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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1answer
26 views
The difference between soundness and completeness
Is anyone able to articulate the difference between the properties of soundness and completeness insofar as they relate to the validity of the tree test?
1
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1answer
42 views
Is the usage of “more” or “less” only plausible when there's a quantitative method for it?
I am a student of mathematics, that afirmation of the question I propose seems plausible to me. But I remember that some days ago, I was talking to a friend and he said that such terms are not exactly ...
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1answer
47 views
What is the Logical Model of an software application that reflects the theory of Change? [closed]
What is the Logical Model of an software application that reflects the theory of Change?
Or
How software should work logically so that it can reflect the theory of Change?
A Logical model of a ...
0
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2answers
80 views
Strong AI vs Gödel's Theorem?
If Gödel's Theorem is true, it means that for every formal system, there is a thesis that is true but can't be proven from the formal system. Every agent system which humans can build by modern ...
1
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1answer
32 views
Reasoning in S5
I'm currently working on implementing reasoning involving time.
Since S5 (every world accessible from any other) is sufficient for what I'm trying to represent, I wanted to know what are the ...
0
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1answer
62 views
I'm running into this weirdness using the concept of certainty. Why?
I cannot be certain of anything. (Assumption.)
I am not certain that I cannot be certain of anything.
By asserting (2), I am certain that I am not certain that I cannot be certain of anything.
I can ...
3
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2answers
50 views
Is there a difference between inconsistent and contrary?
Is there a difference between 'inconsistent' and 'contrary'? As far as I understand two statements are inconsistent when they can not both be true. Does 'contrary' have the same definition?
As far as ...
1
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2answers
37 views
A Full List of Deontic Paradoxes?
Other than the list found in the Stanford Encylopedia article on Deontic Logic, is anyone aware of a comprehensive list of deontic paradoxes (preferably inclusive of the contemporary paradoxes)?
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2answers
115 views
Changing Universe vs Infinity:
If we accept the idea of a dynamic, changing, evolving Universe (Big Bang Theory), must Infinity remain entirely conceptual?
If the Universe is changing and evolving, this necessarily implies borders ...
1
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1answer
96 views
Why is philosophy the root of Wikipedia? [closed]
Go to any English Wikipedia page.
Click the first link (not in brackets, italics or in a box).
Repeat n times.
Why do you end up at the philosophy page 95% of the time?
I expect it has to ...
2
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0answers
46 views
The manuscript Summa Logicae (William of Ockham)
The Summa Logicae (Latin, in English it's the Sum of Logic) is a textbook on logic by William of Ockham. There are articles about the Summa Logicae in Wikipedia and in Logicmuseum.
It was published ...
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2answers
119 views
Do IQ tests measure intelligence?
Okay, I am kind of skeptical about IQ tests. I think they only measures the speed of a person's reasoning abilities as well as a small portion of knowledge (or just knowledge). I kind of think that ...
0
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1answer
29 views
Attacking Factual Detachment in Deontic Logic
Let OB(q/p) represent the conditional ought statement: "If p, we ought q".
(Note that depending on your views of deontic conditionals, the statement "If p, we ought q" could be taken to be ...
5
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2answers
76 views
Criticisms of Categorical Foundations In Logic
One of the modern trend amongst mathematical philosophers has been the application of categorical foundations to logic. Lawvere is probably the best known for his use of closed cartesian categories in ...
5
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3answers
143 views
Order of Premises in Logic
Does anyone have any examples of order-sensitive arguments (that is, arguments in which different conclusions can arguably be drawn depending upon the order that the premises are presented)?
4
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1answer
68 views
How to express Kant's notion of existence on first-order logic according to Ayer?
In Language, Truth, and Logic, Ayer writes:
[As] Kant pointed out, existence is not an attribute. For, when we ascribe an attribute to a thing, we covertly assert that it exists.
However, I ...
0
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0answers
56 views
Check The Validity [closed]
If God is willing to prevent suffering(S), but unable to do so(D), He is not
omnipotent(O). If He is able to prevent suffering(S), but unwilling to do
so(U), He is not loving(L). If God exists, He is ...
