Existence raises deep and important problems in metaphysics, philosophy of language, and philosophical logic. Many of the issues can be organized around the following two questions: Is existence a property of individuals? and Assuming that existence is a property of individuals, are there individuals that lack it? What does it mean to ask if existence is a property?
Prove something exists . The word 'prove' suggests that formal reasoning must be deployed; thus he is implicitly disallowing you to point to the jar of biscuits and say 'that exists'. Turning then to Aristotles Organon his six books on logic) we see that he uses the word 'deduction' (sulligimos); so we ask - what, then is meant by a deduction ...
Logic can't in general prove that something exists by itself. Therefore most logical arguments in philosophy involve premises. The argument isn't definitive unless you can show that the premises are definitively true. Still someone could present something that looks like a logical argument for which the logic doesn't hold.
I'm just pointing out that your opening sentence contradicts the rest of your Answer. $\quad$ 2. Regarding your comment: it isn't complicated/tricky: the proof of "the conditional uniqueness assuming existence" is merely one part of the uniqueness proof, just as the proof of pigs fly ⇒ God exists simply isn't the proof of God exists. $\endgroup$
I prove by absurdity that there is no proof that $\sqrt{2}$ is rational, and because every number is rational or irrational, I proved that there exists a proof that $\sqrt{2}$ is irrational. and actually, because I proved such a proof exists, that proof of existence is itself the proof that $\sqrt{2}$ is irrational. so in logic, the proof of ...
A proof that a proof exists is a proof. However, it is not a direct proof. In essence that one cannot generate the proof, but one knows a proof exists. An example that will probably not count is "let x be the largest even number, prove that there is a prime number larger than x".
A non-constructive existence proof is trickier. One approach is to argue by contradiction – if the thing we’re seeking doesn’t exist that will lead to an absurdity. Another approach is to outline a search algorithm for the desired item and provide an argument as to why it cannot fail! A particularly neat approach is to argue using dilemma.
All logical arguments (logical proofs) start from some premise which is assumed true. The general form is "A, therefore B", or, hypothetically, "If A, then B". Consequently, any proof that something exists has to assume some premise that implies the existence of this thing. Example of a logical proof of God: If I see something, then it exists;
1 Logic. 1. Logical Operations; 2. Quantifiers; 3. De Morgan's Laws; 4. Mixed Quantifiers; 5. Logic and Sets ... Some of the most useful and interesting existence theorems are "existence and uniqueness proofs''—they say that there is one and only one object with a specified property. The symbol $\exists !x P(x)$ stands for "there exists a ...
ical style: a typical proof will omit the enumeration and present the proof as a single paragraph: Assume pis true, so that aand bare integers, ais even, and adivides b. By de nition, there exists an integer kwith a= 2k, and there exists an integer ‘with b= a‘. By substitution, we can write b= a‘= (2k)‘= 2(k‘). Since b= 2(k‘), bis even.
Many interesting and important theorems have the form ∃ x P (x) ∃ x P (x), that is, that there exists an object x x satisfying some formula P P. In such existence proofs, try to be as specific as possible. The most satisfying and useful existence proofs often give a concrete example, or describe explicitly how to produce the object x x.
But proofs depend on what you assume to be true. So, if you restrict what you assume is true, then sometimes there is no proof. Sometimes there is proof both of the assertion and also of its negation. It can also happen that the length of the proof is significantly larger than the length of the assertion. $\endgroup$ –
Existence and Uniqueness proofs are two such proofs. Both of these proofs rely on our understanding of quantification and predicates. Because you will be asked to show that “there exists” at least one element for which a predicate is true and how no other element has that particular property. Mastering Logic Proofs: Existence and Uniqueness
I heard someone make an assertion that 'We cannot really prove that there is reality.'. 'Reality' here would mean the universe and everything in it.You could look at an apple and think its an apple but it could really be something else, and we cannot really prove its "appleness".. My initial answer was the mere fact that having a notion for reality is proof enough that there is such a thing.
In logic, you cannot prove something about a thing unless you first assume something at least as strong as what you are trying to prove. For example, the only reason we can prove the uniqueness of prime factorizations is because the axioms we use are even stronger than that.
It is not defining sunshine; it is just stating something obvious. An axiom has the feel of something that should be justifiable or proved. a Oddly enough, though, axioms cannot be proved. They are jumping points for future logical deductions, but nothing exists to state that the axiom is true initially.
You can logically prove that logical arguments exists, and that something that can use logical arguments exists, and all that that implies. – Ask About Monica. Commented ... Regardless of assumptions. There are weaker frameworks where proofs are possible, but all frameworks themselves are based on assumptions. – rus9384. Commented Jan 25 ...
