POLL on the logical validity of an argument on Joe being a squid

[Angra Mainyu]

You're assuming the conclusion that the definition you use is the correct one.

No, that is not true. You do not understand the exchange. Let us go again:

First, you think I don't know that?! Whoa.

Clearly, this definition is important to mathematicians. So?! The possibility to torture opponents is important to dictators. Is that's any reason we should follow them?

No, you do not understand. It is not that the definition is important to mathematicians. Rather, the property of arguments consisting in taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false is very important in mathematics (and physics, philosophy, and logic). That property is given a name: validity. But even if that were not the name, the property would remain important, because:

a. It preserves truth: as long as you have a form that is a valid argument, true premises result in a true conclusion.
b. It is the strongest property that is truth-preserving, in the sense that other means of deduction that also preserve truth do not allow for all of the derivations that this particular property allows.
c. It is used all the time when thinking of mathematical (and physical) and philosophical arguments.

But even if that were not the name, the property would remain important, because:

a. It preserves truth: as long as you have a form that is a valid argument, true premises result in a true conclusion.

No. Sometimes it leads to taking false conclusion as true, sometimes true conclusions as false. No good.

Not only is your answer false. It is absurd, and to a reader following the exchange rationally, it would be patently absurd. The property we are talking about is the property of arguments consisting in taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. So, obviously, clearly, evidently, by the very definition, my claim that validity so defined preserves truth is true. As long as you have a form that is a valid argument, true premises result in a true conclusion, because the argument takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

You're assuming the conclusion that the definition you use is the correct one.

I hope it is clear to you by now that you are not making sense. But I do not expect that you realize that, so if you do not, I hope that it is clear to readers by now that you are not making sense. It is a problem that you keep confusing people.

No, it works just fine. Look at the development of mathematics, physics, etc., using classical logic - and of course, it never leads from truth to falseness.

It does.

I hope you will keep your cool for a moment, read carefully, and realize that you are mistaken, and that it should be obvious to any reader paying a modicus amount of attention while being epistemically rational that you are mistaken. Obviously - very, very obviously, since it is a trivial, transpartent tautology!!!! -, as long as one deduces conclusions from arguments that have the property consisting in taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false , one would never get falsehoods from truths.

"Logic" and "valid" are not technical terms. "Validity" used in the context of logic is not a technical term. The dictionary I quoted first doesn't say "validity" is a technical term. You are making stuff up. You are an unreliable witness.

Let us take a look:

https://ahdictionary.com/word/howtouse.html

val·id
...
4. Logic
a. Containing premises from which the conclusion may logically be derived: a valid argument.

See the part that says "Logic"?
Now take a look at the explanation of how to use that dictionary: https://ahdictionary.com/word/howtouse.html

Labels

This dictionary uses various labels to identify entries that are part of the terminology of specific subjects and entries for which usage is limited to certain geographical areas. Other labels provide guidance regarding various levels of formality and usage.

A subject label, such as Chemistry or Sports, identifies the special area of knowledge to which an entry word or a single definition applies.

It seems that the label "Logic" in the entry identifies that the usage is "part of the terminology of specific subjects", and "identifies the special area of knowledge to which an entry word or a single definition applies".

Moreover, how do people learn the meaning of "valid" when it comes to arguments?
I can tell you how I learned it: in a logic course.
People who do not learn it in that way tend to learn it in some article they for some reason read, which probably is about a technical argument even if it is not technical itself, or because their parents, guardians, etc., taught them when teaching them logic. It's not a matter that comes up in every day conversation.

But regardless of whether it is a technical definition, you ought to have easily realized by now at least that by your own definition, a conclusion and its negation can both follow (as it has been repeatedly shown in this thread), and if you negate that from a contradiction, anything can be inferred, then we could keep debating that. But you fail to even acknowledge that "Joe is an elephant and Joe is not an elephant" follows from the premises.

You're just contradicting yourself.

