This is a false dichotomy, read up on epigenetics.

I'm rather surprised at some of the responses here. Related to this issue is the coordinated deplatforming and defunding of people like Alex Jones and even non-lunatic websites (like the World Socialists site). Saying that these actions aren't a threat to democracy is a joke considering these entities are or are approaching a monopoly status, are coordinating together in these efforts and are working with government bodies in the U.S. and Israel (among others) to determine whose content and existence on these platforms is "divisve and disruptive".

There's a really weird presumption I'm seeing where people hang their hat on whether or not it's a private entity that's controlling the thing without considering the role such large things occupy. Say someone has a controversial view. Maybe it's false, contentious or even true but disliked by those in the mainstream. If the major avenues of these people putting their views out there are constrained by these platforms, that's stifling speech. It's even worse when the government is, as in this case, working to determine what speech is acceptable or not...

Here I go repeating myself; but, that can only depend on one world from within a stipulation of another possible world can be made. — Wallows

No it doesn't, it's just a collection of worlds. It doesn't matter what world you are in, you're setting up the set of relevant worlds in the modal discourse, the actual world is not necessarily relevant and may even be excluded in some cases. Are you talking about frame conditions? (E.g. the properties of what worlds access others?)

Yes, but I don't understand how you can quantify modal relations. Sure, I can set up a frame of reference wrt. to this world relative to another world where something might have happened otherwise than in this one; but, that's the limit of what I can do. I can't say that something happened if I did nothing in this world that would conditionally restrain another world where the event could have happened otherwise. — Wallows

You're not constraining worlds themselves, you're constraining the worlds that are part of the set you're speaking about basically. Once you have a frame condition and a set of worlds picked out, you just worked out the modal deductions. Your SEP link basically says this I think:

Each of the modal logic axioms we have discussed corresponds to a condition on frames in the same way. The relationship between conditions on frames and corresponding axioms is one of the central topics in the study of modal logics. Once an interpretation of the intensional operator □ has been decided on, the appropriate conditions on R can be determined to fix the corresponding notion of validity. This, in turn, allows us to select the right set of axioms for that logic.

Ok, so this touches the crux of the issue. Basically, I understand logic to be pluralistic not unitary, so predicate logic might converge with modal logic; but, not absolutely. What do you think? The case I'm making is in regards to when do they converge or don't in this thread. — Wallows

Well I don't think that's really a pluralistic view of logic. Logical pluralism - which I accept- is the view that there are more than one legitimate kinds of logic or more than one correct logic. Standard, normal modal logics essentially add on to classical predicate logic, and even have a translation scheme to understand modal statements in classical form, so I don't think it's really entirely different. A real test would be if you accept both classical and intuitionistic logic, because those logics actually disagree with each other about what arguments are valid or not.

You are doing exactly what I mentioned and thus are, wittingly or not, playing a shell game. You're defining philosophy so broadly that it applies to everything and thus fails to pick anything out non-trivially. This is exactly as stupid as scientism. Things growing out of philosophy does not make those outgrowths philosophy anymore than a child being the same thing as their mother because she birthed them. Both grow out of and distinguish themselves from what came prior and thus the forebears do not get to claim direct credit for what the offspring does once they are a distant memory. Philosophy is not defined as having knowledge or applying it to life, that's an incredibly stupid definition or description of philosophy. Most philosophy is about abstract things, concepts and such, even if they have no direct relevance to how one lives their life.

I don't really know what you mean by "political leanings", I was just wondering about this kind of stuff — TogetherTurtle

In nearly every case I see this sort of thing it's some pointless complain by a conservative or libertarian who wants people to stop pointing out that genocide and slavery can't be whitewashed and that they don't count against the morally upstanding nature of their great ancestors. It's so often so clearly self-interested that I'm pessimistic when I see this sort of thing.

As for presenting things as statements and only using your own observations, I don't know what other way you would present an idea. How would you know something unless you read it somewhere or saw it? — TogetherTurtle

Here's my problem. Your post just says things and doesn't give any reason for people to accept what you're saying is true.

Let me preface this next statement by saying I wholeheartedly believe that killing people is wrong. I think it's wrong, and from your statements, I assume you do as well. Clearly, Hitler and many of his followers didn't. What makes us correct morally in thinking that it's wrong? I know that it's wrong, and many people think it's wrong as well, but that's more of an opinion and less of an objective truth. — TogetherTurtle

You're confusing the limits of moral epistemology (which deals with how we know what's moral or immoral) and moral metaphysics (which deals with what actually is moral or immoral). Pick a standard normative moral theory and it will give a fairly robust explanation for thinking that murder is wrong (killing is a broader class of actions, sometimes killing is justified).

