# Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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160 views

### What is an example of a predictive conditional?

Can someone explain to me with an example what a predictive conditional is? Does this type of conditional have necessary and sufficient conditions?
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### syllogism, truth-functional, or neither?

I dreamed that John F. Kennedy was born in 1917, and everything I dream is true. Therefore, Kennedy was born in 1917. All horses are animals. Therefore, all heads of horses are heads of animals. If '...
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### How should one reconcile predicate functor logic with Quine's own ontological theory?

Quine proposed that "to be is to be the value of a variable". However, he also devised predicate functor logic (PFL), which effectively gives a recipe for eliminating bounded variables. How should ...
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### Understanding Lewis Carroll's argument on Modus Ponens

I read in an answer somewhere on this site that Modus Ponens involves an infinite regress. Upon reading Lewis Carroll's Achilles and the tortoise, I fail to see how. This is the excerpt from ...
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### What are the premises and conclusion of the Functionalist claim that “matter doesn't matter”?

I'm referring to the logical framework (the premises and conclusion) of the Functionalist argument that claims that two entities with indistinguishable inputs and outputs are the same thing, "matter ...
88 views

### 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 ...
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### How does one understand the second and third triad in Hegels Logic?

The first dialectical triad in Hegels Logic and put in a mathematical form is Being + Nothing = Becoming Although a strange sum, I find this understandable. His second dialectical triad takes the ...
39 views

### Reduced model of society

When astronomer, stars observer live in a city, they say: "Those artificial lights in the city, they confuse us, we are going out of this place, there the disturbing influences are fewer." When a ...
31 views

### Dictionary English - logic/formal symbols/expresssions

I'd like to know whether there's some kind of database offering the logic or formal" equivalent of English expressions, for example the conjunction "whereas", which has at least two meanings, each ...
83 views

### Is this a valid argument (using probability and uncertainties)?

If A, then B (probability of 0.6 that this is true) If B, then C (probability of 0.6 that this is true) A, Therefore C. I'm not sure whether C is probably true if A is true, or if the probability ...
80 views

### Quantificational vs Referential vs Predicational descriptions

Reading Peter Ludlow's article on descriptions, it's clear to me that descriptions can be interpreted, found or considered in 3 different ways. They can be seen as quantificational, referential or ...
318 views

### Create a statement in propositional logic. This statment must have 2 attributes. (The attributes are specified in the top header)

The following are the 2 attributes: (1) This statement claims the statement after it is true. (2) This statement cannot be not true. This statement would achieve these 2 attributes through its ...
196 views

### The sea battle paradox and the soundness criterion

Again a short look at Aristotle's resolution (one of many) of the sea battle paradox: In one famous example about a hypothetical sea battle, [Aristotle] observes that the necessary truth of a mere ...
162 views

I have a little question on logical fallacies and ad hominems. There's this problem: Person A and B are both hypocrites; they're both aware of this. Person A argues that B is a hypocrite, and ...
78 views

### How may Nikolaus von Kues’ “concept of concept” be applied as a bridge between logic and theology?

I am neither a specialist for logic nor for theology. Yet, I was electrified about Nikolaus von Kues statement that God is the concept of concept. Has Kues’ proposition somehow been applied as a real ...
45 views

### Are semantic inferences between undecidable sentences in a system possible?

For example from the Gödel sentence "G iff ¬P([g])", where g is G's Gödel-number, is it possible to make semantic inference (not syntactic, only at the level of truth between the undecidable sentences ...
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### How do we define a fact?

Got into a discussion today with my Semiotics professor regarding this question and I still had questions in my head on the way home. He was stuck on the notion that facts have just become things ...
235 views

### Axiomatic Proof of Symmetry and Transitivity of Identity

Given the axioms below and the rules of Modus Ponens and Universal Generalization, how can you prove that t=s → s=t for any terms s and t? Additionally, how do you prove that t = s → (s = r → t = r) ? ...
38 views

### Trees/tableaux fir K-IF logic

Are there any attempts for tableaux/ tree rules for Hintikkas K-IF logic?
406 views

### What is the difference between relational logic and predicate logic?

I am studying the Introduction to Logic course from Stanford University and I began learning about relational logic. However when I searched on google for the terms there I end up often with results ...
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### What consequences (types of) exist in the real world (categorical monoidal logic)?

Springer book http://www.springer.com/la/book/9783642128202 "New Structures for Physics" (which contains lot of metaphysics despite the physics in its title) elaborates categorical and monoidal ...
102 views

### Sufficient & necessary conditions for singular and general statements

In David Rynin's 1956 address to the American Philosophical Association, "Vindication of L*G*C*L P*S*T*V*SM", he remarks upon the "tenuous logical relationship" between a general statement, "For any ...
99 views

### Truth functional propositional logic for “If” in Hunter's Metalogic

I encountered a weird question in Hunter's Metalogic. Here's my reasoning: 'If' in 'If Tom marries Mary, Susan will be unhappy', according to Hunter, is not a "truth functional propositional ...
35 views

### What articles or books are currently considered canonical in the discussion of a priori knowledge and justification?

Quine's "Two Dogmas", I think, would be one. Perhaps also Putnam's "Is Logic Empirical". If you wanted to doubt the existence of a priori knowledge or justification on the basis of the apparently ...
55 views

