New answers tagged

0

Conditional is a Logical connective used to form expressions (formulas) of the language. Logical implication is a relation holding between set of formulas and a formula. Thus, they are two different concepts. But they are strongly related: in propositional logic, for example, we have that: the formula A → B is a tautology iff B is a logical consequence of A ...


-1

Saying something is a non-sequitur typically implies that a formal fallacy has been committed; that a deductive argument has been made which has an invalid form. The term can also be used more casually to refer to something which more generally just doesn't make sense (especially by way of the last part of a statement/assertion being unrelated to what came ...


2

The problem is not just scientific, but moreover philosophical (philosophy being the mother of all sciences). Classical science dismissed the subject as if it would not exist. The perspective of the subject was considered always as an absolute truth, which implies that no other truths are valid, and that there's almost no subject, assuming that any ...


1

Short answer: no, statements in physics don't always assume an observer. There are many perfectly legitimate statements in physics that do not (and often cannot) assume an observer. I'll give two examples. The Schrodinger equation tells us how the quantum state evolves in time. But there is no way to observe the full quantum state. So the Schrodinger ...


4

Standard translations for each do require the biconditional. We translate "P, if Q" as "Q -> P" We translate "P only if Q" as "P -> Q" So when we combine "P, if Q" and "P only if Q" we get "P <-> Q" We translate "All As are Bs" as "ALL(x)(Ax -> Bx)" We ...


0

Not really an answer, but an attempt at giving an idea of a the syntactic approach. Suppose you want to prove that if n = a+a then, logically, n = 2a. If you want to prove the statement is true for a small domain say, for 0, 1, 2...... 9 , you may use a semantic method. That is, you will consider all the possible interpretations of the sentence: 0+0 = 2....


2

A problem arises when reasoning with doubly quantified sentences and binary predicates. For example: AxEy R(x,y) (Premise) Ey R(a,y) (UI 1) R(a,a) (EI without respecting the prohibition on reusing names 2) Therefore, Ex R(x,x) (EG 3) Now take the domain to be the natural numbers and R to be the 'is less than' relation, <. Obviously, the premise will be ...


0

You know sometimes official tests ask questions that aren't very good and we just have to be ok with it unfortunately. Nobody and nothing is perfect including standardized tests. I scored fairly well on standardized tests in high school and myself encountered several "bad questions."


3

I will give an example from a recent paper That We See That Some Diagrammatic Proofs Are Perfectly Rigorous by Azzouni. It has been a common opinion since Pasch and Hilbert that proofs relying on diagrams, such as proofs in Euclid, lack in rigor because certain assumptions used in them are left implicit in the proof, and do not come up in the course of it. ...


2

Let me add to the existing (very good) answers. First of all, there's an implicit assumption in your question that philosophical interest comes from strength. This is unjustified, especially given the general tradeoff between strength and tameness. Weaker logics correspond to simpler types of argument, and that might be a very interesting sort of thing in a ...


0

There is no fallacy the reasoning is valid. First, yes both Bibles printed with rare ink formulation suggests their common origin -- that part is simple. For the map, it's just a bit more complicated. Here is the original claim: ".. the presence of titanium in the ink of the purportedly fifteenth century Vinland Map can no longer be regarded as a reason ...


0

I think the best answer to your question is that given your hypothetical example, multiple biases and informal fallacies could apply. For example, secundum quid, an informal fallacy, occurs when the arguer fails to recognise the difference between heuristics and universal truths. In your example, a person had lied before, so what they have just said is also ...


0

"Will these observations lead you to question the validity of Aristotle's syllogism?"   I don't see how. And, like others commenting here, I am surprised that you are considering such a possibility -- but let me explain what I mean.   When confronted with something that defies our expectations, our understanding of the way things are, we, humans, ...


0

I think the best answer to your question is that given your hypothetical example, multiple biases and informal fallacies could apply. For example, secundum quid, an informal fallacy, occurs when the arguer fails to recognise the difference between heuristics and universal truths. In your example, a person had lied before, so what they have just said is also ...


0

Short Answer No, for a complex of reasons. Long Answer From a technical standpoint with logical formalists, a fallacy must be an inference. The statement you have presented here is, strictly speaking, a proposition and is specifically an example of material implication sometimes called the conditional. Generally, an argument is taken to be at least one ...


2

If P is valid, then the tableau for -P eventually closes. only states completeness: If P is valid, the tableau will find out. This does not rule out the possibility that the tableau will also close on the negation of some formulas that are not actually valid. Soundness thus has to be expressed separately; it is the converse direction: If the tableau for -P ...