No, I am not.

You are generally an intelligent person, but your ability in the field of logic is pretty low - not pretty low by the standards of the general population, but still too low for this exchange. Now, given that you are intelligent, you almost certainly have the ability to study and become much better at logic. If you did that, then you would not be making the claims that you are making. I would suggest taking a few logic or math courses in a serious college, and taking the courses seriously, if you want to improve significantly in that regard. But since you regard yourself as far better than you are, you're not likely to be interested.

And how would you know how good I am at logic?! On the basis of a definition you can't justify?!

No, on the basis of reading your exchanges with others and with me, including this thread. That includes your big mistakes in our exchange, your failure to realize those mistakes even after they are repeated to you more than once, etc.

 

[Speakpigeon]

Moreover, how do people learn the meaning of "valid" when it comes to arguments?
I can tell you how I learned it: in a logic course.
People who do not learn it in that way tend to learn it in some article they for some reason read, which probably is about a technical argument even if it is not technical itself, or because their parents, guardians, etc., taught them when teaching them logic. It's not a matter that comes up in every day conversation.

Most people don't get ever the "benefit" of formal logic lessons, even less any tutorial on what it is for an argument to be valid according to some idiot mathematician.

Most people are perfectly capable of making valid inferences without ever having the "benefit" of lessons on the validity of arguments.

In fact, ordinary, everyday speech relies heavily on our intuitive capability to infer validly from what other people say even though hardly anyone ever asserts any proper syllogisms. Instead, we assert the premises and leave it to the listeners to infer the valid conclusion by themselves. And then, if you don't want to assume that people routinely infer the valid conclusion without even thinking about it, indeed without realising they are doing it, and without usually asking for clarification, then you can't explain how people get to understand each other at all when such partial syllogisms are used, and they are used very often, in ordinary conversation at the pub as well as in advertising, political speech and propaganda, i.e. outside any context where formal logic is used. Please note that this fact has been known since Ancient Greece.

enthymeme
Word origin of 'enthymeme'
C16: via Latin from Greek enthumēma, from enthumeisthai to infer (literally: to have in the mind), from en-2 + thumos mind

Enthymeme, literally, to have in the mind.

And, obviously, you couldn't explain what thinkers talked about during 2,300 years since Aristotle when they discussed in minute details syllogisms and enthymemes and what it meant for an argument to be valid.

"Logic" and "valid" are not technical terms. "Validity" used in the context of logic is not a technical term. The dictionary I quoted first doesn't say "validity" is a technical term. You are making stuff up. You are an unreliable witness.

Let us take a look:

https://ahdictionary.com/word/howtouse.html

val·id
...
4. Logic
a. Containing premises from which the conclusion may logically be derived: a valid argument.

See the part that says "Logic"?
Now take a look at the explanation of how to use that dictionary: https://ahdictionary.com/word/howtouse.html

Labels

This dictionary uses various labels to identify entries that are part of the terminology of specific subjects and entries for which usage is limited to certain geographical areas. Other labels provide guidance regarding various levels of formality and usage.

A subject label, such as Chemistry or Sports, identifies the special area of knowledge to which an entry word or a single definition applies.

It seems that the label "Logic" in the entry identifies that the usage is "part of the terminology of specific subjects", and "identifies the special area of knowledge to which an entry word or a single definition applies".

This other dictionary provides definitions based on the empirical evidence of a corpus.

Corpus
A corpus is a large collection of written or spoken texts that is used for language research.

Please take the time to read and to consider all the implications:
EB

Argument
An argument is a statement or set of statements that you use in order to try to convince people that your opinion about something is correct.

