Such inferences are neither deductive (which assumes application of a valid inference rule) nor inductive (which assumes a generalization from a pattern of cases). This type of inference is called abductive, or "inference to the best explanation", see abductive reasoning. "Clearly" indicates that the explanation inferred is the best ...
First, your premises are inconsistent: your second premise implies that turtles do not see other turtles, or themselves, yet, according to the first premise, they see everything. So, taking y=x, we can deduce both ∀xSxx and ∀x¬Sxx. After that you can deduce whatever you want directly using the law of explosion, contradiction implies anything.
If you fix ...
Gensler's star test is a simplified method for determining the validity of a syllogism proposed in 1973. According to the test, one stars (asterisks) the first (capital) letter after "All", and all letters after "not" or "No". The syllogism is valid if and only if every capital letter is starred exactly once and there is exactly ...
When it comes to justification there is indeed a symmetric problem of deduction. But forming general opinions or laws is not part of deduction, it is abductive (or in older terminology inductive), when it comes to science it is the "hypothetical" part of the hypothetico-deductive method, see Are “if smoke then fire” arguments deductive or inductive? for more ...
This argument could hardly be rendered into a valid form without all kinds of additional assumptions and clarifications. For example,
Assumes we know what God wants and what he/she might or might not do to satisfy those wants. It is difficult enough to speculate about what other people might want or might do about their wants, without trying to speculate ...
If the question is raised in an intro to philosophy course (like critical thinking or scientific reasoning), the answer should be that the above inference is an example of inductive logic. There are two kinds of inductive reasoning. One is generalization, as Conifold suggests. But there is also an inductive inference of John Stuart Mill whose purpose is to ...
One issue is that different authors use "argument" and "inference" in ways different from each other, and from the colloquial meaning. For example, your source interprets "argument" as just the list of premises and the conclusion, whereas in the colloquial sense it is the sequence of intermediate logically elementary steps that lead from premises to the ...
The point is that we should use bayesian reasoning to infer a cause from its consequences. The probability that an hypothesis is true given the evidence is not the same as the probability of the evidence given the hypothesis.
For example: the probability that the floor is wet if it has rained is 1 but the probability that it has rained given that the floor ...
The following truth table shows that ~(A↔B) → ~(A→B) is not a tautology:
If A is False and B is True then the antecedent is True but the consequent is False making the conditional False.
Because the truth table does not show a tautology, one should not be able to derive a natural deduction proof of the result.
Michael Rieppel. Truth Table Generator. ...
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.
An argument is deductively valid if and only if it's impossible for all its premises to be true and its conclusion to be false at the same time. If it's impossible for its premises to be true at the same time, then that is itself sufficient to meet that definition, and make the argument valid, independent of the truth-value of the conclusion.
Whether this ...
The argument is not logically valid.
You need a sixth step, along the line of
A method of knowing God without interpretation exists.
As to the point about the circularity;
It's incorrect to reduce the argument to 'I believe he exists because he exists'
The correct reduction is 'It's impossible for God to exist without faith in his existence also ...
The two different symbols on the page you link to are indeed different. The first is the turnstile symbol Ⱶ which may be read as 'proves', while the arrow → is material implication. These are very different. Material implication is a symbol in the object language defined by the truth table that you give, i.e. T/F/T/T. Turnstile is a symbol in the ...
See Enthymeme :
An enthymeme is a logical fallacy in which a categorical syllogism omits a premise that is necessary for the conclusion to be true or omits the conclusion itself. The missing proposition is considered to be implied.
The fallacy is a syllogistic fallacy and a formal fallacy.
Formal fallacy because
a formal deductive arguments is a ...
welcome to PSE. The concept of truth is one of the head-spinners of philosophy.
Some philosophers believe that truth is a property possessed by all and only true propositions, statements, sentences, claims, &c. Just as a square has the property of being a figure in plane geometry with four equal angles, so a true statement has has the property of being ...
You can't derive ~(A→B) from ~(A↔B).
A = I'm in Paris.
B = I'm in France.
~(A↔B) is true, because being in Paris is not equivalent to being in France (I could be in France but not in Paris). But ~(A→B) is false, because if I'm in Paris then necessarily I'm in France. So you can't derive ~(A→B) from ~(A↔B).
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) -> ...
We're given two premises:
(A ∧ B) ∨ (C ∧ D).
The goal is to assume (1-2) and derive: ¬(C ∧ D) → (A ∧ B). I should start by saying that premise (1) is useless and in what follows we'll simply use premise (2). Here is one strategy you can take. It's pretty system-neutral, so try to implement it in your particular proof system ...
We need first-order logic with equality.
We have :
1) ∀x (Fx ∨ x=c)
2) ¬Fb ∧ Gb
3) ¬Fa → Ga
and we want to derive 3) from 1) and 2).
I think that the "trick" is to rewrite 1) as :
a) ∀x (¬Fx → x=c)
b) ¬Fb --- from 2) by ∧-elim
c) ¬Fb → b=c --- from a) by ∀-elim
d) b=c --- from b) and c) by →-elim (modus ponens)
e) ¬Fa --- assumed
"An argument is valid IFF the premises are false or the conclusion is true".
misses an important feature in the textbook's definition. Namely, you've lost the must, but the must is crucial.
The validity of an argument does not hinge on the truth or falisty of its premises or the truth of its conclusion. Instead, validity looks ...
1) ¬∀xFx --- premise
2) ¬∃x¬Fx --- assumed [a]
3) ¬Fy --- assumed [b]
4) ∃x¬Fx --- from 3)
5) ⊥ --- contradiction: from 2) and 3)
6) Fy --- from 3) and 5) by Double Negation, discharging [b]
7) ∀xFx --- from 7): no y free in "open" assumptions (i.e. [a])
8) ⊥ --- contradiction: from 1) and 7)
9) ∃x¬Fx --- from 2) and 8) by Double Negation, ...
The quoted passage is part of an exposition of Hume's original argument. One of the previous paragraphs explains what "deductively" meant to Hume:
"The deductive system that Hume had at hand was just the weak and complex theory of ideas in force at the time, augmented by syllogistic logic. His ‘demonstrations’ rather than structured deductions are often ...
It seems you don't understand the terms. The essence of deductive reasoning:
If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is
Inductive reasoning, on the other hand:
Inductive reasoning is a method of ...
...it seems that any inductive reasoning can be done with deductive
reasoning by adding in some assumption that a particular pattern
continues to hold.
You got it exactly right. The assumption is the Uniformity Principle. Some philosophers have accepted the principle as supported by common observation; others have dropped wet blankets all over it.
Fact 1. ¬(A ∨ B) |= ¬(B ∨ A)
Proof. The negated form of the conclusion hints at an obvious way of proceeding: assume (B ∨ A)
with the hope of deriving a contradiction. The disjunctive form of this assumption suggests the second step (proof by case analysis): assume B, derive some sentence Γ, then assume A and derive that Γ ...
Two usually discussed challenges are by Nozick and Dretske.
Nozick's analysis of knowledge includes the following condition for S to know that p:
(sensitivity) Were p false, S would not believe p.
Truth conditions for subjunctive conditionals are given in the usual way: Sensitivity requires that in the close worlds to the actual world in which not-p ...