So far, what has been said about the shortcomings of philosophy seems quite unfair considering philosophy has played its part of providing the necessary information — BrianW

I'm not sure what you're saying here. Philosophy doesn't interest most people, and isn't all that relevant to most problems outside some fairly specific cases. And the boons to, say, quality of life have no direct and obvious connection to philosophy outside an incredibly hamfisted "Everything is philosophy" idea, so I don't think it's unfair.

Some people just find philosophy fun, and it may have some relevancy in certain academic matters, but that lays outside the realm of what most people care about.

No, a frame is just a set of worlds that share some relevant feature(s). An accessibility relation tells you which worlds can quantify over which other worlds in some particular frame. Your whole lotto thing is a perfect example, you're constraining your modal discourse to worlds where the lotto exists, you exist and in which you play the lotto. That's a frame. You can quantify over other worlds, I'm not sure what the problem is. You mentioned Quine before, but Quine's issue was about quantifying into opaque contexts and it isn't really taken too seriously anymore.

But, what I'm grappling with may be more succinctly described as to how does quantification work for other possible worlds? — Wallows

The same. An accessibility relation is a feature of a modal logic, not of reality (controversial, depending on how you think reality and logic relate).

No one cares about philosophy.

That's not an accessibility relation obtaining, that's merely establishing what frame (the set of worlds) is being quantified over. That you're speaking about winning the lotto presumably restricts the world scope to, for example, worlds where the lottery exists, worlds where you exist, worlds where you actually play the lotto, etc. The frame is determined based on the scenarios described int he situation you gave.

Hardly pointless, friend. The average Joe, utterly unlike a computer, does not do calculations when he understands, thinks, make judements, and uses his mind. . Making distinctions here is necessary. Nor is there a reason to depict logic and math as something only the more intelligent people can do. — Anthony

You're really misunderstanding my point. Yes, I'm in grad school for CS but that's not coloring my view here at all. If anything, I'm far more pessimistic about the over (bear with me) programmatification of language and metaphor but for what I regard as legitimate reasons beyond what words are used to refer to things. But when computers are called "intelligent" all people mean is they do things that are both very difficult for humans to do (formal calculations) and which humans regard as signs of great intelligence when done by people. You can complain and say we shouldn't do that - I don't see what the problem is there, formal math and logic are cognitively difficult operations and require intense training - but that's what people mean. Next to no one actually thinks computers have literal intelligence (maybe kids, but even they treat such things as mere tools). They're regarded as basically a really complicated but useful abacus, not things capable of true thought.

How does one 'know' epistemically when an accessibility relation obtains or is successful or not? I am mainly interested in that regards. — Wallows

I don't understand what you're saying hers. How does an accessibility relation obtain (that is, become actual in the real world)? An AC is just the description of which worlds can access (quantify over, basically) other worlds in a given frame using some specified system of modal logic and it's determined by the axioms of the logic. This relationship may have different properties depending on what you're investigating. S5 has the Euclidean property which S4 does not, for instance. So if two worlds can both access some specified world they can access each other.

So long as you have some frame established and specify the modal logic in use then that seems perfectly justifiable reason to say... whatever it is you're asking (not sure I understand the question).

I'll be the first to point out something that everyone reading your post can tell in a near instant. Your political leanings are showing very clearly, your framing is so upfront (even in your title) that it makes the attempt at an argument in the post quite funny and your references to turns of phrases and cliches, just so you can say "No" to them, is tiresome.

Am I presenting an argument here? No, nor do I intend to. But when I read:

For centuries there have been the subjugated and the subjugators, and it is often said that the victors write history. I challenge this. Often, when looking back at history, modern societies see some as the victim and talk more about them than the aggressors. Of course, they were aggressors. — TogetherTurtle

I immediately realize I am not being given an argument with which to contend. I'm being given statement asserted as fact and expected to either accept it blindly or somehow prove that it isn't true (as if it were inherently credible). Naturally, it being nothing more than, at best, your own experience makes it true in your own eyes but you're just making statements.

. I propose that there is not a "good" or "bad" side of anything, just the side that we agree with now and everything else. Constantly I see historical figures being vilified or being hailed as heroes, which of course is fine on its own, but should we be teaching that to children as objective truth? — TogetherTurtle

I dunno. People who kill thousands or millions of people ought be regarded as evil in any circumstance or scenario. How evil is up for debate and may well depend on how they did so - Hitler killed, what, 20 something million civilians directly and with intent, and used the power of technology and the state to do so, while the bulk of Stalin's kill count seems to have been in the grain shortage - but anyone doing the relativist tap dance shouldn't expect everyone else to care about how they think children, who are impressionable and ignorant, thinks children should be taught.