### How can you intuit Information Implication with 4 Truth Values?

Source: p 158. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. [...] Call this Information Implication. Its truth table looks like this: This ...
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### Omnipotence Paradox Defense and Meinongianism/Neo-Meinongianism

I was considering a solution to the omnipotence paradox in which excluding logical impossibilities from the definition of omnipotence is justified as follows. Consider the proposition, "God could ...
244 views

### What are some active areas of research in proof theory?

Is there any research activity going on in the field of proof theory today? If so, what are some of the most active areas, what types of questions do they deal with, and where can I go to find out ...
102 views

### Using the conception of 'reliable, unchanging' does 'truth' exist?

An 'archaic' definition for TRUE,TRUTH implies constancy, reliability, unchanging, fidelity. Using this concept of TRUTH is the following valid? There exists either that which is TRUE or that which ...
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### Looking for a treatment of multiple interpretations in Model Theory/Formal Semantics

A sentence, such as a Godel string, can be given any intepretation whatsoever, so in a sense, when communicating, we have to be benevolent about the interpretation function that we infer our co-...
34 views

### What does *remediable* mean to philosophers? (Example and context provided)

In his essay, Knowledge of Logic, Paul Boghossian writes Finally, on the inferential path, there is the question whether it is irremediably true that rule‐circular arguments provide no ...
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### In Jain Logic what 'is' or 'can be' asserted to be true and indescribable?

Classically a truth value is asserted of a proposition: thus by its very nature it must be describable. Jain Logic has a 'truth value' which is asserted to be true and indescribable; by the above it ...
1k views

### Concrete Examples of Complex Term Analysis Using Predicate Logic

In all of my textbooks, there are no concrete case studies of how one can use predicate logic to analyze specific characteristics of complex terms. I am therefore looking for an exemplar for the ...
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### Liar paradox from a different view/resolved?

Informally, the statement T: T: "this statement is not both true and not true" a) T is not true if and only if it is both true and not true b) T is true if and only if it is not both true and not ...
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### Quick question on validity of arguments across propositional and predicate logic

Could someone clarify a quick question regarding the following please? From the text: Assume Γ ⊭ ϕ. Then there is an L2-structure A such that all members of Γ are true in A and ϕ is false in A. ...
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### Would logic be respected if we assume that the God's omniscience includes the ability to DIRECTLY OBSERVE future events?

If we assume that God knows the future, we think that the only possible way He could do that would be if He knew all possible states of the system. He could thus "compute" that future. But this "...
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### Social Constructivism and Logical Necessity

I am after some kind of reading list on the topic of logical necessity and social constructivism. Any recommendations? I'd like to be in a position to argue cogently that social constructivism can ...
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### Logical, semantic and self-referential paradoxes: The Truth teller and the Liar (draft) can an expert on the matter give feedback?

Title: Logical semantic and self-referential paradoxes: The Truthteller and the Liar (draft, informal) (major) assumption: A statement is either true or not true (law of excluded middle, classical ...
67 views

### Inductive Logic on Existence

Because we, only by inductive reasoning, are sure about next moment 'happening' (or more precisely, not worried about it not happening), does this mean that there is no logical guarantee that next ...
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### How to self-learn legal arguments, logic, and reasoning?

What are some readable, eloquent (without legalese) books on arguments, fallacies, logic, and reasoning, as applied and used in law? This question is aimed towards a greenhorn/tenderfoot with ...
48 views

### Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
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### Was Russell's purpose in Principia Mathematica to formalize all the possible constructions of logic?

In writing Principia Mathematica, was one Russell's purposes to formally describe all the possible variations of logical concepts and reasoning that can be used in mathematics? For example, suppose ...
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### How to derive P > (Q > R) from (P > Q) > R in Fitch?

I am having a little bit of difficulty coming up with a Fitch-style natural deduction proof. Presumably, I need to use a few conditional introduction rules, but I am not sure what I can get out of ...
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### To connect or to disconnect mathematics and platonism?

How [do philosophers] strongly support or refute the view that: mathematics is a bag of tricks for real-world problem solving; undecidable statements are an irrelevant and harmless side-effect of an ...
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### Complement of “at least two people share the same birthday”

Suppose a room contains 𝑛 people. What is the probability that at least two people share the same birthday? So this is actually a question on probability, but I'm really confused in the logic and ...
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### Logic Question in a fitch style system - disjunction elimination

I am having difficulty in formally proving two arguments. Firstly, given the premises A ∨ (B∧C) ¬B∨¬C∨ D derive A v D. I can see why it has to be either A or D, because if it's B and C, ...
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### Clarifications on 1) Modus Ponens, 2) Modus Tollens, 3) Inductive, 4) Incomplete based on examples

My second lecture on Hypothetico-Deductive methods (based on Popper's falsification theory). In the class, we were given the following examples. We had to classify which examples belong to 1) Modus ...
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### Does Barrow and Tipler's “anthropic principle-multiverse” entail the existence of all logically possible universes?

I've read several texts that indicate that the anthropic principle (applied to cosmology, and more specifically, to the multiverse) yields the existence of all logically possible universes (most like ...
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I noticed something about the liar paradox, when the liar sentences are taken as questions. Let’s start with the liar index, “This sentence is false.” Allow this to be questioned: “Is this sentence ...