Valid
1. having legal force; properly executed and binding under the law
2. well-grounded on principles or evidence; able to withstand criticism or objection, as an argument; sound
3. effective, effectual, cogent, etc.
4. (Rare) robust; strong; healthy
5. (Logic) correctly derived or inferred according to the rules of logic

SYNONYMY NOTE:
valid applies to that which cannot be objected to because it conforms to law, logic, the facts, etc. [a valid criticism]; sound refers to that which is firmly grounded on facts, evidence, logic, etc. and is therefore free from error [a sound method]; cogent implies such a powerful appeal to the mind as to appear conclusive [cogent reasoning]; convincing implies such validity as to persuade or overcome doubts or opposition [a convincing argument]; telling suggests the power to have the required effect by being forcible, striking, relevant, etc. [a telling rejoinder]

Validity
Word origin Fr validité < L validitas, strength

Validity
The validity of something such as a result or a piece of information is whether it can be trusted or believed.

Validity
the state, quality, or fact of being valid in law or in argument, proof, authority, etc.

Valid argument
A valid argument, comment, or idea is based on sensible reasoning.

Valid argument
Example sentences
But that's by no means the only valid argument. (The Sun 2015)
There are simply no valid arguments against switching lights off in broad daylight. (Times, Sunday Times 2006)
Both sides have valid arguments to make and should feel free to do so. (The Sun 2016)

 

[fast]

Argument
An argument is a statement or set of statements that you use in order to try to convince people that your opinion about something is correct.

It seems everywhere we turn, someone, somewhere has written a definition. They shouldn’t be regarded as opinion pieces, but inferior definitions are prevalently abound.

An argument can be used for the purpose of persuasion, but a statement of such has no place in a short and concise definition—unless maybe we were talking about rhetoric.

The major tool of the master logician is the argument, and if his principle-based priority is to committedly stay true to form to his craft and finds greater pride not in his ability to convince others but to provide excellent argumentation, he would gladly fall on his sword and accept defeat from another that aims to merely convince a crowd.

Unfortunately, it’s not always the case that a superior argument (one that perfectionately delivers us to a conclusion worthy of trust) better convinces all audiences. Sometimes the charlatan with shoddy arguments fair better at convincing than others.

 

[Speakpigeon]

Argument
An argument is a statement or set of statements that you use in order to try to convince people that your opinion about something is correct.

It seems everywhere we turn, someone, somewhere has written a definition. They shouldn’t be regarded as opinion pieces, but inferior definitions are prevalently abound.

An argument can be used for the purpose of persuasion, but a statement of such has no place in a short and concise definition—unless maybe we were talking about rhetoric.

The major tool of the master logician is the argument, and if his principle-based priority is to committedly stay true to form to his craft and finds greater pride not in his ability to convince others but to provide excellent argumentation, he would gladly fall on his sword and accept defeat from another that aims to merely convince a crowd.

Unfortunately, it’s not always the case that a superior argument (one that perfectionately delivers us to a conclusion worthy of trust) better convinces all audiences. Sometimes the charlatan with shoddy arguments fair better at convincing than others.

We're not talking about any "master logician", that would be a derail, we're talking specifically about logical arguments, and more specifically deductive arguments. However, a deductive argument is a species of logical argument and a logical argument is a species of argument. And it is true we use, in everyday life, including for rhetorical purposes, complete or partial deductive arguments, as "statement or set of statements that you use in order to try to convince people that your opinion about something is correct".
EB

 

[Speakpigeon]

So again, what is the justification given by professional specialists, mathematicians, logicians, philosophers etc. that would support your claim that the definition of logical validity you use is the correct one.
EB

 

[fast]

So again, what is the justification given by professional specialists, mathematicians, logicians, philosophers etc. that would support your claim that the definition of logical validity you use is the correct one.
EB

Some definitions have a better fit than others. For a nut, some sockets are too small while some are too large. Even two of similar size that do the job fine can provide more coverage area over its surface area than others. The definition provided has a better fit for the purpose in which it is intended. A 9/16th socket is the one with a better fit since the oil pan requires the removal of a 9/16th nut.

