Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [philosophy-of-logic]

Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.

4
votes
1answer
209 views

What exactly is a first-order logic?

Can someone explain in simple terms what exactly is a first-order logic? From my amateur standpoint, I think that first-order logic is a some kind of a system of symbols and general logical rules and ...
0
votes
1answer
87 views

The mechanics of logic [closed]

I am interested in how fundamentally important measurement is in the process of logical thought. At what point in the logical process are we no longer engaged in some form of measurement. Measurement ...
-3
votes
0answers
153 views

How do we get science interested in formal logic as a model of logic? [closed]

To the extent that deductive logic is thought of as a capacity of the human brain, and to the extent that formal logic is meant to be a model of it, I believe a scientific approach is badly needed. ...
2
votes
3answers
121 views

Why are non-logical predicates of 0-arity treated as logical variables?

In the "Non-logical symbols" section of Wikipedia, it states: A predicate symbol (or relation symbol) with some valence (or arity, number of arguments) greater than or equal to 0. These are ...
2
votes
1answer
63 views

'Truth conditions cannot simultaneously serve as both a definition of truth and meaning of sentence' What does this mean?

I am reading Hintikka's article on logical consequence in Oxford handbook of Philosophy of math and logic, and he was talking about the meaings of logical constants, when the following excerpt ...
4
votes
2answers
137 views

Can classical logic have deduction with infinite steps

I've been reading the Stanford Encyclopedia of Philosophy article on classical logic, and I've been confused about Theorem 9, and the preceding statement. They mention how (*), the clause which ...
1
vote
1answer
208 views

Does any mathematician today work on a logic he explicitly presents as somehow true of human logic, as Boole did in his time?

Mathematicians make sure their theories are logically consistent but not necessarily that they are somehow true of anything in the real world. This may be compared with scientists whose research ...
2
votes
1answer
146 views

Understanding Hintikka's scandal of deduction (as depicted by D'Agostino)

I am having trouble understanding Hintikka's Scandal of Deduction, as depicted in D'Agostino's article. According to this account, the problem stems from the fact that, while first order logic is ...
-1
votes
1answer
133 views

Do you know of any mathematical theorem whose proof relies on the use of the principle of explosion (ECQ)?

Ex contradictione (sequitur) quodlibet (ECQ) is almost universally recognised in mathematical logic as a valid inference. In symbolic logic, this inference is usually expressed in the following way: ...
0
votes
0answers
68 views

Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
4
votes
1answer
93 views

Given the principle of innocence, how shall we explain logic's usefulness?

I have been reading Florian Steinberger's dissertation (Harmony and logical inferentialism) and I come across the following on p60: ...two fundamental assumptions (the other one being the principle ...
-3
votes
4answers
182 views

A difficulty I've had with this “This sentence is false” and Russell's Paradox [closed]

I'm not sure if I'm engaging in some sort of circular logical trap but I don't really think "this sentence is false" is all that logically problematic. But it would be helpful if someone could fix up ...
4
votes
3answers
231 views

How is the nature of logical principles commonly defined in contemporary philosophy?

In contemporary philosophy, how exactly is the nature of logical principles defined? For example, the way I've commonly seen logical principles construed are as true propositions which described the ...
4
votes
1answer
127 views

What were the historical interpretations of Aristotle's definition of validity/logical consequence?

What were historically the various interpretations given to Aristotle's notion of validity, implicit in his syllogistic? Here is one authoritative translation of the relevant text: A syllogism is ...
3
votes
0answers
356 views

Which rational thinkers (theologians, philosophers, scientists, mathematicians etc.), prior to 1850, disagreed with Aristotle's logic?

Did any intellectual luminary ever articulate any major disagreement with Aristotle's logic prior to the inception of modern mathematical "classical" logic? Which rational thinkers, such as ...
2
votes
3answers
84 views

What does it mean to be a 'consequence'?

