Descartes has argued that <God> contains <existence> as a property, so God must exist. If one claims that God does not exist, it is a logical contradiction because it is saying that God does not contain <existence> as a property. Because it is a logical contradiction to claim God doesn’t exist, God must exist.
Kant argues that existence is not a property because whether an object contains <existence> as a property changes nothing about the concept of this object. To change the concept of an object, it has to change the properties that form the content of this concept in our minds. Thus, before we decide whether something is a property of an object, we must ask: Is it absolutely necessary to have this property for us to posit this concept in our mind and perceive this concept’s corresponding object in reality? For example, one of the properties of matcha is that it is plant-based. If I take out this property, there is no matcha to think about or perceive because being plant-based is an absolutely necessary property that sustains this concept. Being plant-based passes the test as a property. This is why saying matcha is not plant-based is a logical contradiction because being plant-based is a property/real predicate.
On the other hand, if I say matcha does not exist, I can posit matcha in my mind or identify it in reality regardless. Claiming whether something exists or not cannot lead to a logical contradiction because <existence> is not a real predicate. Today matcha exists, so saying matcha doesn’t exist in the real world is false. Let’s say a person swallows all the matcha tomorrow, then saying matcha doesn’t exist in the real world is true. However, there is no purely logical judgment when one makes claims about an object’s existence because <existence> is not part of the concept’s meaning/content. Therefore, the matcha in reality and the matcha in our minds are referring to the same matcha, regardless of whether matcha contains <existence>, because they have the same properties that determine the content of <matcha>. The only difference <existence> makes to a concept when someone posits it is suggesting an object’s possible existence in reality, which is completely a matter of empirical judgment but adds nothing to the concept itself. <Existence> as a concept, in general, does not pass the property test.
The same goes for God. <Infinity> is in the same category as to being plant-based because they are both properties. One cannot posit God without <infinity> because <infinity> is a necessary predicate of God, but one can posit God regardless of whether it exists. To use logical contradiction to yield knowledge about a concept requires positing the concept’s actual properties. <Existence> is not a real predicate. A God that exists and a God that doesn’t are conceptually the same God. To prove completely analytically through the law of contradiction that God exists by claiming that <existence> necessarily forms the concept of God is thus invalid.
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What’s the Difference Between the Concept of a Thing and a Real Object?