But, the system isn’t absolute. The great divide between deductive arguments and nondeductive arguments didn’t have to come to be what it is, just like it didn’t have to be the case the required electrical outlets in the US had to be uniform.

I look at the consequences and effects of the definition. It’s written as such that keeps form specific to deductive arguments only. Tweaks of a certain kind would violate that separation. The definition isn’t absolute as if to say its function must maintain the integrity’ for which it does, but given the intent for which it’s being used, it provides a better fit.

 

[Speakpigeon]

So again, what is the justification given by professional specialists, mathematicians, logicians, philosophers etc. that would support your claim that the definition of logical validity you use is the correct one.
EB

Some definitions have a better fit than others. For a nut, some sockets are too small while some are too large. Even two of similar size that do the job fine can provide more coverage area over its surface area than others. The definition provided has a better fit for the purpose in which it is intended. A 9/16th socket is the one with a better fit since the oil pan requires the removal of a 9/16th nut.

But, the system isn’t absolute. The great divide between deductive arguments and nondeductive arguments didn’t have to come to be what it is, just like it didn’t have to be the case the required electrical outlets in the US had to be uniform.

I look at the consequences and effects of the definition. It’s written as such that keeps form specific to deductive arguments only. Tweaks of a certain kind would violate that separation. The definition isn’t absolute as if to say its function must maintain the integrity’ for which it does, but given the intent for which it’s being used, it provides a better fit.

You're merely acknowledging that the definition proposed by mathematical logic is essentially arbitrary, just as the metric standard is arbitrary, just as the US customary system of measurement is arbitrary.

And the US customary system is "non-coherent":

In the US customary system of measurement, which is non-coherent, the unit of power is the "horsepower", which is defined as "550 foot-pounds per second" (the pound in this context being the pound-force). Similarly, neither the US gallon nor the imperial gallon is one cubic foot or one cubic yard— the US gallon is 231 cubic inches and the imperial gallon is 277.42 cubic inches.

So, arbitrary systems can be incoherent.

But Angra Mainyu and Bomb both claim the Squid argument valid and both dismiss as wrong people like me who feel intuitively that the argument is not valid. They justify their claim with a formal proof and the definition of validity proposed by mathematicians. Their attitude wouldn't make sense unless they thought their definition as somehow the correct one. Yet, they can't produce any justification given by professional specialists, mathematicians, logicians, philosophers etc. that would support this idea that the definition of logical validity they use is the correct one.
EB

 

[fast]

Those co-opting word-stealing ambiguity-breeding arithmetic-loving mathematican bastards!

 

[Angra Mainyu]

Most people don't get ever the "benefit" of formal logic lessons, even less any tutorial on what it is for an argument to be valid according to some idiot mathematician.

Most people do not use the word "valid" in the sense that involves the validity of deductive arguments only. They might use "valid" to mean other things (e.g., reasonable, or something like that).
Those that do use the word "valid" in that context probably either had those lessons - on logic, or math, or philosophy, or maybe just law, but something -, or they are repeating something someone else (with expertise) said, or something they read somewhere (which might or might not have been accurate), like when they use words such as "electron", or "black hole", or "antimatter". But even if they use the words, they do not understand them very well, and they are using it with the understanding that the technical sense is the relevant one.

Most people are perfectly capable of making valid inferences without ever having the "benefit" of lessons on the validity of arguments.

Certainly. And most people are perfectly capable of making valid inferences without ever grasping the meaning of the word "valid" in this context. For that matter, most people are perfectly capable of making sound inferences without ever even hearing the word "sound" in the sense that is relevant here. But none of this has anything to do with this matter.

In fact, ordinary, everyday speech relies heavily on our intuitive capability to infer validly from what other people say even though hardly anyone ever asserts any proper syllogisms.

