# Questions tagged [philosophy-of-logic]

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

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### What are the philosophical implications of using inconsistent mathematics?

Why mathematicians would prefer at times to work with inconsistent systems (from which I assume everything can be proven unless changing the logic used)? In particular, how could working with an ...
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### 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 ...
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### 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....
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### 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
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### 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 ...
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### 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 ...
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### 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
538 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 ...
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### 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?
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### 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?
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### 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.
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### 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....
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### 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 ...
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### 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 ...
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### 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! :)
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### Can paraconsistent or other logics make the impossible happen?

A paraconsistent logic system it is defined as "a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that ...
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### 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
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### Philosophical feminism and logic

Are there any resources to study about academic works on philosophical feminism and logic?
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### 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 ...
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### 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 ...
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### 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, Carriedo N, ...
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### 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.
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### 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
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Is the set of all true contingent propositions equal to the set of all true propositions?

Since the conjunct of a true contingent proposition and a necessary proposition is contingent and hence it is contained in the set of all contingent propositions. Does that mean that the set of all ...
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### How different would mathematics and science be if we'd assume truth does not exist?

This comes from the question "Is human intuition consistent with current structure of mathematics?" I asked myself. Intuitively we agree on very many things and it seems we can "prove&...
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### What, at present, are the major unsolved problems of logic?

In the 1900s, Hilbert published a list of 23 (later 24) unsolved problems in mathematics, which sparked increased research into each of them and the subsequent resolution of several of these problems. ...
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### Why is Truth the default designated value in logic and language?

It seems that investigations of language and logic have focused on truth as the assumed designated value (the value preserved by valid entailments). It is only in later, non-classical logic that non-...
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### What is the relation between expressive completeness and semantic completeness

A formal system is expressively complete if and only if it is capable of expressing, as a formula, everything that is the subject of that formal system. A deductive system is semantically complete if ...
1 vote
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### Is the Completeness of a logical system considered an integral part any 'good' logical system?

Most logical systems will have two distinct forms of entailment, one is system-based entailment (logical consequence), and the other is proof-based entailment (derivability). In the former, an ...
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### The flaw of disproving the extreme by citing the norm

Let me first begin by saying that I do not have a formal background in philosophy. I was looking into formal logic and common fallacies and could not find a formal framework for the following ...
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### If the premises of an argument CANNOT all be true, then said argument is valid

Based on the fact that a deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false, I am ...
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### Why do we seek to "limit" our scope for the search after truth?

In philosophy and science, we quite often make systematic approaches that limits our thoughts to be as accurate as possible. Examples are endless - basically every logical system, every ...
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### Would you know if an answer is 'illogical' or just 'incomprehensible' (to you)?

I've seen good answers up voted and brilliant answers down voted. I understand that not everybody has the same intellectual ability. And, we do not know, what we do not know. Good answers are ...
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### Can you imagine a completely different logical/mathematical system than that we have?

Can you imagine a different logic and mathematics? For example, with a different arithmetic, or even a universe with no logic or mathematics and contradictions? A non consistent system?...
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### How could mathematics and logic exist without us, if they are concepts created by us independent of reality?

Would maths and logic exist if we didn't exist despite we created them, and do not have correspondence with reality?
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### What do we mean when we say there's only one type of logic/mathematics and that they can’t change?

Do we want to say that if they changed, they would not be logic/mathematics (as we know) anymore? How can we be sure that there's no other type of logic/mathematics?
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### Does computer science have an impact on Philosophy?

Recently I found some books in the domain "Philosophy of Computer Science." However, the majority of these books described how the logic and analytical philosophy can develop and understand computer ...
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### Philosophy of Time

I have a question about time. What philosophical arguments can be presented for the reality of time? And I would like sources to be posted too. It is confusing me.
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### Can 2 logical deductions starting from 2 different and independent sets of assumptions lead to 2 contradictory conclusions?

Can two formal logical deductions A and B, starting from different sets of assumptions H1 and H2 (if it helps, consensual facts about reality), each of them independent (that is, they don't imply any ...
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### Are all Informal Logic really just Formal Logic in disguise?

Are all systems of informal logic really just systems of formal logic that have not yet been understood mathematically?
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### Quantified Logic and Unquantified Modal Logic

Is there a need to study unquantified modal logic if one knows the quantified PC logic very well? There seems to be an obvious connection between Possibility and the Existential Quantifier, and ...
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