1
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1answer
27 views
Interpreting Non-Deontic Formulas in Deontic Logics
Consider an arbitrary system of logic that handles deontic notions such as "it is obligatory that..." or "it is permissible that...". My question is how -- in these systems -- are we supposed to ...
1
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1answer
29 views
Disentangling Conditional Statements from their Corresponding Inference Schemes
Suppose we're looking at two objects:
(i) the conditional statement (A --> B)
(ii) the inference A |- B
In propositional logic, we have that (i) is true if and only if (ii) is valid. My ...
1
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1answer
77 views
How does one explain (apparent) nonexistence?
There is quite a bit of fun in building a little web of questions and answers throughout StackExchange. (Let's call it an exercise in interdisciplinarity.)
"Molecular biologist Robin Holliday has ...
0
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1answer
93 views
A simple paradox of True or False [duplicate]
In a piece of paper, it was written:
The statement written in the paper is false.
Is that statement actually true or false?
3
votes
2answers
110 views
How do correspondence theories handle statements like these?
I have a number of true statements. Each of these statements is a case where I have difficulty seeing how (assuming physicalism) the statement could correspond to a state of affairs. My question is: ...
2
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2answers
95 views
An exception proves the universal truth
Can I ask a logical question here? I had a dispute with somebody who claims that "you need 3 DIMMs for 3 channel motherboard". I presented an example when 4 channels also work. He says that my case is ...
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3answers
99 views
Do I need to implicitly or explicitly have a value to rationally claim that I 'ought to do something'?
I use Humes idea about the 'is..ought to gap' (or my spin on it) mainly to make sure I have good reasons for what I do -and what I advise others to do- and to make sure actions are not based purely on ...
1
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2answers
109 views
What are some popular ways of trying to resolve the “Hangman's Paradox”?
In a harsh totalitarian country an innocent person is arrested on Sunday
evening and summarily condemned to execution, which they are told will
take place on one of the following five mornings. To ...
2
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3answers
102 views
Is communication effective without the logical connectives such as or, and, implies, not, if and only if?
Is communication effective without the logical connectives such as or, and, implies, not, if and only
if ?
I know the answer is no but how can it explain it in detail.
I know I cannot say "A is not ...
1
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1answer
47 views
Is it beneficial for you to think in a logically consistent 1 manner?
Is it beneficial for you to think in a logically consistent 1 manner?
I mean when we have to make logical inferences out of some paragraph we decide it always by converting that in into logical ...
8
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2answers
124 views
What are the dialetheist semantics for logical negation?
This question is in a sense a follow-up, or elaboration, of the question "What are the motivations for Dialetheism?". Reflecting on the way I phrased that question, and the way I remarked on answers, ...
10
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2answers
112 views
What Precisely Does “Semantics” Mean?
What do logicians mean when they refer to the notion of "semantics"? I don't find the definition "the connection between words and meaning of those words" to be that satisfactory here.
Informally, ...
1
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1answer
71 views
How to test a second order logic argument for validity
I'm doing some research on second order logic and I'd like to write down a proof for the following argument:
where x is a first order variable and P and Q are predicate symbols.
A plain ...
8
votes
1answer
230 views
What formal logical systems “resolve” the Liar Paradox?
Short version of my question.
What formal logical systems can represent, and seem robust against, the Liar Paradox?
N.B. I would like to avoid reference to truth-values, except inasmuch as they ...
5
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1answer
111 views
What does “aggregative mechanical thought” mean in Frege's works?
In *The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number" by G. Frege pages XV and XVi we read:
A typical crudity confronts me, when I find calculation
...
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1answer
41 views
Distinction Between Deontic Logic and Formal Ethics
What, if any, is the distinction between "formal ethics" and "deontic logic"?
2
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1answer
50 views
The coherentist solution to Agrippa’s Trilemma and the possibility of pure/impure justification?
I'm trying to get a grasp on coherentism and what is proposes is the epistemological justification for knowledge. From what I've taken so far, coherentism relies on what is commonly referred to as ...
0
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0answers
45 views
What was the importance of the Liars Paradox in Stoic Logic?