Well, it relies on human intuitive capability of doing that more or less, even though in a pretty flawed manner but in most cases sufficient. However, it surely does not rely at all in our ability to grasp the meaning of the term "valid". Of course, people who do study proper thought - like logicians - realized that an important property of arguments is that of consisting in taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. But most people have not even thought about that. They just make valid inferences, and then when it comes to politics, religion, ideology, etc., they make plenty of bad ones - and even in cases not involving those, due to cognitive bias.
But regardless, there is a human intuitive capability here - even if a very flawed one -, but not a general concern among humans to try to study that capability and/or the properties of arguments and/or to learn the terminology used in the study of such properties.

Instead, we assert the premises and leave it to the listeners to infer the valid conclusion by themselves. And then, if you don't want to assume that people routinely infer the valid conclusion without even thinking about it, indeed without realising they are doing it, and without usually asking for clarification, then you can't explain how people get to understand each other at all when such partial syllogisms are used, and they are used very often, in ordinary conversation at the pub as well as in advertising, political speech and propaganda, i.e. outside any context where formal logic is used. Please note that this fact has been known since Ancient Greece.

You are not even grazing my arguments. Of course, people do that all the time. They make valid inferences. They make sound inferences - they also make lots of invalid ones due to all sorts of cognitive flaws, but that aside, at least generally they can do it -, but they do all that without even realizing that they are doing it, without studying what they are doing, and without caring about the terms such as 'sound' or 'valid' in this context, which they probably have never heard of, except maybe from experts and without really understanding what the experts were talking about.

And, obviously, you couldn't explain what thinkers talked about during 2,300 years since Aristotle when they discussed in minute details syllogisms and enthymemes and what it meant for an argument to be valid.

Of course I can. Those were actually the very small minority of people who did not just make valid inferences, etc., but actually decided to study the principles underlying them - and generally, other principles of reasoning.

This other dictionary provides definitions based on the empirical evidence of a corpus.

Let us see. You should provide the relevant links by the way.

Argument
An argument is a statement or set of statements that you use in order to try to convince people that your opinion about something is correct.

That is one of the meanings of "argument". It is certainly not the meaning that is relevant here. Otherwise, it would also not make sense for you to say things like:

Mathematical logic, as it is recognised by most mathematicians today as the standard method of logical calculus, says the argument is valid.

Surely, mathematical logic says nothing about statements or sets of statements that you use in order to try to convince people that your opinion about something is correct. Being very charitable, what you are saying is that the conception of validity used in mathematical logic is such that the deductive argument in the OP is valid in accordance to it. This is true. But - again - it makes no sense with the new definition.

 

[Speakpigeon]

Initially, since Aristotle, the Stoics, through the Scholastics and people like Leibnitz, l'école de Port-Royal in France etc. and broadly up until Frege, formal logic was conceived as the formalisation of logical reasoning, where logical reasoning was thought of as a capability of the human mind. All during this very long period, formal logic was understood as a practical discipline, a tool. The Scholastic in particular developed a debating procedure which was essentially a procedure to prove claims during theological debates. The method of proof mathematicians use today is a mathematical formalisation of this debating procedure, though with some major differences. Even Frege developed his method of formal logic to do exactly the same thing as what human logical reasoning does, only formally, which would have allowed mathematicians to formalise the proofs of their theorems, something Frege thought would help improve rigour.

In that context, the notions of argument and validity of argument were at the heart of the discipline. The term "argument" referred to all reasoned arguments, and "validity" referred to all deductive arguments. These were actual argument people had. Not the kind of abstract formulas we find in maths textbooks which are disconnected from human reasoning.

Read Boole and Frege. That's the way they still expressed themselves. Boole titled his own book, published in 1854, "An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities". The idea, clearly was to model what all human beings do when they reason logically, including by using logically valid arguments: Socrates is a man,; All men are mortal; Therefore, Socrates is mortal. That was 2,400 years ago! Contrary to Plato, Aristotle was interested essentially in the idea of developing empirical sciences. His formal logic was meant to be an operational model of human logical reasoning, not some abstraction cut off from the reality of life.

