5

It's incorrect because its logical form is incorrect. If we use notation similar to what's used in Tarski's world (a good program to learn the basics of first-order logic, see the lecture notes on it here, especially the first one on atomic sentences), the general form of the first two premises would be something like this: For all x, Property1(x) -> ...


4

It would be worthwhile distinguishing between a conditional sentence in the object language and a conditional in the metalanguage. Some deductive arguments have a conditional in the object language, e.g. those of the form modus ponens or modus tollens. Some arguments do not, e.g. those of the form conjunction elimination, disjunction elimination, etc. But ...


3

Your derivation is not legible to me; I've put down mine for you to compare. Simply MS Word with Cambria Math font may suffice for many short derivations.


3

The Principle of Identity is the Principle of Identity, or The Principle of Non Contradiction is the Principle of Non Contradiction. It is not right to say, of the propositions making up this disjunction, that "the law of excluded middle requires one to be negated". I'm not exactly sure what is causing the confusion, but it seems to me that you think the ...


2

Some of the rules that might be present in another system may have to be derived separately in this proof checker as they are needed. Here is the question: I'm looking for Hypothetical Syll, Constructive Dilemma, Communication, association, distribution, transportation, material implication, material equiv, exportation, and tautology (even though it's ...


2

If an axiom in a deductive system is contingently false (i.e. could be true, but isn't), you can come to some false conclucions. For example, if you axiomatically assume all mammals are viviparous, you can come to the conclusion that momotremes are viviparous, which they are not. If an axiom in a deductive system is logically false (i.e. cannot be true for ...


2

"Wrong" is not the correct term.  We'd simply rather axioms not be "Inconsistent". This happened to be the case with the axioms of Cantorian Set Theory.  It was found to derive several contradictions, or paradoxes, such as the infamous Russell's Paradox. As a result, the axioms of Cantorian set theory were formalised and refined in the hopes of ...


1

This is, I believe, the Fallacy of the Undistributed Middle, one of the classical syllogistic fallacies.


1

This sounds like a HW question, so you need to edit your question to contain your argument for finding answers 3 and 4 correct, so that instead of just giving you answers, you are forced to defend your reasoning and learn from the question. This also seems to be a duplicate post here. It would help to keep in mind that deductive inference is that which has a ...


1

Initially, mathematics was the systematic deduction of the logical consequences of axioms, axioms understood as constituting together, somehow, a model of some particular aspect of the real world. The most historically glorified example of that is probably Euclid's geometry: Euclidean geometry is an example of synthetic geometry, in that it proceeds ...


1

| 1. P > (S v R) |_ 2. ~((~P v ~Q) v (R v ~L)] To conclude S from the first premise you need to derive P and ~R from the second. So, judging by your rule abbreviations , your proof should look somewhat like> | 3. ~(~P v ~Q) ^ ~(R v ~L) DM 2 De Morgan's | 4. ~(~P v ~Q) SIMP 3 Simplification | 5. ~~P ^ ~~Q ...


1

Here is a solution to compare with what you have. Also you might find the proof checker helpful to check the other proofs you are asked to do: For this proof checker DeM is De Morgan rule, ∧E is conjunction elimination, DNE is double negative elimination, →E is conditional elimination and DS is disjunctive syllogism. Kevin Klement's JavaScript/PHP Fitch-...


1

Deduction and induction are not about observation, but certainty in inference. It may be tempting to define deduction as moving from general to specific claims, and induction vice versa, but this is not entirely accurate. Let's take an example to show the difference between deduction and induction. DEDUCTION: If a man is in a kitchen, then he is in the ...


1

Tacit inference is the norm, not the exception. In a real sense, language is merely pointing with words, and we all have to infer referents from the inherently ambiguous symbols that others provide for us. Consider our interactions with young children: a young child will point and make a grasping gesture with a hand, and say (perhaps) "Gagrlagaaagah"; we are ...


1

The premise ∃x∃y∀z(x = z ∨ y = z) says that there exists at most two distinct values in the domain. The conclusion ∀x∀y(¬x = y → ∀z(x = z ∨ y = z)) says that for any two distinct values in the domain, there does not exist a third. Clearly we need to utilise existential elimination and universal introduction. ∃-elim here will be tricky. The 'trick' is ...


Only top voted, non community-wiki answers of a minimum length are eligible