0

Answer Both CraiglCraigl and Bumble have done a good job pointing out the two important issues in flaws in your reasoning, and I am going to approach the problem from a slightly different angle. For starters, it is important to see that there is no Bayesian reasoning presented conceptually in the text. So, what you are looking for is feedback on how your ...


1

You say: "There was strong evidence that the Vinland Map was from the 15th century..." but this is not actually given in the question. We are only told that the map's authenticity has been challenged on the grounds that its ink contains titanium and this was previously believed to be unknown in the 15th century. The discovery that two 15th century ...


0

We recently discussed 'Does reality have axioms?' and I think my answer there applies to this too Does reality have axioms? We see patterns, in our minds and the world. That is what our minds are built to do. Logic is within definitions, like sets of axioms. But the universe is not - when it is alogical or illogical we know our understanding of the patterns ...


0

By "logical," I assume you mean orderly. If so, the answer is all over the map. The desire to either discover something orderly or impose order on chaos appears to be human nature. However, a philosopher named Albert Camus is known for his principle of absurdism. From The Stanford Encyclopedia of Philosophy's article "[Albert Camus]"...1 ...


1

it depends on what you mean by "Logical". Do you mean whether the laws hold regardless of any changes in circumstances such as Newton's Law of Gravitation? OR that the laws are derived via logical means? Philosophers sometimes differ on their conception of meaning and there have been arguments in the Philosophy of Logic about how much logic there ...


1

Set theory tells us that the empty set is a subset of every set, meaning that, whatever the set S may be, the empty set in included in S. The set of goblins is identical to the empty set ( for there is no goblin). So, the set of goblins is included in the set of people you talk, have talked or will talk to. Now, why is the empty set included in any set ...


-4

It's simply not a valid deduction. The premises have no relevance to the conclusion. A valid deduction requires all 3 to be relevant to one another. I understand there are lots and lots of theories, wordplay and semantics about terms in philosophy, but in the main they seek to confuse and not clarify nor reach knowledge. The reason why so many deductions ...


1

Either the word " this" ( used as subject in the conclusion) refers to something or not. If it does not, the alledged conclusion has no meaning and therefore is not a proposition. In that case , there is no question as to the validity of the " argument" for there is no argument. For an argument is a sequence of genuine propositions. ( ...


9

Some of these might plausibly be called extensions of classical logic rather than non-classical in the strict sense, but I'll take your question as a broad one about logics that progress beyond elementary classical first order predicate logic. It is not exhaustive. Valency: Bivalent. Multivalent. Not n-valent for any n. Fuzzy. Probabilistic. Order: First-...


3

Peirce introduces objective and subjective possibilities in the context of describing gamma graphs, an extension of his diagrammatic proof system (existential graphs that are expressively equivalent to the usual predicate calculus) to modal logic. "Subjective" means what we today call epistemic (possibility), while the earlier accounts of modal ...


-4

Aristotle? 2,500 years ago? Example? Yes, the implication φ → ξ is of course not true: φ → ξ Now, look here: (φ → ψ) ∧ (ψ → ξ) ⊢ φ → ξ Hey presto, the same implication, φ → ξ, now is true, given some assumptions, namely, φ → ψ and ψ → ξ. One mistaken comment on my answer led me to edit it to replace Aristotle with Theophrastus as the first logician to ...


2

Logic is commonly, though not universally, understood as separating form from content. On this understanding, the form is the logical part, and is traditionally taken to be a priori, while the content is the empirical part. If we can completely and successfully separate the parts of a sentence that are formal from the parts that are not, then we have grounds ...


0

Always meaningful would be closer to the point. There are three contingencies for any spiritual (non-material) questions, salience (which is akin to having skin in the game - the situation having expected and meaningful effects to you), perspective, and priority. Having skin the game aka being invested, means that since you care, you're more likely to ...


1

Long comemnt The key point in Tarski'approach is in the clause: "apart from purely logical constants". The logical constants (aka: syncategorematic terms) are... constants: they are not "reinterpreted" when we change the interpretation of the signs: [they are not] affected by replacing the designations of the objects refereed to in these ...


0

I'm going to offer an answer to the first of your three to show a strategy for getting from the natural language to an artificial formalism. Q1: Everything with a moon orbiting around it is bigger than a planet. I'm going to take 'a planet' as all planets because I'm interested in presumptions in natural language convention. If someone says 'Everything ...


