如果A为假而B为假，为什么A暗示B为真？

在我看来，英语中的“隐含”与逻辑运算符“隐含”的含义不同，在大多数情况下，“或”一词在我们日常语言使用中的含义类似于“异或”。

让我们举两个例子：

如果今天是星期一，那么明天是星期二。

这是真的。

但是，如果我们说：

如果太阳是绿色的，那么草是绿色的。

这也被认为是正确的。为什么？这背后的自然英语“逻辑”是什么？这让我震惊。

在必须使用逻辑来解决人的事情之前，人对逻辑是不好的。可以将“ 如果然后$A$$B$ ”视为一种承诺：“我向您保证，如果您执行那么我将执行B ”。这样的承诺并没有说明如果你不做A我会做些什么。实际上，无论如何我可能都会做B，但这不会使我成为骗子。$A$$B$$A$$B$

例如，假设您的母亲告诉您：

如果您打扫房间，我会做煎饼。

让我们说您没有打扫房间，但是当您走进厨房时，妈妈正在做煎饼。问问自己，这是否使你的妈妈成为骗子。它不是！仅当您打扫房间但她拒绝做煎饼时，她才是骗子。她决定做煎饼可能还有其他原因（也许是您姐姐打扫了她的房间）。您妈妈没有告诉您“如果您不打扫房间，我不会做煎饼”，对吗？

所以，如果我说

“如果太阳是绿色的，那么草是绿色的。”

这不会使我成为骗子。太阳不是绿色的（您没有打扫房间），但是草还是变成了绿色（但是您的妈妈还是制作了煎饼）。

这是一个约定-我们可以使用其他约定，但这很方便。这是陶德伦所说的：

我的书[分析1]的附录A.2中对此进行了讨论。在数学中使用的蕴涵概念是物质蕴涵的概念，它特别为任何虚无的蕴涵赋予了真实的价值。当然，人们可以对蕴涵概念使用不同的约定，但是，物质蕴涵对于证明数学定理非常有用，因为它允许人们使用诸如“ if A，then B”之类的含义而不必先检查是否A是否正确。物质蕴涵也服从许多有用的属性，例如专门化：例如，如果每个x都知道P（x）暗示Q（x），则可以将其专门化为x的特定值$x$，说3，并得出结论P（3）暗示Q（3）。请注意，尽管如此，非空洞的暗示可能会变成空洞的暗示。例如，我们知道，意味着X 2 ≥ 25 对任意实数X ; 这个专业的实数3，我们得到的空洞暗示3 ≥ 5暗示3 2 ≥ 25。$x \geq 5$$x^2 \geq 25$$x$$3 \geq 5$$3^2 \geq 25$

我喜欢思考实质性暗示的方式如下：A暗示B的主张只是说“ B至少与A一样真实”。特别地，如果A为真，那么B也必须为真；但是，如果A为假，则实质蕴涵允许B为真或假，因此无论B的真值是多少，蕴涵都是真实的。

“ A暗含B”表示（简短）“如果A为真，则B为真”。

意思是（更长一点）“如果A为真，那么我声称B为真；如果A为假，那么我就不对B提出任何要求”。

现在采取“如果太阳是绿色的，那么草是绿色的”。

在长格式中，它被翻译为“如果太阳是绿色的，那么我就声称草是绿色的；如果太阳不是绿色的，那么我就不会对草的颜色做出任何声明”。太阳不是绿色的，所以我对草的颜色一无所知。

Let's take an example. Suppose that we want to express that $a$ is the only element of the set $S$ that satisfies property $P$. Then we can write

It's important to note that many forms of logic have no concept of chronology or causality. If something is true, then it will--within its context--have been and continue to be true forever. Saying that X implies Y does not mean in any sense that X will in any way cause Y to be true. It merely means that X cannot be true without Y also being true, and Y cannot be false without X also being false.

To usefully describe causal relationships in the real world requires something beyond the constructs used in "timeless" logic. A concept like "For any action Y such that X would cause Y to be reasonable, Y shall be deemed reasonable" can be useful in a causal universe even if X might be false, but the implication operator completely blows up in such cases. If one were to say "X implies that Y shall be deemed reasonable" and it turned out that X was never true, that would imply that all actions shall be deemed reasonable.

I'm not sure what forms of logic include the constructs necessary to allow statements involving one-way causality, but recognizing that the logical definition of "implies" does not recognize the concepts of time and causality should make it easier to understand why they behave in counter-intuitive fashion.

While using Implication In English it not about the things or objects we consider.

Like in your given example which is blowing you mind is that If the $sun$ is $green$ and then $grass$ is $green$.

Sun is just is an object here, don't make any emotional attachments to it, that a sun can't be green.

You can just replace sun with a book or a letter $S$, green with $G$ and grass with $GG$. Now see the sentence If the S is G then GG is G.

{{S->G} $->$ {GG->G}}

This seems less confusing then while writing in English.

To put your head in the right place for my answer, I want to mention what I like to call the Flying Monkeys Theorem, or what Wikipedia likes to call the Principle of Explosion, which states:

Or, in English, this says "given a contradiction, monkeys might fly out of my butt (NSFW audio)", or alternately "from falsehood, anything follows". One way to think about this is that if $2+2=4$ and $2+2=5$ then $4=5$, which means that $0=1$, or it could mean that $16=25$, etc., and you can basically generate any equality you want. This is why there are so many tricks that result in $1=0$ or $1=-1$ by abusing a hidden division by zero, because you are not allowed to divide by zero so you can make anything you want true.

Once we're in this realm where we know $p$ is false, we're no longer in reality. We're in some alternate dimension where the Babel Fish is real, black is white and watch out for that Zebra crossing. So given that we're no longer in reality, of course the statement could be true. Specifically, I can use my false thing that I'm assuming to prove anything I want. So of course $F \rightarrow T$ and $F \rightarrow F$ are both true statements.