Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the few fundamental philosophical subdisciplines, along with metaphysics, ontology and aesthetics. Logic has taken on considerable importance in recent mathematical developments, and one of the ...

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How is temporal logic not vacuously true?

This has been bothering me for a while and I really need your help. A proposition "It will rain tomorrow" isn't like any other proposition, it most resembles an implication of the form "If it is ...
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75 views

Is there a logic of married bachelors?

I'm sure this question must have a simple clarification, but I am largely unfamiliar with the branches of formal logic and not sure where to look for it. We know that "All bachelors are unmarried ...
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A logical fallacy? [on hold]

Just recently my friend and I were discussing marriage statistics, and I jokingly told him that how every woman that I've met so far was either married or engaged. In response, he said something like, ...
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How to prove “Cube(a), LeftOf(a,b), a=c, Then (Cube(c)^LeftOf(c,b))” with Fitch?

(Tet(a)^Tet(b)), Then Tet(b) Cube(a), LeftOf(a,b), a=c, Then (Cube(c)^LeftOf(c,b)) I think the first one would be | 1.Tet(a)^Tet(b) | 2.Tet(a) | 3.Tet(b) ^Intro: 1,2 But I have no idea how ...
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45 views

Do impossible properties include all properties?

As part of Gödel's ontological proof of God's existence he offers a Theorem that all positive properties are possible. In his proof of it he says that impossible properties entail all properties. But ...
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30 views

Is there a logical fallacy in “dropping down” to a different level of abstraction?

Is there a logical fallacy for differing abstractive levels. As in, you start talking on the level of demographics until someone counters with verifiable data on the same level of abstraction, at ...
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108 views

Is it legitimate to win a moral debate with logic?

Is it legitimate to win a moral, political or ethical argument by using logical methods? If you demonstrate that an opponent's statements are somehow illogical, the reason the opponent is ...
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38 views

If a formula φ contains at most one occurrence of any sentence letter, then φ is not a tautology [closed]

If a formula φ contains at most one occurrence of any sentence letter, then φ is not a tautology. The only connectives in my system are → and ¬. I think I should attempt this by induction on the ...
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39 views

Why must the sentence form of a valid argument be tautological? [closed]

I was thinking along the lines of the obvious, such as when found tautological the form must have been valid but I'm sure there is a more in-depth explanation that I can't reach.
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Are the prisoner's dilemma and game theory relevant to this competitive workplace scenario?

A friend of mine who works as a car sales person recently explained to me how she and her colleagues are paid. They get a very low base salary and make most of their money of off commissions and ...
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25 views

If you bet on something unenforceable does it still happen some how? [closed]

So let's say a person was lying and said "I bet on my life." This is just a theory to determine if I should ever consider lying and doing this at the same time; but would you actually die early or get ...
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76 views

How do mathematical Platonists think about formal systems?

I read that platonists believe there are abstract mathematical objects. How do they think about formal systems? For example, (1)Do they discriminate the set of natural numbers N on ZF and that on ...
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63 views

Intuitively, why does a Necessary Condition = the opposite of a Sufficient Condition?

Abbreviate Modus Tollens to MT, Necessary Condition to NC, and Sufficient Condition to SC. I pursue only intuition; please do not answer with formal proofs or Truth Tables. I think that I understand ...
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160 views

Is logic subjective?

If logic is constructed from axioms, and axioms are depended on observation which in term could be subjective, does this means that logic could be limited to our observation, and not really absolute ...
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95 views

Was Kant anticipating Gödel's incompleteness with his antinomies?

Kant's attempts to prove that there's a limit to pure reason based on the existence of antinomies, i.e. pairs of propositions where each one is rational, but the proportions contradict each other. One ...
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32 views

Can Kant's antinomies be translated into formal logic?

Kant proves the limits of human reason by providing 4 antinomies, pairs of rational but contradictory statements, which he claims pure reason can never help us decide which one of the pair is correct. ...
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1answer
52 views

Which 20th century analytic philosopher wrote about a thought-experiment of a king and a jester?