1

See Charles Sanders Peirce, Collected Papers : Volume 4. The Simplest Mathematics (1933), page 13: [4.12] A Boolian Algebra with One Constant [untitled paper c.1880] Every logical notation hitherto proposed has un unnecessary number of signs. It is by means of this excess that the calculus is rendered easy to use [...]; at the same time, the number of ...


0

Your "computationally omnipotent God" is really just an oracle in disguise (as it should be). Call it oracle and be done.


1

Hi these would be my answers: Q1: Everything with a moon orbiting around it is bigger than a planet. (∀x)(∃y)((My & Oyx) ⊃ (∃z)(Pz & Bxz)) I think you would require a third z to indicate the predicate "planet". Q2: Some galaxy is not bigger than all of the moons. (∃x)(Gx & (∀y)(My ⊃ ~Bxy)) This would my answer for Q2 although I ...


1

Short Answer There is no royal road to a strong argument. It takes a lot of diligence and mastery of a number of subject matters including mastery of the facts of the domain of discourse, formal and informal logic, linguistics, argumentation theory, and having a good range of argumentation examples. Professional philosophers spend their whole lives trying to ...


-1

Only stars have planets orbiting around them. AxAy(S(x) /\ O(y,x)) -> P(y)) "Only A B" means "if B then A", not "if A then B": "Only stars have planets which orbit them" translates as if there is a planet orbiting x, then x must be a star, which by the truth table of -> is false exactly when something has a ...


0

I'd like to hear more about what you mean by "computational step." If by "computational" you mean what we normally mean when we speak of computation, then my hunch is that there is no such entity, since we finite humans have a pretty good grasp on what computation is, and there are some sets with Turing degrees >1. If you mean ...


2

The expression " the number of sheep in this problem" is a definite description , " the so and so". And definite descriptions seem to be referring expressions, while they may not be, either due to the fact that (1) there is more than one object that satisfies the property, or (2) there is no such object. More deeply, definite descriptions ...


2

There's a point of view that topics of inquiry move out of the realm of philosophy and into the realm of science when they become codified, standardized, well-understood and reliable. In contrast, live philosophical topics are speculative, open-ended, dimly understood, and controversial, almost by definition. In other words, philosophers invent sciences, ...


1

I will assume that by A being logical, you are tacitly implying that one can deduce A from certain established premises. When you say that B is proven to be logical, that is a dubious claim. Let us first define when we mean as being 'logical' in this exigent. The proper language is 'sound'. Suppose there are certain true facts about the world (suppose). You ...


2

Short Answer FOL is a simple model of human reasoning, and much like simple models in general, it is a pedagogical aid in introducing students to the formal aspects of logic without being unwieldy and overcomplicated. One, after all, could make the argument, why teach many formal logics since they are clearly a limited aspect of human reason itself which is ...


1

There are certain limitations to FOL, particularly the Lowenheim-Skolem theorem which is why we have to use HOL for models which are uncountably infinite because using an countably infinite number of sentences we can always construct a countable model. For very elementary definitions in Mathematics such as the least upper bound property for real numbers (or ...


6

Firstly, the fact that the ancestor relation cannot be defined in FOL is not itself a philosophical difficulty. It relates mainly to the issue of consistency and completeness and their omega counterparts over infinite domains. It hardly means that FOL is extremely limited. Your question could reasonably be split up into separate components. Why are ...


0

Yes, that is valid, although the justifications are "conjunction elimination" and "conjunction introduction". You should also include citation of line numbers.


0

Jane not "actable" - limits of deontic logic Let's write some sentences using traditional normative statuses : You must kill Julius Caesar You are permitted to kill Julius Caesar You must not kill Julius Caesar You are permitted not to kill Julius Caesar You may kill or not kill Julius Caesar as you wish Does any of these sentences have any value ? ...


1

To say of two sentences that they are logically equivalent is usually understood to mean something like they are true under the same interpretations, or they share the same models. To use less technical language, there is no possible way for one of them to come out true and the other false. Any two contradictions are logically equivalent, since there is no ...


-2

Logic (Logic) the branch of philosophy concerned with analysing the patterns of reasoning by which a conclusion is properly drawn from a set of premises, without reference to meaning or context. See also formal logic, deduction4, induction4 (Logic) any particular formal system in which are defined axioms and rules of inference. Compare formal system, formal ...


Top 50 recent answers are included