To refer to a machine as being intelligent is a blunder of intelligence. None of the definitions of "intelligence" can be satisfied by machines. Every definition (save the misnomer referring to computers) of intelligence includes terms like capacity to understand, to think, reason, make judgments; and mental capacity. These terms are precisely outside the ambit of what computers can do, so why was such a poor term chosen for computing operations and data processing of a machine — Anthony

I'm sorry but I think this is about the most pointless question to ask because the explanation is obvious if you ask nearly any regular Joe. Computers perform actions - namely complex mathematical and logical calculations - in fractiona of a second that humans take much longer to do and do so with much more proneness to error. So we call them intelligent in that respect, even though we know they find processes that aren't strictly formal much harder to implement (forget what the name of this paradox is called). Humans have a hard time doing them, if they can do them at all (some discoveries in math had to be found by computers), for instance.

Complaining that it's a 'poor term' or is a 'blunder of intelligence' is just a complete failure to understand simple reason people use certain terms.

I mean as little as possible by it so as to leave open to interpretation what it could mean. Most generally, I take just to mean "capable of being understood" whether by humans or any other rational creature. My intuition for its truth is that any "world" that were completely incapable of being conceptualized in any way by any kind of rational creature would not qualify as a world at all. It would essentially be chaos. — Mentalusion

Something about this seems mistaken. You say an incomprehensible world be would chaos, but is that a preclusion to existence?

Agree about the math formalism, but I don't see why the premise wouldn't work with whatever theory of numbers you accept, whether platonic, intuitionist, whatever. Are you suggesting it makes sense to suppose there could be different possible worlds where, say, constructivist , platonic, etc. interpretations hold in each? I guess my assumption is you would first have to decide what you think numbers are before running off to look for them in different possible worlds. — Mentalusion

Sure, why not? It's fairly common (for logicians anyway) to speak of worlds where different logics obtain. If this couldn't be done I don't even think such logics could be given semantics. Now this is the sort of thing I meant when I said the world's might well be incomprehensible (in the sense of running very counter to the intuitions our world has shaped) and yet still have some kind of existence.

1. Any possible world that is intelligible is such that it contains some structure and form.
1a. All possible worlds are intelligible
2. At least some aspect of all structure and form is inherently quantifiable
3. Anything quantifiable is capable of being expressed numerically
4. All possible worlds contain aspects that are capable of numeric expression
5. The capacity for expressing numbers is sufficient for numbers to exist (whether or not anyone uses them or has discovered how to use them)
6. Numbers exist in all possible worlds
7. Therefore, numbers necessarily exist — Mentalusion

1a is probably false, depending on what you mean by intelligible. Lots of worlds are presumably unintelligible if their structure is such that it runs very counter to our own universe. So say a universe where objects are clearly distinguished would probably appear as very unintelligible to most or all people. But if by "intelligible" you mean "coherent" (i.e. not logically trivial) then 1a is true.

2 & 3 are suspicious because there are different ways of assigning quantity to thing. Numbers are not the same thing across all mathematical formalisms, and so it does not follow that some numerical system that is apt to one particular possible world is applicable to all of them. Constructive mathematics and classical mathematics - not to mention Paraconsistent mathematics - look quite different. Some numbering systems lack entire types of numbers. Standard, classical mathematics doesn't have the hyperreals, for instance.

Anyway, talking about the necessary existence of numbers (this is aimed the OP and Mentalusion) in the same way one does for non-abstract objects just sounds wrong. "Existence" in mathematics is very different than the colloquial and philosophical use of that term. This seems relevant since lots of different abstract objects that correspond to our notion of numbers and such might come out differently depending on the math you're using.

Logically I would state that the reason why aleph-null makes no sense is because like both aleph-null and the numbers on the list are infinity, then to say that aleph-null is in any way different from the numbers on the list is to state that the numbers on the list have an ending. This is because for them to actually be different is for both numbers to end in a difference. Such statement may sound illogical at first glance because no matter what number appears it will always be different, however the point is that if we think about it aleph-null is still impossible to fully become different. — Emmanuele

That does not follow. For one to be larger than the other all that need be true is that one set has a greater cardinality. What this will mean is that when you try to place them in a one-to-one correspondence with each other, it fails to be possible to do so. After all, sets that can be mapped together in this way are the same size. What Cantor showed was that it's impossible to map the naturals with the reals on pain of contradiction, it turned out the reals were larger not that the naturals had an end (in the sense of a final member). That's what makes them different, despite being infinite. They're different levels of infinity.