The following thought-experiment was put forward by a 20th century analytic philosopher. Unfortunately I cannot remember the exact context in which it was proposed. Does anybody know how may have come ...
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'But wage controls limit worker spending, which, in turn, results in reduced corporate profits if price controls are in place.' [closed]

Source: A Concise Introduction to Logic (10 Ed, 2008) by Patrick Hurley Natural Deduction Question [Question on p 601:] 14. [1.] Price and wage controls are the only way to control inflation. ...
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73 views

'Money is an essential part of self-esteem.' : How is this the missing premise?

Source: A Concise Introduction to Logic (10 Ed, 2008) by Patrick Hurley [Question on p 597:] 6. Missing Premise Question Unequal pay for men and women is a completely indefensible practice ...
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63 views

How to show -(P -> -Q) ⊢ P&Q?

I'm unsure how to prove -(P -> -Q) ⊢ P&Q I know I can assume -(P -> -Q) and use RAA to assume -(P&Q), but from there I'm stuck on how to proceed because of the negations on the outside of the ...
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3answers
106 views

Has anyone ever argued that the laws of Nature and physics are necessary truths?

Looking at Putnam's twin earth thought experiment, his argument for semantic externalism is based on possibility of their being a twin earth, where everything is the same except for water being made ...
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24 views

How do Ad Hoc Modifications produce a vacuous explanation?

Hereafter, abbreviate ad hoc modifications to AHM and hypothesis to HT. Source: p 636, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley. To minimise this post's length, I do not quote ...
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33 views

How do Ad Hoc Modifications corrupt and pervert Hypotheses?

Hereafter, abbreviate ad hoc modifications to AHM and hypothesis to HT. Source: p 636, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley. To minimise this post's length, I do not quote ...
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1answer
21 views

How can many Methods of Agreement or Difference overpower 1 Joint Method?

Abbreviate Method of Agreement to MoA, Method of Difference to MoD, Joint Method to JM, Necessary Conditions to NC, and Sufficient Conditions to SC. Source: p 552, A Concise Introduction to Logic (12 ...
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43 views

How does negating an existential quantifier work?

I'm revising counterexamples for my logic exam next term, and one of them has me absolutely stumped. I have to provide a counterexample to refute the following claim: ∀x∃yPxyy v ∃x¬∃y∃zPxyz is ...
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6answers
89 views

For preventing something, why do we usually search for the Necessary and not the Sufficient Conditions?

Abbreviate Necessary Conditions to NC and Sufficient Conditions to SC. Source: p 545, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Sometimes the context provides an immediate ...
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48 views

When does ℱx ≡ (x)ℱx ? What if x has the same domain in both?

Abbreviate Universal Generalisation to UG. The longitude of this earlier question motivates me to pose further questions separately. Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick ...
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1answer
26 views

Why must Rules of Inference be applied only to whole lines, without quantifiers?

Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley [p 415:] Since, however, the first eight of these rules are applicable only to whole lines in an argument, as long as the ...
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91 views

(∃x)(∃y)(Jxy v Kxy) ⊃ (∃x)Lx : Why can this not be instantiated?

Source: p 502, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Because line 1 cannot be instantiated, the only strategy is to derive the antecedent of the conditional with ...
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33 views

'Any heavyweight can defeat any lightweight.' : How do you bracket the Nested Conditional?

Source: p 498, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Any heavyweight can defeat any lightweight. [1.] (x) [ Hx ⊃ (y) ( Ly ⊃ Dxy ) ] Even after reading this, ...
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'Any heavyweight can defeat any lightweight' : Why are all the quantifiers not at the front?

Source: p 498, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Any heavyweight can defeat any lightweight. [1.] (x) [ Hx ⊃ (y)(Ly ⊃ Dxy) ] I bolded the only change. Why is ...
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1answer
56 views

Does a rejection of the principle of sufficient reason result in blurring the distinction between being and non-being?

Celestine Bittle in 'Reality and the Mind' holds that if we do not grant that there is a reason for being rather than non-being, then there is no actual distinction between being and non-being since ...
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153 views

What is wrong with my intuition of Modus Tollens?

Abbreviate Modus Tollens to MT, Necessary Condition to NC, and Sufficient Condition to SC. I pursue only intuition; please do not answer with formal proofs or Truth Tables. I already know of the ...
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50 views

Besides notation, how does (x)ℱx differ from ℱx?