A Logical Consequence, in terms for formal language, is derivable from a given set of statements by manipulating symbols according to fixed rules. That I understand, for that is the only way to move ...
1
vote
0answers
155 views

Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ ...
4
votes
2answers
136 views

How much the world is logical [closed]

In her book The Art of Logic in an Illogical World, Eugenia Cheng writes:"I have already asserted the fact that nothing in the world actually behaves according to logic. So how can we use logic in the ...
2
votes
2answers
123 views

Justification of existing methods of formal logic [duplicate]

What is it that mathematicians, and more likely perhaps philosophers, give as an explicit justification that any method of formal logic, which is actually used by mathematicians, or even by automatic ...
2
votes
1answer
162 views

How did Wittgenstein become interested in the philosophy of language?

As far as I know he was doing engineering and became interested in the foundations of mathematics and went to Frege and upon his advice he went to study logic from Russell. So what happened which ...
5
votes
2answers
671 views

What are the philosophical implications of using inconsistent mathematics?

I have stumbled across the idea of 'inconsistent mathematics' and could not fully understand: why mathematicians would prefer at times to work with inconsistent systems (from which I assume everything ...
1
vote
1answer
64 views

Is logic a consequence of structure of language i.e. syntax?

I was reading the paper An elucidatory reading of the Tractatus and in page-3 section- Ineffabilist Readings, it was written "The order in our propositions, which renders them capable of thus ...
2
votes
1answer
183 views

What is the subject of Tractatus by Wittgenstein?

Is Tractatus about the Philosophy of language or Philosophy of logic. I was hearing John Searle's lecture and he said there are two strands in Philosophy of language :- 1. Logical theory of language 2....
2
votes
2answers
88 views

Completeness/Soundess of Second Order Logic

I recently read that Gödel's incompleteness theorem entails that second order logic cannot simultaneously hold the traits of: (i) completeness, (ii) soundness, and (iii) effectiveness. However, I saw ...
1
vote
0answers
34 views

Recommendation: Second Order Logic textbook

I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...
3
votes
1answer
60 views

What does predicative mean?

I'm reading this page https://plato.stanford.edu/entries/type-theory/ where the words predicative and impredicative are used in this context: Notice that for defining the predicate R, we have ...
2
votes
2answers
51 views

Are Statements with Existential Quantifiers General or Particular?

Consider the following argument: The number 2 is a prime number and is divisible by 2. Thus, some prime number is divisible by 2. The first statement in this argument concerns a particular, i.e. ...
1
vote
10answers
257 views

How could we get a world where only impossible things happen? [closed]

Imagine a universe where 1+1=3. This contradiction would trigger the effects of the principle of explosion, and thus, literally everything (possible and impossible things) could happen. If we lived in ...
6
votes
5answers
1k views

What is the difference between the “is” of predication and the “is” of identity?

What is the difference between these, the "is" of predication and the "is" of identity? For example, when I say, "my pet is a cat", am I using "is" as an identity or as a predicate?
2
votes
0answers
64 views

Is there such a thing as unary logic?

Is there such a thing as unary (as opposed to binary, ternary, …, n-ary) logic? cf. Is there any reason for the heavy focus on binary relations in formal logic?
3
votes
1answer
58 views

Concept Formation

I would like some suggestions about Concept Formation. Especially if there is a reference to Plato's Theory of Forms. I believe the two are linked but cannot find appropriate material. Thank you.
1
vote
2answers
953 views

Are the following statements necessarily true, necessarily false, empirically true, or empirically false?

All cats are animals. TV's did not exist before the 20th century. All bachelors who are married are both married and unmarried. What I think is the classification of each statement: Necessarily true....
3
votes
1answer
138 views

Can any logic system provide the impossible solution to Russell's paradox in naive set theory?

In naive set theory in classical logic, we cannot describe or find a solution to Russell's set paradox (it is impossible). But is it there any logic system or any method that can provide this ...
4
votes
2answers
1k views

Is there an English language example where modus tollens is valid but contraposition is not valid?