As I said, and provided examples for, some divisions of degree are arbitrary, I didn't say that all are arbitrary. But the fact that some are, is all that's required to disprove Ikolos' claim that quantity is what is measured. Actually, quantity is the measurement. — Metaphysician Undercover

Incorrect, their argument was that some were not "qualities" as you deemed them because they are part of reality. Pointing out that some aren't (as that user already admitted) is very much besides the point when they already admitted so.

That's not even an argument, the number of degrees in a circle is not arbitrary, it was chosen because it's "easy to do basic math with". — Metaphysician Undercover

How is that not an argument? Ease of use is a perfectly legitimate reason to do prefer something. You user particular kinds of screw heads in because they're easier to use for particular kind of screws (this generalizes to tools in general). Hell, the entire reason a radian is defined as 2 x Pi is because it makes calculus and trigonometry easier if angles are measured in radians instead. Again, you're working under a strange definition of "arbitrary" if practicality doesn't count because it's very helpful that a circle has 360 degrees. Also, try to do set a circle equal to 4 degrees and see how the math works out for you. Other numbers have many divisors, but they aren't as useful mathematically (example, 2570 can be cleanly divided by every number 1 - 10 but it's not very useful in geometrical calculations to set it that way).

1. Infinity is a never ending quantity.

2. Infinity is not a number. — Emmanuele

#1 is false in some sense. Unless you ignore modern math, there are a hierarchy of infinities. #2 is extremely wrong, there are many infinite numbers. The transfinite cardinals and ordinals will fit any sensible, non-arbitrary definition of a number.

Btw, countable and uncountable infinity is counterintuitive, insane and nonsensical. Cantor was a lunatic. — Emmanuele

Except the Diagonal argument is a proof by contradiction, the most standard argument type of all.

First of all the new number has conditioned itself to be infinitely different from the one on the list. In no possible way can the number be the one on the list, however the same can be said by the number on the list ever actually being a quantity. It has and will never end. Thus they're both infinite numbers, and thus they both have the same length. The only difference is the rate at which they grow. — Emmanuele

Who cares if it's "conditioned"? That is not a criticism, you're whining with this non-objection. The mere fact (proven by the opposite entailing a contradiction) that such a number necessarily exists is why mathematicians accept Cantor's diagonal argument. "Never actually being a quantity" is, naturally, something you do not demonstrate to be the case. That the number "never ends" does not mean they have the same length, that's a non sequitur. Show exactly where the "conditioned" number will appear in the original set. That you cannot (again, because it would be a contradiction) entails the different sizes of the respective sets.

Second of all the rate of growth in infinite numbers is not a valid argument to define N (aleph-null) as an ordinal 'uncountable infinite'. This is because the rate of growth can still be achieved without ever actually having the list to being with. This new number N is in no way different or special from the numbers on the list. — Emmanuele

Aleph-null is not an ordinal, it's a transfinite cardinal. Literally the smallest, first transfinite cardinal is aleph-null. And thus it is not uncountably infinite, it's countably infinite, because the definition of that is "being capable of being put into a function with the set of natural numbers".

Third of all the rate of growth to infinity does not change at all the fact that they're both infinite. Saying that some N1 is infinite will then have an N2 being infinite proceed from that one makes no sense and is mathematically possible but absolutely irrational, and a waste of time for your brain to acknowledge. But people don't understand these three simple concepts. — Emmanuele

"Both infinite" says nothing more than that they're both the same type of number. That "0.33" and "0.44" are both real numbers doesn't mean they're both the same number. You are under a terrible misapprehension. If the sets were the same size they could be mapped onto each other. That's how size is defined in math, they have to have the same cardinality. But of course, if you cannot even accept Cantor's proof by contradiction that the naturals and the reals cannot be the same size then I'm not surprised you fail to grasp this.

Cut the nonsense. Show exactly where the sets map together to make them the same size. That you cannot means they aren't the same size. Ergo, one is larger and the other smaller. It's funny you say it's mathematically possible yet "absolutely irrational". I'm sure you can defend that characterization as coherent. One would assume mathematics cannot be incoherent, given incoherency in mathematics means triviality; everything becomes a theorem if the math is incoherent, but there's absolutely no evidence that current mathematics is trivial. Show the formal contradiction. You'll win a Fields Medal.

