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The metaphysical presuppositions of formal logic

edwardfeser.blogspot.com

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Re: The metaphysical presuppositions of formal logic

#71

Post by ukj »

the_af wrote: post #51
ukj wrote: post #49

Earlier quoted context omitted.

What does it mean to compare a function to itself without evaluating it?

There are many ways of comparing functions. A straightforward way can be to simply compare the text of the functions, as written in your programming language of choice, in this case Ruby. Just take the text of both functions, do a diff, and if it says they are the same, they are the same. Another comparison could be more abstract, since we know there's more than one way to accomplish the same with a programming langu…

>There are many ways of comparing functions.

Indeed. I pointed this out and provided a link in my first post on this thread.

>You don't see them because they are implicit!

The fact that my function takes no arguments is implicit in the specification of my function. I know because I said the English sentence "The function that I have in mind takes no arguments".

You seem to be suggesting that I don't know what function I am thinking about but you do. This is a very peculiar hypothesis.

Re: The metaphysical presuppositions of formal logic

#72

Post by alentist »

benlivengood wrote: post #63

Essentialists are map-makers eternally searching for a map that exactly matches the territory, and will forever be disappointed. Some of the metaphysical problems with logic that the article tries to approach do exist, but in my opinion they are the domain of decision theory, not philosophy.

That's incorrect. Essentialism is more like the claim that there is a territory in the first place.

Re: The metaphysical presuppositions of formal logic

#73

Post by gjm11 »

lisper wrote: post #39
continuational wrote: post #6

This seems too vague to me, like a lot of philosophical posts out there. > For example, if it is true that Aunt May believes that Spider-Man fights crime, then even though Spider-Man = Peter Parker, it does not follow that Aunt May believes that Peter Parker fights crime. If you can't substitute Peter Parker for Spider-Man, then they are by definition not equal...

I wrote my master's thesis on this exact topic back in 1989. The answer IMHO (which is due to Bertrand Russel [1]) is that the correct rendering of "Aunt May believes that spider man fights crime" is not BELIEVES(AUNT-MAY, FIGHTS-CRIME(SPIDER-MAN)), it is EXISTS(X): BELIEVES(AUNT-MAY, FIGHTS-CRIME(X)) AND BELIEVES(AUNT-MAY, NAME-OF(X, "SPIDER-MAN")) and then you can also throw in BELIEVES(AUNT-MAY, NOT(NAME-OF(X, "PE…

I think this is wrong, because it can happen that Aunt May believes "Spider-Man fights crime" (she's read lots of newspaper articles saying so) without there being any specific entity that she believes to be Spider-Man.

That is, these two things are different: EXISTS(X): BELIEVES(AUNT-MAY, FIGHTS-CRIME(X)) AND BELIEVES(AUNT-MAY, NAME-OF(X, "SPIDER-MAN")) and BELIEVES(AUNT-MAY, EXISTS(X): FIGHTS-CRIME(X) AND NAME-OF(X, "SPIDER-MAN")), and the second seems to me like a better translation of "Aunt May believes that Spider-Man fights crime", at least for some of the states of affairs you might summarize with that sentence.

Re: The metaphysical presuppositions of formal logic

#74

Post by lisper »

gjm11 wrote: post #73
lisper wrote: post #39

Earlier quoted context omitted.

I wrote my master's thesis on this exact topic back in 1989. The answer IMHO (which is due to Bertrand Russel [1]) is that the correct rendering of "Aunt May believes that spider man fights crime" is not BELIEVES(AUNT-MAY, FIGHTS-CRIME(SPIDER-MAN)), it is EXISTS(X): BELIEVES(AUNT-MAY, FIGHTS-CRIME(X)) AND BELIEVES(AUNT-MAY, NAME-OF(X, "SPIDER-MAN")) and then you can also throw in BELIEVES(AUNT-MAY, NOT(NAME-OF(X, "PE…

I think this is wrong, because it can happen that Aunt May believes "Spider-Man fights crime" (she's read lots of newspaper articles saying so) without there being any specific entity that she believes to be Spider-Man. That is, these two things are different: EXISTS(X): BELIEVES(AUNT-MAY, FIGHTS-CRIME(X)) AND BELIEVES(AUNT-MAY, NAME-OF(X, "SPIDER-MAN")) and BELIEVES(AUNT-MAY, EXISTS(X): FIGHTS-CRIME(X) AND NAME-OF(X…

You are exactly right. The natural language version is ambiguous. c.f.: "Aunt May believes that Santa Claus fights crime." Philosophers actually argue about things like this, not so much for Santa Claus fighting crime, but whether e.g. "Santa Claus has a beard" is true or false.

Re: The metaphysical presuppositions of formal logic

#75

Post by alentist »

Cybotron5000 wrote: post #53

Edward Feser doesn’t seem to me to be genuinely interested in challenging his own presuppositions through metaphysics or philosophy, or in communicating the work of others to a wider audience. If the posts that appear on this site are anything to go by, he seems to specialize in a specious species of polemic and obfuscation designed solely to justify and promulgate his political and religious views. If it lends a sen…

Your entire comment is an ad-hominem. And a nasty one at that. Frankly, it sounds like you're projecting all these negative things because you hate to see your assumptions challenged.

