Thanks for your clarifications! It cleared up all of my written confusions. Though I have one major confusion that I am only able to pinpoint after your reply: from wiki, I understand syllogism as the 24 out of 256 2-premise deductions that are always true, but you seem to be saying that syllogism is not what I think it is. You said ”… a fundamental misunderstanding of the fact that syllogisms work by being generally true across specific categories of arguments”, so syllogisms does not work universally with any words substituted into it, and only work when a specific category of words are used? If so, then can you provide an example of syllogism generating a false proposition when the wrong category of words are used?
Glad I could clear some things up! Your follow-up suspicions are correct, syllogisms do not work universally with any words substituted into them, because syllogisms operate over concepts and not syntax categories. There is often a rough correspondence between concepts and syntax categories, but only in one direction. For example, the collection of concepts that refer to humans taking actions can often be described/captured in verb phrases, however not all verb phrases represent humans taking actions. In general, for every syntax category (except for closed-class items like “and”) there are many concepts and concept groupings that can be expressed as that syntax category.
Going back to the Wiki page, the error I was trying to explain in my original comment happens when choosing of the subject, middle, and predicate (SMP) for a given syllogism (let’s say, one of the 24[1]). The first example I can think of concerns the use of the modifier “fake,” but let’s start with another syllogism first:
All cars have value.
Green cars are cars.
Green cars have value.
This is a true syllogism, there’s nothing wrong with it. What we’ve done is found a subset of cars, green cars, and inserted them as the subject into the minor premise. However, a nieve person might think that the actual trick was that we found a syntactic modifier of cars, green, and inserted the modified phrase “green cars” into the minor premise. They might then make the same mistake with the modifier “fake,” which does not (most of the time[2]) select out a subset of the set it takes as an argument. For example:
All money has value.
Fake money is money.
Fake money has value.
Obviously the problem occurs in the minor premise, “Fake money is money.” The counterfeit money that exists in the real world is in fact not money. But the linguistic construction “fake money” bears some kind of relationship to “money” such that a nieve person might agree to this minor premise while thinking, “well, fake money is money, it’s just fake,” or something like that.
Though when I say syllogism I’m actually referring to a more general notion of functions over symbols that return other symbols or propositions or truth values.
Thanks for your clarifications! It cleared up all of my written confusions. Though I have one major confusion that I am only able to pinpoint after your reply: from wiki, I understand syllogism as the 24 out of 256 2-premise deductions that are always true, but you seem to be saying that syllogism is not what I think it is. You said ”… a fundamental misunderstanding of the fact that syllogisms work by being generally true across specific categories of arguments”, so syllogisms does not work universally with any words substituted into it, and only work when a specific category of words are used? If so, then can you provide an example of syllogism generating a false proposition when the wrong category of words are used?
Glad I could clear some things up! Your follow-up suspicions are correct, syllogisms do not work universally with any words substituted into them, because syllogisms operate over concepts and not syntax categories. There is often a rough correspondence between concepts and syntax categories, but only in one direction. For example, the collection of concepts that refer to humans taking actions can often be described/captured in verb phrases, however not all verb phrases represent humans taking actions. In general, for every syntax category (except for closed-class items like “and”) there are many concepts and concept groupings that can be expressed as that syntax category.
Going back to the Wiki page, the error I was trying to explain in my original comment happens when choosing of the subject, middle, and predicate (SMP) for a given syllogism (let’s say, one of the 24[1]). The first example I can think of concerns the use of the modifier “fake,” but let’s start with another syllogism first:
All cars have value.
Green cars are cars.
Green cars have value.
This is a true syllogism, there’s nothing wrong with it. What we’ve done is found a subset of cars, green cars, and inserted them as the subject into the minor premise. However, a nieve person might think that the actual trick was that we found a syntactic modifier of cars, green, and inserted the modified phrase “green cars” into the minor premise. They might then make the same mistake with the modifier “fake,” which does not (most of the time[2]) select out a subset of the set it takes as an argument. For example:
All money has value.
Fake money is money.
Fake money has value.
Obviously the problem occurs in the minor premise, “Fake money is money.” The counterfeit money that exists in the real world is in fact not money. But the linguistic construction “fake money” bears some kind of relationship to “money” such that a nieve person might agree to this minor premise while thinking, “well, fake money is money, it’s just fake,” or something like that.
Though when I say syllogism I’m actually referring to a more general notion of functions over symbols that return other symbols or propositions or truth values.
Actually, it’s contextual, some fake things are still those things.
this seem related: word aren’t type safe