The units of measurement, which are counted as a quantity, are very often created by the human mind, for the purpose of measurement, they are artificial. So "quantity", as the thing measured, is not necessarily presupposed. In the cases where we cannot find individual units to count, we simply create them, giving us the capacity to measure without there being any real quantity which is being measured. — Metaphysician Undercover

Planck Length, Planck Scale, speed of light (which is basically a scale constant) are not in any sense arbitrary. Unless Im mistaken, the SI system is based on non-arbitrary physical constants not this nonsensical notion of "qualities" or whatever. And even if it isn't, such a thing is possible but the gain is little for all the work required. See Natural units.

That number of degrees around a circle is complete arbitrary. The circle could be divided into an infinite number of degrees, and there could be an infinite number of degrees between each of the four right angles, — Metaphysician Undercover

That something could be done a different way does not make something arbitrary. There are perfectly sensible reasons to put the number of degrees at 360. It's a highly composite number allowing us to avoid fractions (which are hard for humans to do, hence the preference for decimal expressions), it's not a large whole number so it's fairly easy to do basic math with (particularly division), etc. I'm thinking you're using a weird definition of "arbitrary" or not explaining why it is (supposedly) so.

I always find these descend into throwing around words that obfuscate conclusions that aren't pretty. So the idea that we need to be capable of sinning have free will, for instance. Well, there's absolutely no way to avoid the entailment there: God doesn't have free will, because he cannot sin. Or the idea that God could not have created us in Heaven (presumably a sinless world) without us losing free will, when many Christians believe Earth originally was sinless. Ergo, that entails Adam and Eve lacked free will, and yet were punished (along with humanity, in perpetuity) for actions not freely chosen.

But of course, I'm sure those aren't REALLY problems. No no, what I'll inevitably be told is either God has a special kind of free will, or he could (in some technical sense of "could" that means the opposite) sin but he never would. Naturally, we couldn't get that. Of course, he's till praiseworthy for being incapable of sinning.

Or I'll be told Earth was never sinless, in which case one can't help but wonder why the fault of sin is laid at the feet of humanity who must have been born in a world of sin and so never had a choice not to partake in it. The literalists are only slightly more worsened in this case, since another of God's goofs led to it in the first place.

Nothing is ever straight here, there's a litany of excuses and redefinitions of terms to an extent that no one will actually understand what the key terms mean at any given point. Free will means one thing and is necessary for moral responsibility, until it's not. Going to heaven requires a certain path and obstacles called sin and necessitate the possibility of failure, unless you're God.

If so, the cure is then to abstain from philosophy. — javra

Fine by me. No one will miss the debate about whether or not holes exist.

Rocks are just ideas, man~



No one better give me grief about this

↪MindForged Our cranky and inarticulate friend has a point in that there is a difference between a conceptual definition of a number, which describes the properties that anything fitting the definition of a 'number' ought to have, and its particular theoretical construction, such as von Neumann's (which was designed to meet the requirements of the conceptual definition). — SophistiCat

Hm, okay but I don't really get what their point about infinity was supposed to be. It didn't really sound like something which would accurately characterize how the concept is used and understood in modern math. Aleph-null is definitely not a quantity above all others, for instance.

This is the condition to CONSIDER the 'singleton'(I trust you on the term) as the number one, but not to DEFINE it. Numbers are defined by a postulate and succession: see Peano Arithmetics( 0 is number(POSTULATE). If n is a number, then n+1 is number.(AXIOM) Then 1 is a number, as 0+1=1.) — Ikolos

How is this different from what I said?

Thinking infinity has THE QUANTITY OF WHICH NO QUANTITY IS GREATER is the MEDIEVAL conception of infinity. — Ikolos

Well I that's definitely not how I described infinity, and it doesn't even seem correct because it's too vague. As there are many sizes of infinity, I don't even think I could pretend to accept "the quantity of which no quantity is greater" as a description of infinity.

This is the 'singoletto'(I don't know the English word, kind of 'single set') not of a number. — Ikolos

The word you're thinking of is "singleton" I believe. And no, that's not just the singleton of a set. It was the definition of the number one in set theory. If Zero is defined as the empty set, One can be defined as it's successor; the union of Zero with singleton-Zero.

I'm still confused about what you meant when you said I had a medieval theologian type of thinking...

I didn't reference going through with suicide or the morality of it. In fact, I think people ought to be legally allowed to seek assisted suicide methods (with a few caveats). What I meant is that the people don't want someone they know to be thinking about it for many reasons.

Even if one thinks it's permissible to do X doesn't mean they think one ought to consider it, for various reasons (context, severity, repercussions, and so on).