Chrysippus, an influential stoic philosopher wrote 21 books (chapters) in 12 works on the Liars Paradox. This implies that this paradox was of some importance to their epistomology and logic. Why?
2
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1answer
64 views
Why did the Western Philosophical tradition favour the logic of the Academy than the logic of the Stoics?
The logic of the Academy was centered around Aristotle, and that of the Stoics inspired by Zeno. Given the close association of Stoicism with the elite of the Roman Empire, and the eventual adoption ...
0
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3answers
132 views
Analyze this argument [duplicate]
Analyze the following argument:
God is All Powerful, omnipotent and omniscient.
If God can do anything, can He create something that even He can't affect (e.g. a stone so heavy that He can't lift ...
4
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2answers
129 views
Suspending some of the usual laws of logic
What would the consequences be, if we suspended some of the usual laws of logic so that they were no longer available as tools in proofs?
(a) The Law of Self-Implication
A ⇒ A for any proposition A
...
4
votes
2answers
115 views
Why does logic emphasize tautologies rather than contradictions?
Why does logic emphasize tautologies rather than contradictions?
I think the answer is something like the following:
We can't cover all cases by contradictions. For example: if I have to prove that ...
6
votes
3answers
208 views
Is infinite regress of logical causation possible? Is infinite regress of logical causation necessary?
For a number of reasons — including perhaps a desire to feel that we have a complete understanding of where we came from, or at least an understanding which is completely sufficient for all of ...
3
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2answers
184 views
What is the difference between an Ordinal number and a Cardinal number?
I'm trying to understand the real difference between an Ordinal and a Cardinal, especially in relation with transfinite cardinals. The stuff on Wiki is a bit too complicated. Can anyone make it simple ...
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votes
2answers
103 views
what kind of branch of philosophy using symbolic logic as a fundamental tool?
I have read a book about "Philosophy of Language",the discussion of Frege and Russell are excellent,using logic symbol to introduce ideas.However,the rest chapters does not approach in this way,the ...
3
votes
3answers
156 views
Where is a good place to start reading about logic?
I would like to learn logic as an introductory subject. I am an undergraduate student and would appreciate any suggestions for books/articles where I can start from, also any books/articles about ...
3
votes
3answers
193 views
Can we ever know the origin of universe? [closed]
For sake of argument, let's assume that everything has to come from something. In this case, our universe must have come from something, lets call it 'thing 1'. 'Thing 1' in turn must have come from ...
2
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3answers
118 views
I've confounded myself with this formal logic “proof”
Let "r" mean "it's raining" and "s" mean "it's snowing."
"->" is "implies"; "V" is "or" (inclusive); "~" is "not"; "^" is "and"
Here's the "proof":
(1) (r->s)V(s->r) is true because it's a ...
3
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3answers
177 views
Are there practical advantages of knowing more advanced forms of logic, as opposed to just classical logic?
For example, classical logic allows one to express arguments more clearly. The LSAT's logical reasoning section tests a kind of reasoning that it considers practical, and an understanding of classical ...
5
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1answer
59 views
What are the advantages to intentionally omit (small) parts from first order logic?
I wonder why "Mathematical Logic" from Ebbinghaus et al. omits 0-ary relational symbols (which would normally be interpreted as propositions, similar to how 0-ary functional symbols are normally ...
3
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1answer
72 views
Has there been any success in using modal logic to interpret Quantum Mechanics?
Quantum Mechanics rather famously has problems in interpretation - straightforward realism doesn't appear to work. Is there any work with modal logic that throws light on this question?
The SEP has ...
3
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3answers
111 views
Modal Logic: a question concerning accessibility
I’m reading a lot about modal logic lately, right now Lewis “On the Plurality of Worlds” and Priests “Introduction to Non-classical Logics”.
It is postulated that the different worlds have nothing to ...
4
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0answers
91 views
Is there a One True Set Theory?
From the description of Category Theory in nlab:
Category theory is a structural approach to mathematics that can (through such methods as Lawvere's ETCS) provide foundations of mathematics and ...