However, once mathematicians, starting with Boole, Frege and Russell, started the formalisation of logic using a mathematical formalisation, they also started to cut corners. Unable to reproduce the logic of human reasoning, they opted for the best approximation they could find, which was essentially the material implication. The irony is, this makes 1st order logic, in effect, a first order approximation of the logic of human reasoning. Since then, no progress has been made in that direction. The whole field of mathematical logic is based on this approximation. Approximation here means that the more complex the formula, the more likely the result will be different from human logical reasoning, and therefore what we would all qualify as just plain wrong.

There is now, and since several generations, everywhere in the world, a class of self-appointed ignoramuses who assert against all empirical evidence that logic, argument and validity are nothing but what mathematicians have decided to formalise as such. Whatever human logical reasoning might be, it's just not logic and not valid if it doesn't comply with this first order approximation that is the mathematical model. What a load of bullshit.
EB

 

[Angra Mainyu]

Initially, since Aristotle, the Stoics, through the Scholastics and people like Leibnitz, l'école de Port-Royal in France etc. and broadly up until Frege, formal logic was conceived as the formalisation of logical reasoning, where logical reasoning was thought of as a capability of the human mind. All during this very long period, formal logic was understood as a practical discipline, a tool. The Scholastic in particular developed a debating procedure which was essentially a procedure to prove claims during theological debates. The method of proof mathematicians use today is a mathematical formalisation of this debating procedure, though with some major differences. Even Frege developed his method of formal logic to do exactly the same thing as what human logical reasoning does, only formally, which would have allowed mathematicians to formalise the proofs of their theorems, something Frege thought would help improve rigour.

In that context, the notions of argument and validity of argument were at the heart of the discipline. The term "argument" referred to all reasoned arguments, and "validity" referred to all deductive arguments. These were actual argument people had. Not the kind of abstract formulas we find in maths textbooks which are disconnected from human reasoning.

Actually, those terms are in English, so they were not known to Aristotle and all. But that aside, Aristotle and others over time did study logic by studying how to properly reason, and that included deductive arguments - even though it was not limited to them. When it comes to deductions, the Aristotelian system was a contribution, but it was too weak in many instances (see this post for an example). The fact is that if one knows that some statements are true and one has the modern concept of validity and understands modern logic, one can figure out other truths that one would be unable to figure out with the Aristotelian system. That is progress, and regardless of the context in which it developed, it is also applicable to contexts other than mathematics. That is why it is in fact so applied (e.g., it is widely applied in philosophy).

In general, the modern concept of validity has allowed progress in mathematics - and, as a result, in science, in particular physics - that would not have been available with the previous tools.

The idea, clearly was to model what all human beings do when they reason logically, including by using logically valid arguments: Socrates is a man,; All men are mortal; Therefore, Socrates is mortal. That was 2,400 years ago! Contrary to Plato, Aristotle was interested essentially in the idea of developing empirical sciences. His formal logic was meant to be an operational model of human logical reasoning, not some abstraction cut off from the reality of life.

Of course it was not meant to be cut off from the reality of life, but on the other hand, the study was not meant to make an empirical model of human reasoning regardless of what it was - even when in error. He meant to study proper reasoning, and find the principles behind it (and also, he studied errors, but in order to avoid them).

However, once mathematicians, starting with Boole, Frege and Russell, started the formalisation of logic using a mathematical formalisation, they also started to cut corners. Unable to reproduce the logic of human reasoning, they opted for the best approximation they could find, which was essentially the material implication. The irony is, this makes 1st order logic, in effect, a first order approximation of the logic of human reasoning. Since then, no progress has been made in that direction. The whole field of mathematical logic is based on this approximation. Approximation here means that the more complex the formula, the more likely the result will be different from human logical reasoning, and therefore what we would all qualify as just plain wrong.