It seems easy enough to modify the above argument so that it is sound. For example, in Greek mythology all winged horses are horses ... in Greek mythology there is at least one winged horse, namely Pegasus.[/quote]

I should note the argument you quoted is valid in modern logic, but if the third premise is dropped it's not. It will become valid in Aristotle's logic but will render it unsound. I wasn't sure if you were disputing that, I'm reading this in a hurry at the moment.

That said, as I said, Aristotle does not take logic to regard fictional things so I don't think adding "In Greek Mythology" will render it a valid syllogism. He takes it to be that while something might be a necessary relation, that doesn't make it a syllogism. See above for my quote of him in Prior Analytics.

I'm curious about what the problems really are — Andrew M

Now I REALLY have to do this quickly, so I had to just copy paste this from Graham Priest's book "Doubt Truth to be a Liar" where he covers this. Sorry about this, but I have to go to work and I'll likely forget about coming back to it later after work tires me out! Sorry for any formatting errors I missed. I don't know if this forum supports math libs so I tried to make everything look close enough to how the book displays them:

I really don't know what you're talking about. Infinity (as in the cardinality and ordinality of sets which can be put into a function with a proper subset of themselves) is a quantity. Finite Numbers can be defined in terms of the cardinality of sets in just the same way.

E.g. 1=0∪{0}={0}={{ }}

I read you as saying that certain arguments that presuppose existential import are out-of-court because the presupposition is not in all cases justified, and therefor the form of the argument is no good. — tim wood

Hm, I think that is exactly what I'm saying. The usual defense I see of this is that Aristotelian logic was intended for real things so existential import is sort of a given, but as I said I believe this severely limits the use for that logic. That's why Frege made classical logic, the old logic just wasn't good for mathematical reasoning. I'm not saying the logic is useless or something, but that modern logic is more useful.

There are two errors: 1 proof is not 'defined' either by axioms or inference rules. Proof is the results of applying inference rules by means of axioms. This is not at all a definition, just as the egg is not a definition of the chicken. — Ikolos

This is either nonsense or splitting hairs in a way that changes nothing. What counts as a "proof" is determined by the axioms and the inference rules. Me referring to that as a definition seems perfectly comprehensible. What counts as a "proof" in Intuitionistic logic is very clearly and certainly distinct from what counts as a "proof" in Classical logic. Because the rules for a valid proof is not the same in different formalisms.

2 It is false that you can not prove validity of 'such things'(axioms? rules of inference?) independently(even if your statement is incomplete, because you do not specify independent from what).The proof of a logical theory is obtained by verifying the coherence of axioms, i.e. through the non contradiction principle in a certain form: iff from the set of axioms you can not derive, through rule of inference, a contradiction, then the set of axiom is coherent. You can even proof the independency of some axioms from others by verifying that the same theorem deducible by n axioms+ x axioms is deducible even just through n(or x) axioms. — Ikolos

You are rather proving my point. "Coherency" here is exactly another way of saying "non-contradictory". In other words, it's reliance on another axiom (Non-contradiction). I explained what I meant by the incoherency of the idea of a purely independent proof of all axioms. Let's quote myself, then:




So let's make this even clearer, since apparently it wasn't. What counts as a proof requires one to adopt some set of rules by which to establish what will count as a proof. But the reasoning employed in the metatheory (what we're using to reason about the construction of the logic in question) doesn't have some inherent correctness to them, one just ends up presuming some set of inference rules and axioms in the background and those show up in the object theory because of that. So for example, classical logic can be constructed from a boolean algebra, as the two are basically equivalent, so we see that a boolean algebra of sets naturally gives us a certain kind of logic (and the reverse can be done as well). But we know numerous metatheories exist independently of the others using other set theories and such, but you never get to some independently proven axioms or something. You have to assume something is just off the table to get going. I'm not saying this is a problem, it's just how things have to be.

But not because it is incoherent, but because is IMPOSSIBLE. — Ikolos

Sure, I took those words to be mean same thing. I used the word incoherent the idea itself is without meaning because I'm skeptical one could even conceive of how it could even be done. The idea of an independent proof of all axioms makes the mistake of forgetting that what constitutes a proof is determined by some set of axioms and inference rules. The inference rules in proof systems are, after all, taken to be primitive. If they could be proven, we would not take them to be primitive.

I find much to disagree with in your post, but this can stand for most of it. There is an implied if in all logic. — tim wood

I said in Aristotle's logic. I'd agree if you said the rest of logic has an implied conditional. It's in the definition of logical consequence, after all.

And hypothetical syllogisms are discussed in (by) Aristotle. — tim wood

I did not deny that. What I said was that Aristotle says conditionals are not syllogisms, and even goes so far as to say hypothetical syllogisms are not reducible to syllogisms.

