# Questions tagged [propositions]

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### What is the truth value of the proposition 'All unicorns are beautiful'?

If we let Fx denotes that which has the property of being a unicorn, and Gx denotes that which has the property of being beautiful, then this proposition would be signified by the following: ∀x(Fx→Gx)...
636 views

### Shouldn't statements be considered equivalent based on their meaning rather than truth tables?

Consider the following truth table, which serves to define the logical connective ⇔, P | Q || P⇔Q T | T || T T | F || F F | T || F F | F || T According to the above truth table, the logical ...
639 views

### Existential import: in logic, do propositions default to true or false when objects in them do not exist?

In this hypothetical: Firefighters always tell the truth, while politicians always tell lies. Suppose three people, who are either a mix of firefighters and politicians, all politicians, or all ...
1k views

### Intuitively, why are Universal Statements true in the Empty Universe?

Source: p 165. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. I read this on Math SE; please advise if it pertains to my simpler question.   One property of ...
209 views

### Is the principle of non-contradiction self-evident?

The principle of non-contradiction is that contradictory propositions cannot both be true, e. g. the two propositions "A is B" and "A is not B" are mutually exclusive. However, whenever something is ...
181 views

### How does one judge “complexity” of assumptions for the purposes of “best explanation”?

The context for this question is from assessing theological arguments from the point of view of 'inference to the best explanation'. In philosophy (and science), we may wish to argue that some ...
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### The nature of elementary propositions in the Tractatus

So all complex objects in the world are, at the most fundamental level, made up of simple un-analysable objects which are denoted by 'names'. Combinations of simple objects constitute 'states of ...
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### Definition of proposition

The term proposition has a broad use in contemporary philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other "propositional ...
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### Making 'sense' of Wittgenstein's senselessness / nonsense distinction in the Tractatus

For this question I'm just considering Wittgenstein's theory at the time of the Tractatus. As far as I know, for Wittgenstein: Meaning - The object denoted by a word (i.e. referent). Sense - The ...
17k views

### Difference between a sentence and a proposition in philosophy [closed]

Explain and illustrate the difference between a sentence and a proposition in philosophy
213 views

### Can one have propositional knowledge without knowing the corresponding proposition?

The concept of propositional knowledge -- knowledge that one has through holding a justified belief in a proposition that states a fact -- is a foundational one in epistemology (for example, it is ...
207 views

### Why isn't “I am Bill” a proposition?

In fleshing out the traditional definition of omniscience, William Lane Craig distinguishes between propositional knowledge and non-propositional knowledge, claiming that to be omniscient is to know ...
90 views

### Are analytic propositions always vacuously true?

In a possible world where there are no bachelors is the proposition "bachelors are unmarried" vacuously true? Or is it tautologically true and you would then need to quantify bachelors as "all ...
471 views

### Implication Introduction formulated as a theorem?

While making a list of the rules of inference for my math students, I came across this list on Wikipedia: I noticed a pattern: for every introduction rule, there seems to be an elimination rule, and ...
269 views

### can we know whether the self-referential statement: “It's not possible to deduce whether P1 is true or false” is undecidable?

Update: Simple concise version Thanks to Nick R for pointing in the right direction. The statement P0: "this statement is false" is undecidable. The statement P1: "this statement is undecidable" is ...
1k views

### How do you prove that this is a tautology?

((p->q) and (r->s) and (p or r)) -> (q or s) How would you prove that this is a tautology? Using natural deduction? My attempt on this question is the following. Since a tautology means W entails ...
102 views

### Analyticity and a priority

(1) Every bachelor is unmarried. I know this is one of the most famous examples (intensionally) denoting analytic and a priori propositions. No problems yet. (2) Every apple is a fruit. This one ...
191 views

### What are the rules for a zero-premise derivation involving disjunctions?

I'm having trouble with the following zero-premise deduction that involves two disjunctions: The solution seems simple, but I'm unsure of how to proceed with the two disjunctions. If it were just ...
130 views

### Wittgenstein and Picturing Relationships

I've been listening to BBC's "In Our Time" on Wittgenstein here, but I can't seem to understand why Wittgenstein thought that "a proposition can't picture the pictorial relationship." One of the ...
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### If we assume that principles are the simplest propositions that can be said about an object, can they coherently be rejected?

An argument for some sort of 'principles' in the Aristotelian sense is as follows: 1.) If we can think something about something, we must be able to think at least the most simple of propositions ...
159 views

### Problem with propositions about future

I have some questions about propositions of future like “tomorrow, there will be rain” or “you won’t go to school tomorrow” 1) Are there certain truth values of future propositions? For example, ...
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### Understanding multiple values in a single cell of a truth table (P v ~Q) as (1 1 0 1) when P and Q are 1

This might seem basic to most here but I am struggling with a truth table for a disjunct. As I am looking at it further, I actually think the issue I am struggling with how to interpret truth values ...
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### Conjunctive and disjunctive assertions

I am a new learner to logic and philosophy, after spending some time reading Introduction to Logic by Copi, Cohen & McMahon, I'm stuck on this matter... please help me so I can read forward... ...
956 views

### In propositional logic, why can a FALSE antecedent of conditional be simplified to TRUE?

Please help me formulate my sentences/thoughts here into logical jargon and solve Case 2 below. Why does the truth table for an implication → look like this: | p | q | p → q| | T | T | T | | T | ...
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### Why is questioning everything around us so important?

