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Consider an example

A

A V ~B (addition)

B > A
It seems logically vaild .

Now assume A is being apple and B is banana .

So its equivalent

**It's Apple

It's apple or not banana

If it's Banana then it's apple **

Clearly it's not valid .

So what kind of fallacy I did here ? This addition step is always confusing for me ? I am unable to distinguish when this step is vaild or not ?

Rishi
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  • You seem to be confusing VALID with being TRUE in the real world. Valid does not mean true in the real world. Consult a logic text or a professional to clarify. The step of addition is always valid. An argument can be logically valid but false in reality. You are having issues with that it seems. – Logikal Feb 04 '21 at 19:03
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    @Logikal - A valid argument can only be false in reality if one or more of the premises is false in reality, but I think Rishi is assuming a situation where the object under consideration really is an apple, in which case the premises "it's an apple" and "its an apple or a non-banana" would both be true. The real problem here is that Rishi is confusing the material conditional in logic, which has a specialized meaning, with an if-then statement in ordinary English, i.e. an indicative conditional (I commented on the difference [here](https://philosophy.stackexchange.com/a/69416/10780)). – Hypnosifl Feb 04 '21 at 23:23
  • @hynosifl, the point I was making was that truth is an entirely different matter to validity in Mathematical logic. Whether there is a false premise is irrelevant to the argument validity. As such validity has no direct correlation to reality. Sure you can sometimes make valid arguments that apply to reality but for each one you make another person can show an impractical valid argument in reality. What do you have left: a system of thinking that at beat gives you 50 - 50 chances on applying to reality. One would have to state that logic is more than being about validity which is taught. – Logikal Feb 04 '21 at 23:54
  • @Logikal - I agree truth and validity are different, and that an argument can be valid even with false premises, but do you agree that *all* logically valid arguments that have premises that are true in reality also have conclusions that are true in reality, assuming no semantic ambiguity in the meaning of the propositions expressing the premises and conclusions? – Hypnosifl Feb 05 '21 at 03:40
  • @hynosifl, YES but the term soundness is usually not mentioned right away but people focus on validity & are taught that way. So when I was taught the focus was NOT VALIDITY but soundness so that the reasoning DOES APPLY TO REALITY. So yes we can agree on if the premises are true in reality the conclusion and reasoning will apply. Focusing on soundness instead of validity is more of an epistemological concern. When I went to school we just said LOGIC. Today epistemology is a distinct field due to the rise of Mathematical logic. So the term logic is still ambiguous due to the other ttpes. – Logikal Feb 05 '21 at 04:18
  • @Logikal Yes that's what I am confuse about ? Even though both premises are true and conclusion is vaild , logic fails in real world . Does that mean that all vaild logic Arguments are not necessarily universal ? They can both be true and false from different cases . If that's the case then , how logic is trust worthy ? – Rishi Feb 05 '21 at 05:50
  • @Rishi stop confusing VALIDITY WITH TRUTH. Understand that Mathematical logic doesn't always apply to reality. Sometimes it will apply and sometimes it doesn't work in reality. I get it that confuses plenty of people only use true premises and then you have nothing to worry about. Focus on soundness then your reasoning applies to reality. – Logikal Feb 05 '21 at 05:58
  • @Rishi - Why do you say "logic fails in the real world"? If "Apple(a)" is true then "Banana(a) -> Apple(a)" is a true statement, as long as you understand the material implication symbol -> is defined entirely by [its truth table](https://en.wikipedia.org/wiki/Material_conditional#Truth_table) and don't confuse it with an ordinary English if-then statement, which it is not meant to be equivalent to. Did you see my earlier comment on the difference between the material conditional and the [indicative conditional](https://plato.stanford.edu/entries/conditionals/) of ordinary language? – Hypnosifl Feb 06 '21 at 17:40
  • @Logikal - "stop confusing VALIDITY WITH TRUTH" It doesn't look like Rishi is doing this, they are talking specifically about a logically valid argument from two premises in a situation where both premises are true in reality, therefore it is completely correct to say that the conclusion should be true as well. I agree it's common for ppl to confuse validity with truth, but nothing about this specific question suggests such a confusion. Again, the problem is that Rishi is translating "Banana(a) -> Apple(a)" as "If it's Banana then it's apple", but the latter isn't necc. equivalent in meaning. – Hypnosifl Feb 06 '21 at 22:21
  • @Hypnosifl, you are WRONG! Rishi directly says so in a few comments above this one. He posted it yesterday. You need to read it. He is directly stating that the validity is confusing him because the reasoning in some cases ends up false in reality. Hence the question and example he used. Your comprehension of his text is off. This is what many people who listen to the math people feel but maybe scared to say something face to face with direct faculty in school. Math teaches logic is about VALIDITY. This was not always so. I was not taught that. I focused on soundness when I was learning. – Logikal Feb 07 '21 at 00:01
  • @Logikal I did read his comment, I think you are interpreting it wrong. Seems to me that Rishi's confusion is that he's familiar with the idea that a logically valid deduction from true conclusions should also be true (that's why he said 'Even though both premises are true and conclusion is vaild'), but he thinks in this case we have a logically valid argument from true premises that leads a false conclusion, namely "If it's Banana then it's apple". Again, his mistake is a mistranslation of the logical conclusion "Banana(a) -> Apple(a)" into an English statement with an indicative conditional. – Hypnosifl Feb 07 '21 at 01:50
  • @hypnosifl, it is more like he is confusing validity with truth himself and as a result he formed an argument where the conclusion is clearly false. Why don't you see it that way? He seems to already know the premises are true. He even says "clearly it is not valid". This indicates he is expecting the conclusion to match reality and it DOESN'T. This is why he is asking the question. Why do you not see it this way? He is thinking validity is supposed to match reality. – Logikal Feb 07 '21 at 03:13

2 Answers2

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No fallacy at all: the argument is valid.

It is the way the Conditional works in classical logic.

If we assume A, our assumption amounts to saying that we accept it as true.

Thus, also B → A will be true, because a conditional with true consequent is true.

Obviously, you have not proved that B → A is a tautology (i.e. valid, always true); you have proved that A implies B → A.

It's apple. Therefore, If it's banana then it's apple.

Mauro ALLEGRANZA
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I think you misunderstand the difference between the (formal) logical implication and the material implication.

Material implication is a binary connective that can be used to create new sentences; so → is a compound sentence using the material implication symbol →. Alternatively, in some contexts, material implication is the truth function of this connective.

Logical implication is a relation between two sentences and , which says that any model that makes true also makes true. This can be written as ⊨, or sometimes, confusingly, as ⇒, although some people use ⇒ for material implication.

k-wasilewski
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