Oh, to add to my previous post. I found the bit of Aristotle I was thinking of, but it was in the Prior Analytics. Relevant to this discussion (emphasis added):

In some arguments it is easy to see what is lacking, but others escape our notice and appear to syllogize because something necessary results from what is
supposed. For example, if one had assumed that if a non-substance is destroyed then
a substance will not be destroyed, and that if those-things-out-of-which are destroyed,
the-thing-out-of-them also perished—when these things have been laid down, it is necessary indeed that the part of a substance should be a substance, but this has not been syllogized through the things taken, but rather premises are left out.
[...]
Again, if it is necessary, if a human is, for an animal to be and, if an animal, a substance, then it is necessary, if a human is, for a substance to be; but it has not yet been syllogized, since the premises are not related as we have said. We are misled in cases like these by the fact that something necessary results
from what is supposed, because a syllogism is also necessary. But ‘necessary’ is more extensive than ‘syllogism’: for every syllogism is necessary, but not everything necessary is a syllogism. Consequently, if something does result when certain things have been
posited, one should not try straight off to lead it back <into the figures>. Instead, one
must first get the two premises and next divide them this way into terms, and that
term which is stated in both the premises must be put as the middle (for the middle
must occur in both of them in all of the figures) — Aristotle

The problem is logic is supposed to work everywhere. There's no way to demarcate fictional or formal objects as a realm where logic need not apply. So the comparison to the practical use of Newtons an dynamics (despite technically not holding in all cases (relativistic speeds)) is seems like a false comparison to me. As I said, unless you're willing to severely limit and falsify much of mathematics (namely pure mathematics, which bear no known relationship to the actual world) then this seems doubly unacceptable. The transition away from Aristotle's logic to Frege's "classical" logic was Precisely because of these and other issues with the former.

Your 3 isn't part of the syllogism. There is always an implied if before every proposition; for the conclusion, it might be if 1 and 2 are true, then.... — tim wood

That's not true. Syllogistic doesn't have conditionals at all. I added number 3 to show the argument as it would be rendered in modern logic if it is the be valid. If you remove the 3rd premise in a modern logic, the resulting argument is Darapti and that commits the existential fallacy.

Syllogistic uses universal and particular declarations (although one should note that an actual theory of quantifiers did not exist until Frege created one). It doesn't have conditionals, connectives and such. So there is no implied "If" in Aristotle's logic. He actually mentions knowing (maybe in his work "Metaphysics", can't remember off hand) that there are examples of necessary relationships between premises and conclusions but which he does not consider syllogisms. He names what we call conditionals as one such non-syllogism.

Yeah it's existential implication. Because I'm going from talking about a class of things and proceeding to a conclusion about a particular. But of course in the real world, categories can fail to have members that populate it (empty sets). Hence, in modern logical systems, the translation of the Darapti mood is invalid in virtue of committing the existential fallacy. You cannot go from a universal claim to a conclusion about a particular thing without first asserting that there is at least one member which falls into that class. So,

All winged horses are horses,
All winged horses have wings,
There is at least one winged horse,
Therefore some horses have wings.

That's valid. But we know it's not sound since the third premise is clearly false.

Some people try to defend Syllogistic on this point by saying Aristotle thought logic was only concerned with existing things and so it's not really invalid. Of course, this is just stupid. If you try to keep this as valid and say that, for example, Syllogistic doesn't get anything wrong you end up invalidating other argument forms that are considered valid (I can go into this if you want) and you might as well exhaust mathematics since mathematics cannot function with the limited inference resources of Syllogistic (and besides, lots of math (pure mathematics) isn't "real" so this is a death knell). With the creation of Classical Logic, Frege set up a nice foundation for standard mathematics and its underlying reasoning.

Surely a winged horse is just a type of horse? I mean, Pegasus is just a horse with wings...

That's fine. "Pure" energy isn't a thing, so yeah it's the energy of X of in some form (chemical, thermal, mechanical and so on). As I said in another post, I wouldn't say it's reified into its own thing, existing alone.

No, that was not Bramantip, it was Darapti. Like Bramantip, Darapti is also not a valid argument in modern logic because as we see is Syllogistic, it can lead from truth to falsity due to existential quantification.

Having X joules of energy in state Y causes Y to evolve to state Z. The ~5 joules of energy in the sunlight caused 1g of water to increase by 1 degree Celsius.