I've heard something disturbing from my friend. He said he's grateful to his father because his father taught him to question everything that was around us. Why is this so important?
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### What are factual propositions?

I've been reading up on epistemology, after having studied a bit of logic. Given that, I am in a good (or at least better) position to understand a proposition, and it's properties. One such property ...
86 views

### A∧B-worlds and law of enrichment in Stalnaker semantics

In Stalnaker semantics a conditional A↦B is true in world u if either A is not logically possible (ex absurdo quodlibet holds in the semantics) or A is logically possible and B is true in the nearest ...
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### A set of three statements, of which only two at a time can be true: is there a specific term for this type of combination game?

Here's two examples of what I'm talking about 1 An ideal citizen would be smart, ethical and politically engaged. However, what usually happens in reality is this: If they're smart ...
367 views

### How does a truth tree provide positive and negative effect tests for implication?

I'm trying to prove that the truth-tree method can be used to give a positive effect test for implication, and a negative effect test for non-implication. I've been given the fact that The truth-tree ...
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### Can the word “probably” be used in a proposition? (logic)

I'm interested in applying logic to day-to-day reasoning. The problem is that formal logic seems really restrictive to limit inductive arguments to be only universal ("all swans are white"). Few ...
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### How did Aristotelian logic view this?

I am very interested in the logical aspect of Aristotelian philosophy, especially how it was used by al Farabi and Ibn Sina in explaining understanding and breaking this complicated process down ...
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### Why don't two equivalent propositions contribute to the same semantics?

We often have 2 propositions that have the same truth table, in that they are true and false given the same conditions. Nevertheless, we still feel as though there different semantics (i.e meaning..),...
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### Russell on Negative Facts

Okay. I am reading Russell's paper "On Propositions: What They are and How They Mean". Since the truth or falsehood of a belief depends upon a fact to which the belief "refers", and propositions are ...
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### Can the material conditional be used in other situations?

Can the material conditional in classical logic (e.g. propositional logic or predicate logic like first-order logic) be used to reason about propositions that are not factual? E.g., using a ...
374 views

### Is there a logical system that accounts for cause and effect relationship?

The reason I ask is because of the ambiguity of some statements when the conditionals of a condition are not referenced by tense i.e time. For example, in the Cognito Ergo Sum 'I think therefore I am',...
799 views

### Why is the statement false: If (A⊃B)∨(A⊃C) is true, then A implies either B or C

I'm reviewing my previous exams for the final, and the only two true or false questions that confuse me are: If (A⊃B)∨(A⊃C) is true, then A implies either B or C. (P⊃Q)∨(P⊃~Q) means P⊃(Q∨~Q). The ...
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### Wittgenstein criticizes Coffey's work 'The Science of Logic' in its assumption that every proposition requires a subject and a predicate. Why?

Why does Wittgenstein believe there can be propositions that lack a subject or predicate? What examples does Wittgenstein give in support of this belief?
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True or False? If monkeys can fly, then 1 + 1 = 3. What is logically equivalent to all x (p(x) + ~q(x))? For the first one I think it is False.
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### Can we know a predicate without a subject, non-propositionally? [closed]

Can we have non-propositional knowledge, for example knowledge of a predicate without a subject? I think an example would be: only this is now, which uses indexicals. I'm asking because I wonder ...
179 views

### Into what category does following view place me in moral philosophy?

At first, I believe the statements like "Pete is wrong" and "Mike acts in a bad way" have some cognitive value. At first glance, this puts me to ethical cognitivism. But at the same time I think the ...
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### Confusion about an implication's contrapositive

I just begin learning propositional logic and find a little bit confused when trying to translate the contrapositive of an implication back to the English language. For example, I have an ...
369 views

### How is this premises and conclusion to refute Searle's CR experiment?

So I've been digging into this topic for days now. I've gone through his paper and also some threads here, which I found were very helpful. I came up with these premises and following conclusions in ...
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### Is what makes a proposition true only determined by its referent?

I was wondering if it is trivial that when the content of a belief can be given or "determined" by mind independent reality, the belief is "about" mind independent reality. I think that the content ...
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### Would the absence of universals not make it impossible to make and/or express judgments?

Predication is an integral part of making a judgement, which is expressed in propositions (such as 'the sun is round'). Predication itself is possible because in some sense something can be said of ...
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### Alternate axioms for relevant logic R

Relevant logic system R can be defined -as I read in D. Palladino, C. Palladino, Logiche non classiche- by the following axioms A→A (A→B)→((C→A)→(C→B)) (A→(A→B))→(A→B) (A→(B→C))→(B→(A→C)) A∧B→A, A∧B→...
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One theory of propositions is that they're "useful fictions." However, this faces the formidable objection that fictionalism makes it hard to explain how something fictional can tell us about the ...
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### If logical propositions aren't tautologies (a la Wittgenstein), then what could they be?

This is a historical question about philosophical views. I believe I understand the claim made by Wittgenstein and others that logical propositions are tautologies. I'd like to know what other views ...
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### 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 wording....