There is now, and since several generations, everywhere in the world, a class of self-appointed ignoramuses who assert against all empirical evidence that logic, argument and validity are nothing but what mathematicians have decided to formalise as such. Whatever human logical reasoning might be, it's just not logic and not valid if it doesn't comply with this first order approximation that is the mathematical model. What a load of bullshit.

You got this badly wrong.

Much of the progress of modern mathematics would not have been possible without new discoveries about the correct way of reasoning. It is not as if mathematicians were not interested in finding truth. They were, and they made progress. But similarly, much of the progress in modern physics needs at least a portion of modern mathematics. You would not be able to do that with the Aristotelian system. In even much simpler cases, the Aristotelian system would not have been successful (see Bomb#20's example). Now, perhaps some people would be able to figure out intuitively that an inference like that in the example is correct, even if they do not realize that the Aristotelian system is not enough to generate it. However, when it comes to much more complicated inferences, having modern logic is very helpful. It was not a whim of some mathematicians. Much progress resulted from it.

 

[Speakpigeon]

Actually, those terms are in English, so they were not known to Aristotle and all. But that aside, Aristotle and others over time did study logic by studying how to properly reason, and that included deductive arguments - even though it was not limited to them. When it comes to deductions, the Aristotelian system was a contribution, but it was too weak in many instances (see this post for an example). The fact is that if one knows that some statements are true and one has the modern concept of validity and understands modern logic, one can figure out other truths that one would be unable to figure out with the Aristotelian system. That is progress, and regardless of the context in which it developed, it is also applicable to contexts other than mathematics. That is why it is in fact so applied (e.g., it is widely applied in philosophy).

In general, the modern concept of validity has allowed progress in mathematics - and, as a result, in science, in particular physics - that would not have been available with the previous tools.


Of course it was not meant to be cut off from the reality of life, but on the other hand, the study was not meant to make an empirical model of human reasoning regardless of what it was - even when in error. He meant to study proper reasoning, and find the principles behind it (and also, he studied errors, but in order to avoid them).

However, once mathematicians, starting with Boole, Frege and Russell, started the formalisation of logic using a mathematical formalisation, they also started to cut corners. Unable to reproduce the logic of human reasoning, they opted for the best approximation they could find, which was essentially the material implication. The irony is, this makes 1st order logic, in effect, a first order approximation of the logic of human reasoning. Since then, no progress has been made in that direction. The whole field of mathematical logic is based on this approximation. Approximation here means that the more complex the formula, the more likely the result will be different from human logical reasoning, and therefore what we would all qualify as just plain wrong.

There is now, and since several generations, everywhere in the world, a class of self-appointed ignoramuses who assert against all empirical evidence that logic, argument and validity are nothing but what mathematicians have decided to formalise as such. Whatever human logical reasoning might be, it's just not logic and not valid if it doesn't comply with this first order approximation that is the mathematical model. What a load of bullshit.

You got this badly wrong.

Much of the progress of modern mathematics would not have been possible without new discoveries about the correct way of reasoning. It is not as if mathematicians were not interested in finding truth. They were, and they made progress. But similarly, much of the progress in modern physics needs at least a portion of modern mathematics. You would not be able to do that with the Aristotelian system. In even much simpler cases, the Aristotelian system would not have been successful (see Bomb#20's example). Now, perhaps some people would be able to figure out intuitively that an inference like that in the example is correct, even if they do not realize that the Aristotelian system is not enough to generate it. However, when it comes to much more complicated inferences, having modern logic is very helpful. It was not a whim of some mathematicians. Much progress resulted from it.

That's all irrelevant to what I said. You're not up to it, man.

Further, you'd be at pain to give even one example of something the material implication could prove that formal logic prior to it couldn't prove.

Me, on the other hand I could give you any number of examples of implications most people would find intuitively not valid that the material implication takes to be valid.

Oh, wait, we've done that already.