I see what you call "convenient speech patterns" as sources of endless confusion. In all these speech patterns energy is reified as some sort of thing that makes up tangible things. Energy is just a tool, and yet it is said to be a cause, to convert, to be the fundamental constituent that makes up tangible things, to you that may be convenient, to me that apparent convenience in using improper language leads to much more inconvenience in the misunderstandings and misconceptions it creates. — leo

Who else is being confused by it? Physicists and those studying the subject know very well that energy isn't this other thing, tangibly out in the world. No one is actually reifying it in any substantive way. What are the supposed confusions resulting from this? The actual ones, ones that really do - in the real world - cause confusions and errors in thinking. You keep saying it's a problem without showing how the problem manifests. This is like complaining if one said "Math is hard" and saying "But math is just subject, a subject cannot have hardness. People might think you're talking about rocks instead of difficulty". This is how your view comes off to me, because I don't see any actual error in saying energy causes some such phenomena.

You're saying people don't confuse these speech patterns with literal beliefs, then why is it that even some professional physicists confuse space as an actual entity that stretches or expands between galaxies, because we keep talking about expanding space? — leo

...Because space is expanding? Or more specifically, the metric governing the geometry and size of the universe is increasing (the metric tensors change over time), so calling that expansion is perfectly sensible.

n principle you might use string theory to say, strings make up particles which make up atoms which make up molecules which make up our brain and body, then the brain and body behave in such a way so as to protect themselves and survive, and communicate with other brains and bodies to survive better, which you could describe as politics, — leo

Um, how? Show me how in principle string theory can be used to analyze politics in the appropriate way. No one would even try such a thing because it's obviously besides the point, it doesn't answer questions in the way that is relevant to political issues. Just pointing out things are constituted from smaller things doesn't mean understanding those smaller things will allow one to understand everything about what they make up. That just sounds like a composition fallacy.

I would avoid using the term "necessarily," because that suggests that we're instead doing modal logic. — Terrapin Station

While I think it's certainly true that we have to be careful in throwing out modal language and respecting where certain semantics apply and do not, I think in this case using "necessarily" isn't actually undue. Logical consequence is defined modally, as it's the relationship between the premises and what necessarily follows from them. Quoting the SEP on logical consequence:

"Contemporary analyses of the concept of consequence—of the follows from relation—take it to be both necessary and formal, with such answers often being explicated via proofs or models (or, in some cases, both)."

Here's where I'm getting tripped up in talking about soundness. While validity does not rely upon soundness for its conceptual clarity, soundness does rely upon validity -- since it must satisfy both that the argument is valid and the argument uses true premises. That's what I'm trying to get at at least, though I do not think I'm putting it well since I basically just restated validity as you note. — Moliere

Well, what's wrong with soundness relying on validity? :) For validity, we just want to ensure the logic cannot take us from truth in to falsity out because the point of logic is to have this clean rules for reasoning. We want to move from truth to further truths. Soundness of an argument is, really, just a confirmation that the conclusion is actually true.

Is veridicality the same as soundness? — Moliere

I'm just saying that in the case of a sound argument the conclusion is really true. "Veridical" isn't really a logic term, I was just trying to use a word besides "true" lol.

At least with informal logic usually the procedure is to show some kind of argument that uses a form with true premises and a false conclusion to demonstrate that some form of argument is invalid. Granted that's not the same as validity, but that's where I'm coming from in my (admittedly rambly) ruminations; that the demonstration of invalidity, rather than validity, relies upon true premises reaching a false conclusion. — Moliere

Ahhh, I see. An argument for can be shown to be invalid in the way you mention. But that isn't because of soundness is prioritized (though it is relevant in an indirect way). By showing that an inference pattern can in at least one case take you from truth to falsity, you're showing it isn't valid because, remember, validity is defined as "Truth preservation over all cases". So if you show that there's one case where it doesn't, the argument isn't valid. It doesn't really have to do with the truth of the premises, the exercise just shows a flaw with the logical machinery.

Perhaps an example is in order. Take the following Aristotlean syllogism:

All As are Bs
All As are Cs
Therefore some Bs are Cs

In this very abstract formulation, it might seem reasonable to think it valid. It kind of looks like it might be. And a simple substitution of terms seems to give it credence:

All Mammals are life forms.
All Mammals have blood.
Therefore some life forms have blood.

But as it turns out, Aristotle's logical system is flawed because we know this argument form fails to go from truth to truth in some cases, like:

All winged horses are horses
All winged horses have wings
Therefore some horses have wings

And obviously there are no winged horses in reality. The problem is with the actual argument form, we are merely using real world things and truth value to bring the flaw in the argument form to light. Lack of soundness here just shows us that the argument form cannot be valid since soundness requires validity. It's about this truth-in, truth-out requirement.