I was reading an answer by Bumble where the topic of modus tollens being valid but contraposition being not valid came up: https://philosophy.stackexchange.com/a/43004/29944 More importantly, there ...
0
votes
2answers
104 views

Are mathematics and philosophy in contradiction here?

Have I committed any mistake? Would you please enlighten me about the validity of this derivation? Thanks in advance! :)
2
votes
1answer
214 views

What is the relationship between “truth” and logic?

I'm fairly new to logic. What I've surmised from the book I'm reading is that Logic is the science of evaluating arguments Arguments are composed of statements Statements are sentences that can be ...
1
vote
2answers
54 views

Are syllogisms independent of humans?

For example, if "All a are b" and "All b are c" then "All a are c". To make this syllogism, does a conscious being need to exist? Or is it inferred from the sentences?
11
votes
7answers
2k views

Do premises need to be valid conclusions themselves?

I'm pretty new to logic. I recently purchased "A Concise Introduction to Logic" by Patrick Hurley based on reviews. So far I'm liking the book. I'm really focusing hard on the first chapter to get a ...
2
votes
2answers
270 views

Is causality a type of necessary and sufficient condition?

Does 'A caused B' mean that A is a necessary and sufficient condition for B? Imagine that we go to a shop and buy two items with a total cost 40 dollars (30 for 1st item and 10 for the 2nd). Is the ...
2
votes
2answers
65 views

Is coherence subjective

When an argument is dismissed by an individual for being incoherent, is there an objective standard to which coherence can be held? I'm trying to determine the difference between the statement "that ...
2
votes
1answer
131 views

Philosophical feminism and logic

Are there any resources to study about academic works on philosophical feminism and logic?
2
votes
1answer
168 views

How can “who is the creator of god” question make any sense?

Whenever the god as a first cause discussion comes up, somebody posts the rebuttal: "If everything needs a cause, then what is the cause of the creator god?". Let's define the universe as everything ...
2
votes
2answers
120 views

The possibility of talking about logic

I often come to think about the limits of logic, and the idea of thinking outside logic - but that seem like a very odd thought, as logic is suppose to represent our way of thinking, so to say "think ...
0
votes
3answers
242 views

Is Deductive Reasoning Alien to the Material World?

A quick survey of literature: Goel V. Anatomy of deductive reasoning. Trends Cogn Sci. 2007 Oct https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2685028/ García-Madruga JA, Gutiérrez F, ...
1
vote
3answers
297 views

Justification of deductive reasoning

Is a justification of deductive reasoning possible? If so, please tell me how because whenever I try to form a justification of deductive reasoning I end up committing the fallacy of circularity.
1
vote
1answer
83 views

Clarification of material conditional, logical necessity and causation

Are the following four statements always true - If Proposition B is the Logical consequence of proposition A, then B is material conditionally connected with A. If Proposition E is material ...
1
vote
5answers
129 views

Does the individual meaning of two propositions determine or constrain what kind of logical connectives can be formed between them?

What is the basis for the definition of logical connectives? Are they just arbitrary convention? Or does it depend on the meaning of the constituent propositions? Does the individual meaning of two ...
2
votes
3answers
192 views

What justifications have been given for using particular systems of logical calculus?

I think that using any particular system of logical calculus should be properly justified. This justification should be seen as particularly important and pressing in science and technology, and ...
0
votes
2answers
213 views

Do mathematicians take Modern Logic to be an appropriate representation of our sense of logic?

What examples do we have of mathematicians who explicitly and publicly expressed their personal confidence that mainstream modern logic, as used in mathematics, either as object of study in itself or ...
3
votes
1answer
67 views

On Putnam's belief that we can choose a logic system based on the task at hand

I was reading "A Graphic Guide to Logic" and a little speech bubble from Hilary Putnam says that "I still believe that there are facts in the world that determine which logic it is appropriate to use ...