Regarding valid/ invalid deductive arguments.
P1 Grass is green
P2 Paris is the capital of France
C Poodles are dogs
How is this ‘deductively’ valid (or invalid) since no claim of inference is being made? Or for that matter, how can it be considered an ‘argument’ at all if what is meant by an argument is an attempt at persuasion? A series of unrelated but true statements placed together in ‘argument’ form do not make a deductive argument if that is the intent. It isn’t a bad argument either, a bicycle isn’t a car even if the speaker wants it to be. No one in the real world would seek to persuade by forming such an ‘argument’. Please give an example of invalid argument with true premises and true conclusions that is not nonsense.
And whatever you give, let that argument fail on logic not knowledge.
P1 Atoms are tiny
P2 The smallest particles of hydrogen gas are tiny
C Therefore the smallest particles of hydrogen gas are atoms
This is invalid based on the counterexample of oxygen gas in place of hydrogen gas. But the difference between the two is that we have knowledge of of oxygen gas as a molecule, not that the logical form is wrong (?)
We use knowledge as the basis to make true statements to form valid arguments, but the knowledge may be flawed, does that mean that logic is?
Answer by Craig Skinner
I will say what an argument is, distinguish a deductive from an inductive one, distinguish the three features of a good deductive argument, then answer the queries you raise.
An argument is a movement of thought in which a series (one or more) propositions (premises, Ps) warrant a final one (conclusion, C).
Arguments can be deductive, inductive or abductive. I wont say any more about the last two, except that they are not logically watertight, lacking the logical feature of entailment which is intended in a deductive argument.
A deductive argument has the intended feature that the Ps logically entail the C. If the Ps are true, the C must be true. It is impossible for the Ps to be true and the C false. The C is a logical inference from the Ps.
A good deductive argument is:
Let’s deal with each:
Validity: the C does follow from the Ps. The logic is correct, the intended feature (entailment) is present. This is decidable from the form of the argument. No knowledge of the world is needed.
P1 All As are Bs
P2 All Bs are Cs
C All As are Cs
A useful way to see this (and other deductive arguments) is Venn diagrams: make a small circle (the As); make a bigger circle around it (the Bs); then a yet bigger circle around the Bs (the Cs). You can now see that if all As are Bs and all Bs are Cs then all As are Cs.
Notice that validity says nothing of truth, the Ps may be true or false, the C true or false. Validity only guarantees is that if the Ps are true, then the C is definitely true.
Soundness: the C is true because the Ps are true and the argument valid. In short, a sound argument is a valid one with true Ps, so that the C can be relied on. These are the arguments we want in real life (including philosophy).
Persuasiveness: this is not just a question of arguments of course (flattery, threats, bribes, images, endorsement by authority or a celebrity may all make a poor argument more persuasive). However an argument is more likely to be persuasive, especially to a critical, impartial listener, if it is sound, short and simple. As an aside, Lewis Carroll dreamed up ‘fun’ arguments with, say, twenty connected Ps, so that long before the C one had completely lost the thread.
Now to the points you raise:
Your Ex 1 could be called a non-argument (as you suggest) or else a very bad one (invalid, unsound, unpersuasive). The fact that it’s set out with Ps and C, and that the C implicitly, as in all arguments, starts with an unstated ‘Therefore’, inclines me to call it a very bad argument.
You ask for an invalid argument with true Ps and true C. Here is one:
P1 Poodles are mammals
P2 Dogs are mammals
C Poodles are dogs
Make a Venn diagram: in the circle for mammals are two smaller circles, one for dogs, one for poodles. But, from what is said in the Ps, these little circles needn’t connect or overlap. In short, if As are Bs and Cs are Bs, we can’t say whether or not any As are Cs.
This argument fails on logic, not on knowledge, as you asked. In fact the knowledge, that all poodles really are dogs, just gets in the way of seeing the invalidity.
Your Ex 2 is invalid. It has the same form as my above example i.e. As are B and Cs are B, and it doesn’t follow that Cs are As. Again draw a Venn diagram. The invalidity, to repeat, is a logical notion, decidable from the form of the argument without reference to the world, so that knowledge about oxygen isn’t needed and isn’t what makes the argument invalid. Substituting ‘oxygen’ for ‘hydrogen’ simply illustrates that the argument is flawed. Substituting more familiar terms is often an alternative to a Venn diagram in illustrating validity/invalidity. For example, the following has the same form as your Ex 2 and helps convince us of its invalidity:
P1 Ants are tiny
P2 Dust specks are tiny
C Dust specks are ants
You talk about knowledge being flawed, and could logic be flawed.
I’m not sure what you mean by ‘flawed’ knowledge. Certainly, some of the things we take as knowledge turn out to be untrue (mere gossip, misleading appearances or deceit, say). Or knowledge may be incomplete. But knowledge by definition is true.
As regards logic being flawed, I think we can take it for all practical purposes, including argumentation, that classical logic is correct. Paraconsistent Logic holds that classical logic is incomplete because some contradictions are true, but that’s a wholly different matter and irrelevant to your question.
In conclusion, distinguish validity (a purely logical matter of entailment), soundness (combines validity with truth) and persuasiveness (a practical, pragmatic matter); and, if unsure about validity, use Venn diagrams to picture all Xs are Ys, some Ys are Zs etc.