Abbreviate Bound Variable to BV, Free Variable to FV, Universal Generalisation to UG, and Universal Quantifier to UQ. Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley [p ...
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1answer
40 views

In Predicate Logic, for a Conditional Proof, why can you directly assume the Statement Function?

Abbreviate Conditional Proof to CP, Statement Function to SF, and Universal Quantifier to UQ. Source: p 483, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley The next example ...
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195 views

Are there any proofs that miracles are impossible? [duplicate]

Are there any logical proofs that miracles are impossible? In this case I define a miracle as an interference with nature by a supernatural power. [Edit: Possibly due to confusion about the ...
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62 views

How does the ambiguity of 'All S are not P' not disturb the 4 Quantifier Negation Rules?

Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley. Caution: In earlier editions, the Quantifier Negation Rule was called the Change of Quantifier Rule. [p 202:] Two ...
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1answer
30 views

Is it really problematic for Universal Instantiation to precede Existential Instantiation?

Abbreviate: Existential Statement to ES, Existential Instantiation to EI, Universal Instantiation to UI, and Universal Statement to US. Source: A Concise Introduction to Logic (12 Ed, 2014) by ...
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45 views

In a utilitarian calculus, where do I find the values that I assign each “feeling” or action?

I'm to do a utilitarian calculation but nobody mentions where I find the values that I assign each "feeling" or action? Where can I find these values? If I don't find them, do I just make them up ...
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30 views

Is it ethically correct for a physician to refuse a course of treatment demanded by the patient?

I'm writing about the medical ethical dilemma of whether or not to give life-sustaining therapy if it is judged to be futile by the doctor anyhow. I'm to write a logically valid argument FOR or ...
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1answer
32 views

How to translate 'azaleas bloom if and only if they are fertilized' into symbolic logic?

Source: p 460, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Statement: [S1.] Azaleas [(Wiktionary)] bloom if and only if they are fertilized. Symbolic translation: [S2.] (x) [ ...
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1answer
43 views

For Universal Instantiation of a Variable, besides notation, does (x)ℱx differ from ℱy?

Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley [p 464:] Since, however, the first eight of these rules [of Inference] [hereafter ROI] are applicable only to whole lines ...
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26 views

What 'certain liberties' inject meaning to Statement Functions?

Source: p 465, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley [...] 5. Py ⊃ Cy    3, 4, Hypothetical Syllogism 6. (x)(Px ⊃ Cx)     5, Universal Generalisation [...] As ...
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32 views

Does any person truly need anything? [closed]

Need: To require something because it is essential People often say that they need things. "I need you to do the dishes." "I need a new car." "I need to eat breakfast." However, these statements are ...
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Do we truly have free will? [duplicate]

Are people truly agents of their own individual destiny? Or was everything a person did yesterday, an hour ago, or two seconds ago destined to happen from the beginning of time? People are constantly ...
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48 views

What is the 4th Dimension? [closed]

I don't think that the fourth dimension would be time, if it were discovered. Time is a measure of physical change that presumably should exist in and separately from all conceivable (and otherwise) ...
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1answer
35 views

What distinctions between Exclusive vs Exceptive Propositions have I overlooked?

Abbreviate 'Standard Form Categorical Propositions' to SFCP and 'Ordinary Statements' to OS. Source: p 256-257, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley. The textbook did not ...
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1answer
15 views

What are the steps and thought process behind translating Exclusive Propositions into Standard Categorical Form?

Source: p 256, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Many propositions that involve the words “only,” “none but,” “none except,” and “no . . . except” are exclusive ...
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36 views

How does a Statement Function 'make no definite assertion about anything'?

Source: p 456 (chart), 457 (Quote), A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley In these examples, the expressions [...] [that I coloured in green], and so on are called ...
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42 views

Before starting the Reductio Ad Absurdum, how can you guess or divine that F causes the contradiction?

As with most proofs by Indirect Method or Reductio Ad Absurdum, the key step is to discover (at least, to divine or presage) the location of the contradiction. So for the following example, what ...