, if z is Elvis, then z is the king of rock and roll." Wow! We've already named our light rail driver 'Elvis'! How convenient - we can use our new premise to prove that the light rail driver is the king of rock and roll. The king of rock and roll is alive and well, and driving light rail trains in Minneapolis.
Ummm.... not so much. That's the fallacy of the temporary name - an incorrect choice of the temporary name has led us from true premises to a false conclusion. We have an invalid arguement. With Elvis and the light rail train, it's pretty easy to see. But consider another arguement (sometimes known as the 'watchmaker arguement':
Premise 1) "For all x and n, if x is a system above a number n, then that system requires a designer" (We'll postulate that this is true)
Premise 2) "for all n, n is an arbitrary measure of complexity,"
Premise 3) "For all b and m, if b is the system of biological life on Earth then b has a complexity of m"
Premise 4) "There is a b, such that b is the system of biological life on Earth"
Premise 5) "Both m and n are numbers, and m is equal to or greather than n"
Premise 6) "For all y, if y requires a designer, then there must exist q, such that q designed y"
Premise 7) "For all z, if z is God, then z so loved the world that he sent his only begotten son."
What comes of this arguement? Well, Premise 3 and 4 together say 8) that there is a b* that has a complexity of m. (b* being a temporary name for the object whose existence is asserted in 4). Lines 8 and 5 say 9) that b* has an m larger than n. Lines 9 and 2 assert that 10) m is a measure of complexity. 10, 4, and 1 all come together to say that 11) the system of biological life on Earth requires a designer. 11 and 6 together say that 12) there is a q such that q designed the system of biological life on Earth. This is all kosher so far, and if one accepts the premises as true, then one has reached a true conclusion. But if we use E-elimination incorrectly and say "Let's call q 'God'", then we go on to argue "Since we've proven that there must have been a designer of biological life on Earth, and that that designer is God, and since we know God so loved the world that he sent his only begotten son, then God must exist as stated in John 3:16!"
This is a fallacy of the temporary name. The only thing we can use this arguement for is proof that something designed the system of biological life on Earth. We can say nothing else about that something unless we can prove that those qualities adhere to the something, and aren't predicates of whatever name we arbitrarily selected. If we had selected 'George' as the temporary name of the designer, then we would only be able to say that something exists that we've decided to name 'George', not that the God of Abraham, Jesus, and Mohammed must exist necessarily exist because of the complexity of life on Earth.
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For instance, I was riding the light rail yesterday. At that time, I could assert the premise, "Someone is driving this train." It would follow in a valid way that I could argue "Let's call the driver of this train 'Elvis'." Something similar happens in geometry: One begins (for instance) by asserting "A triangle exists", and then one can assert in a valid way "Let's call said triangle 'ABC'." So good so far.
How is E-elimination useful? Let's take a more comlex arguement. In our light rail arguement, we can accept another premise - a universal one this time - that "For all x, if x is a light rail driver, then x works for the MTCO." Taking our previous premise of "Someone is driving this train", or more formally "There is an y, such that y is a light rail driver". Then E-elimination allows us to say "We'll call y 'Elvis'. 'Elvis' is a light rail driver." This assertion then allows us to say "Since 'Elvis' is a light rail driver, and all light rail drivers work for the MTCO, then 'Elvis' must work for the MTCO." Then we wrap things up by asserting "There is an x, such that x is an employee of the MCTO" A valid arguement. If we had a more complicated arguement, we can continue to assert in a valid way that 'Elvis' is an employee of the light rail - that's a quality 'Elvis' has been proved to have working simply from already established premises. The limitation to 'E-elimination' or as it's sometimes called 'giving a temporary name' is that no other information can be asserted by the temporary name than what has already been proven from the arguement, and the choice of the temporary name should reflect that.
The fallacy of the temporary name is when that limitation is violated. Let's go back to our example. We could add another premise, "For all z, if z is Elvis, then z is the king of rock and roll." Wow! We've already named our light rail driver 'Elvis'! How convenient - we can use our new premise to prove that the light rail driver is the king of rock and roll. The king of rock and roll is alive and well, and driving light rail trains in Minneapolis.
Ummm.... not so much. That's the fallacy of the temporary name - an incorrect choice of the temporary name has led us from true premises to a false conclusion. We have an invalid arguement. With Elvis and the light rail train, it's pretty easy to see. But consider another arguement (sometimes known as the 'watchmaker arguement':
Premise 1) "For all x and n, if x is a system above a number n, then that system requires a designer" (We'll postulate that this is true)
Premise 2) "for all n, n is an arbitrary measure of complexity,"
Premise 3) "For all b and m, if b is the system of biological life on Earth then b has a complexity of m"
Premise 4) "There is a b, such that b is the system of biological life on Earth"
Premise 5) "Both m and n are numbers, and m is equal to or greather than n"
Premise 6) "For all y, if y requires a designer, then there must exist q, such that q designed y"
Premise 7) "For all z, if z is God, then z so loved the world that he sent his only begotten son."
What comes of this arguement? Well, Premise 3 and 4 together say 8) that there is a b* that has a complexity of m. (b* being a temporary name for the object whose existence is asserted in 4). Lines 8 and 5 say 9) that b* has an m larger than n. Lines 9 and 2 assert that 10) m is a measure of complexity. 10, 4, and 1 all come together to say that 11) the system of biological life on Earth requires a designer. 11 and 6 together say that 12) there is a q such that q designed the system of biological life on Earth. This is all kosher so far, and if one accepts the premises as true, then one has reached a true conclusion. But if we use E-elimination incorrectly and say "Let's call q 'God'", then we go on to argue "Since we've proven that there must have been a designer of biological life on Earth, and that that designer is God, and since we know God so loved the world that he sent his only begotten son, then God must exist as stated in John 3:16!"
This is a fallacy of the temporary name. The only thing we can use this arguement for is proof that something designed the system of biological life on Earth. We can say nothing else about that something unless we can prove that those qualities adhere to the something, and aren't predicates of whatever name we arbitrarily selected. If we had selected 'George' as the temporary name of the designer, then we would only be able to say that something exists that we've decided to name 'George', not that the God of Abraham, Jesus, and Mohammed must exist necessarily exist because of the complexity of life on Earth.
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Googlebombing for a cause: www.minnesotangos.org
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