First: we don't really say that arguments are true or false. Statements are true or false, but arguments have different kinds of properties.
One of those properties is, as you are obviously aware of, validity. However, another important property is well-foundedness, which means that the premises are true (or, for more practical everyday purposes, plausible ...
Premise : All dogs are mortal (true)
Premise : All birds are dogs (false)
Conclusion : All birds are mortal (true)
The argument is valid because there is a correct relation between premises and conclusion. This is not because the conclusion is actually true but, crucially, because granted the premises the conclusion must follow even though one of ...
(Promoting this from @MauroALLEGRANZA's comment, since it deserves a full answer.)
Yes, an argument can be valid but still not be sound.
This is really just a matter of understanding the terminology:
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to ...
Hence, I think this one is a sound sentence.
Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. Since this argument is invalid, it is not sound, even though all the sentences in the argument happen to be true. My sense is that the fact that all these ...
The sky is blue
Therefore, grass is green.
The premise and the conclusion are both true. But the argument is not sound, because it's not valid. And it's not valid because the conclusion doesn't follow from the premise.
Let's look at the translations (into first-order logic):
(1) ∃x : Man(x) ∧ Married(x).
(2) ∃x : Man(x) ∧ ¬Married(x).
The first is true in universes where there is at least one married man; the second is true in universes where there is at least one bachelor. To show that the argument from (1) to (2) is not valid, consider the counterexample: a universe ...
If Δ ⊢ Φ, then Δ ⊨ Φ
has an implicit universal quantification to it:
For all Δ, Φ: if Δ ⊢ Φ, then Δ ⊨ Φ
Unsoundness of a proof system then means
Not for all Δ, Φ: if Δ ⊢ Φ, then Δ ⊨ Φ
This is equivalent to
There exist Δ, Φ such that not: if Δ ⊢ Φ, then Δ ⊨ Φ
which is in turn equivalent to
There exist Δ, Φ such that Δ ⊢ Φ but not Δ ⊨ Φ
Counterfactual conditionals do appear in arguments, and we tend to treat them as contributing to validity and soundness, but their logic is much more problematic than other conditionals. Consider, for example:
If Caesar had not crossed the Rubicon, the Roman Republic would have survived for another hundred years;
If the Roman Republic had survived for ...
It sounds like you are trying to ask if you can have logical premises that are false, yet support a conclusion that is true - in other words, an example of presenting facts that lead to a true statement, but the facts themselves are wrong.
This is entirely possible - the other answers provided give absurd examples of demonstrably false things, but they ...
The answer to this question depends in part of the symbolization resources you have available to you.
If we translate as follows:
Anything that travels in time necessarily changes the past
T -> C
But necessarily, nothing changes the past.
to not C
Thus, necessarily, nothing travels in time.
and the conclusion to not T.
Then we wind ...
One typically does not, soundness and completeness are not particularly natural properties from the proof-theoretic point of view. Although rarely spelled out explicitly, there is in the background this idea of "correspondence" of the formal theory F to some Platonized fragment of "reality". "Sound" means that everything provable in F is "true", and "...
Goedel's 1930 completeness theorem showed that first-order predicate calculus is complete in the sense that every valid formula is a theorem. There are many calculi that have as theorems all and only the tautologies, that is, the valid formulas of propositional logic, as pointed out in the answer given previously by Kjos-Hanssen. Furthermore, as stated in ...
Yes, you can give axioms and rules of inference so that all and only the tautologies are derivable. Propositional calculus is better behaved than first order logic in that sense. That doesn't mean you can find the proofs quickly though, unless P=NP.
The argument is not sound because there could be things named Socrates that are mortal that are not human- for instance, my cat is named Socrates, and he's definitely not human. A sound argument would be the inverse:
Socrates is human
All humans are mortal
Socrates is mortal
Premise 1: All humans are mortal.
Premise 2: Socrates is mortal.
Conclusion: Socrates is human.
This reasoning is unsound because the middle term (mortal) is undistributed. Thus there is no idea which links the two premises; together they cannot add up to any broader conclusion.
The general form of both premises is an A statement: All P are Q. "...
I think that you're confusing validity and soundness.
The validity of an argument is determined purely by its form, not by whether or not its premises are true.
On the other hand, a sound deductive argument is a valid argument where all of the premises are true.
Immaterial causes are unfalsifiable, so your argument doesn't/can't falsify them. It just tries to convince, but cannot prove anything.
The first part is also questionable. There are plenty of things where we don't know the cause, can't observe it, or there is none (radioactivity is spontaneous - while you can argue it has a material cause, there is nothing ...
The definitions are relevant to a Logical system and can be extended to Formal mathematical theories.
See the Wiki's page (some lines below your quote):
Soundness of a deductive system is the property that any sentence that is provable in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon ...
An argument generally consists of two parts: premises and logic.
If the premises are true and the logic is valid, then the conclusion must be true.
But if either the premises are false or the logic is invalid, then the conclusion does not follow.
All bald men are master criminals.
Fred is bald.
Fred is a criminal.
The logic is impeccable. If ...
Technically, in all classical, standard logics, if an argument with any number of true premises is valid, its conclusion must be true as well, based on the fixed meaning of the logical constants occurring in them. If you then add an arbitrary false premise to the given true premises, this does not invalidate the argument, as long as the conclusion remains ...
As well as soundness and validity and such, it may also be worth considering that an argument can (although it may be considered poor form) have redundancies. In that case, it could be that one false premise does not break the overall argument.
The clouds are black
The weatherman predicts rain
If the clouds are black or the weatherman predicts ...
If humans have flaws then they are imperfect beings. Humans have flaws. Therefore they are imperfect beings.
Valid, although ambiguous in quantifiers. This could be fallacious if the inconsistent quantifiers are added. Two examples of consistent insertion of quantifiers would be "If a human has a flaw, then that human is an imperfect being. Some humans have ...
Soundness and completeness proofs establish a relationship between a formal proof system (derivability) and a formal semantics (validity). Soundness means that anything that is derivable is also valid, and completeness means that anything that is valid is also derivable.
The fact that most soundness and completeness proofs refer to models and/or ...
It's lexical. In 1) you've used Criminal as an adjective to mean that the action is criminal. In 2) you've used it to mean actions pertaining to criminal things.
The second use isn't common in English which is presumably why you stated that it isn't true.
so to make your original formulation consistent:
All criminal actions are illegal
All murder ...
The argument is valid, but does leave room for some ambiguity.
The first is true just by virtue of the fact that 'illegal' and 'criminal' are interchangeable in the jurisprudential argot.
The second is doubtful given that some murders (if we define 'murder' as 'killing a person') are done from the self-defence and hence wouldn't be considered criminal. ...
If you like reductionism and you have an Occam prior, the answer is yes.
Given any phenomenon, the simplest explanation is best. But 'Simple' is a word in English, so what does that actually mean? Preferably in numbers, so you can compare which is simpler with a single complexity(argumentX)>complexity(argumentY) therefore Y?
Occam's Razor is often phrased ...