Re: The metaphysical presuppositions of formal logic

#76

Post by the_af »

ukj wrote: post #71
the_af wrote: post #51

Earlier quoted context omitted.

There are many ways of comparing functions. A straightforward way can be to simply compare the text of the functions, as written in your programming language of choice, in this case Ruby. Just take the text of both functions, do a diff, and if it says they are the same, they are the same. Another comparison could be more abstract, since we know there's more than one way to accomplish the same with a programming langu…

>There are many ways of comparing functions. Indeed. I pointed this out and provided a link in my first post on this thread. >You don't see them because they are implicit! The fact that my function takes no arguments is implicit in the specification of my function. I know because I said the English sentence "The function that I have in mind takes no arguments". You seem to be suggesting that I don't know what functio…

Your function does take implicit arguments. There's no way your Ruby function can return the current time ("now") without external dependencies that supply that time.

If you want to argue otherwise, you must provide this hypothetical implementation that complies with your specs. I'm telling you that your function effectively can't exist as you describe it. In order for your function to work it requires an implicit argument (the "world" if you want to be coarse, though in this case we know it's the time).

If you want to argue that

    magical function is not magical function
that's fine, but also uninteresting. Magic is not bound by the constraints of the physical universe. We generally don't find arguing about leprechauns and unicorns for this reason (at least, not seriously).

Re: The metaphysical presuppositions of formal logic

#77

Post by Cybotron5000 »

alentist wrote: post #75
Cybotron5000 wrote: post #53

Edward Feser doesn’t seem to me to be genuinely interested in challenging his own presuppositions through metaphysics or philosophy, or in communicating the work of others to a wider audience. If the posts that appear on this site are anything to go by, he seems to specialize in a specious species of polemic and obfuscation designed solely to justify and promulgate his political and religious views. If it lends a sen…

Your entire comment is an ad-hominem. And a nasty one at that. Frankly, it sounds like you're projecting all these negative things because you hate to see your assumptions challenged.

What do you consider to be my assumptions? As I said in the comment below, I am not attacking the guy personally (that’s what ad hominem means) - I’m sure he may be perfectly lovely and if he is genuine in his pursuits then I genuinely wish him (and you) all the best in life…

Re: The metaphysical presuppositions of formal logic

#78

Post by alentist »

Cybotron5000 wrote: post #77
alentist wrote: post #75

Earlier quoted context omitted.

Your entire comment is an ad-hominem. And a nasty one at that. Frankly, it sounds like you're projecting all these negative things because you hate to see your assumptions challenged.

What do you consider to be my assumptions? As I said in the comment below, I am not attacking the guy personally (that’s what ad hominem means) - I’m sure he may be perfectly lovely and if he is genuine in his pursuits then I genuinely wish him (and you) all the best in life…

> What, pray tell, do you consider to be my assumptions?

I don't know, because you didn't engage with the content of the article at all. You merely casted nasty aspersions on its author.

> I am not attacking the guy personally

Yes, you are.

he seems to specialize in a specious species of polemic and obfuscation designed solely to justify and promulgate his political and religious views. If it lends a sense of purpose to his life, makes him a living or gives him a feeling of self-importance/bolsters his worth among his peers, who am I to criticize? Perhaps it is actually a deep satire with some ulterior motive.

So not only do you throw around unsubstantiated aspersions, but you are also dishonest.

Re: The metaphysical presuppositions of formal logic

#79

Post by the_af »

ukj wrote: post #69
dragonwriter wrote: post #57

Earlier quoted context omitted.

> The function I am talking about doesn't take any arguments. All impure functions have an implicit dependency on (some subset of) the state of the universe when they execute; in mathematics and logic something with this kind of dependency is typically noted by parameterizing it by time when the actual precise nature of the dependency is outside of the scope of the immediate analysis (because a dependency on the stat…

You know what the state of the universe is when you do logic? Tell us more! I didn't believe in omniscience until now. Time.now(t1) and Time.now(t2) is meaningless in this context because t1 and t2 are unbound variables. What are you passing to your function? Where is it coming from? My function says you are overlooking something. [1] pry(main)> Time.now(t1) NameError: undefined local variable or method `t1' for main…

If you're familiar with the literature of programming languages, you'll see references to the "world" or the "universe" all the time. That's the kind of universe we mean in this discussion, not the one Carl Sagan talked about.

As for the rest: please provide the implementation of your Time.now function and I'll tell you its implicit parameters. If you're not talking about an actual function that can be run by a computer, then please tell me so and I'll drop it -- I'm not interested in hypothetical functions tautologically defined not to be equal to themselves.

Re: The metaphysical presuppositions of formal logic

#80

Post by creata »

practal wrote: post #5

It's important to sometimes step back and think about whether what you are doing actually makes sense. There are some assumptions about how formal logic is done in ITP (interactive theorem proving) systems that should be challenged. Here is my opinion about that: https://doi.org/10.47757/practal.1

> Instead, coercions are used to emulate some of the advantages of subtyping.

Maybe I missed it in the article, but what does subtyping give you that coercions don't?

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