Still, given you haven't been able to get yourself to provide the justification I have been asking for, there is not point having this conversation. You are an ignoramus and a dogmatic fool. You're the perfect example of the guy who knows a lot but just not enough to understand why he is doing what he is doing.
EB

 

[fast]

Hasn’t the shift in meanings changed similarly to how “possibility” has?

Once upon a time, anything physically impossible would have remained intuitively impossible despite the expanded version (logically possible) that includes the physically impossible. Any once upon a time meaning of “valid” doesn’t seem to compartmentalize pure form from the soundness of an argument. Heck, older versions don’t even render the term exclusive to deductive arguments.

The definition that’s been offered (the new version) is at odds (on occasion) with other usages.

 

[Speakpigeon]

Hasn’t the shift in meanings changed similarly to how “possibility” has?

Yes and no.

Yes, logical possibility is an extension.

No, because unlike purported experts in mathematical logic here, philosophers don't assert you're wrong if you mean physically possible.

Once upon a time, anything physically impossible would have remained intuitively impossible despite the expanded version (logically possible) that includes the physically impossible. Any once upon a time meaning of “valid” doesn’t seem to compartmentalize pure form from the soundness of an argument. Heck, older versions don’t even render the term exclusive to deductive arguments.

Indeed, but for each thing we consider as possibly valid or invalid, we have a specific notion of validity, as demonstrated by the various senses defined here. Each time you have a particular kind of validity:

Valid
1. Well grounded; just: a valid objection.
2. Producing the desired results; efficacious: valid methods.
3. Having legal force; effective or binding: a valid title.
4. Logic
a. Containing premises from which the conclusion may logically be derived: a valid argument.
b. Correctly inferred or deduced from a premise: a valid conclusion.

And so there is a long established notion of validity as applied to argument which goes back to at least Aristotle, a syllogism being nothing else than a valid argument.

The definition that’s been offered (the new version) is at odds (on occasion) with other usages.

I don't mind that it's at odds with the legal sense of validity because it's just irrelevant. Angra Mainyu is unlikely to try to castigate a lawyer or a judge for using "valid" in the legal sense. What's wrong and idiotic with Angra Mainyu is that he really believes the notion of validity as applied to logical arguments has been invented or somehow put straight by mathematicians like Russell. A notion 2,400 years old and that is definitely not in any need of being straightened. What mathematicians have successfully achieved is to convince themselves, and apparently most philosophers and computer scientists, and most intellectuals generally, that the mathematical notion of validity is somehow correct.

There are a few dissenting voices but there are just ignored because presumably of the perceived authority of mathematics in general. And yet, the notion of validity used in mathematical logic is wrong in the same way as a first order approximation is not the exact value.

This is an ersatz. Like Muzak passing off as not only music, but good music, but best music you could hear. This is insane.

And this, even though we all have our own private, portable, free, and very, very good logical intuition. We really don't need mathematical logic.
EB

 

[Speakpigeon]

Yes, it's valid, because the conclusion follows from the premises. (It's unsound, since at least one of the premises is false, but plenty of unsound arguments are valid.)

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.
Joe is either a squid or a giraffe.
------------------------------------
Joe is a giraffe.
A giraffe is not an elephant.
-------------------------------
Joe is not an elephant.
-------------------------
Joe is an elephant and Joe is not an elephant.
---------------------------------------------------
(Joe is not a squid) implies (Joe is an elephant and Joe is not an elephant.)
------------------------------------------------------------------------------------
Joe is a squid. Q.E.D.

So yes, the conclusion follows from the premises.

It's valid in the sense that he has listed six sequential statements and the sixth logically follows from the first five. (Well, from the second through the fifth. Statement 1 was unnecessary. Statements 3 through 5 imply that statement 2 is false. So 3 through 5 plus 2 are mutually contradictory; and a contradiction implies anything, even that an elephant is a squid.)

???

It's not logic at all.

It's "logistic".

Logistic
2. Mathematical logic; Symbolic logic.

You can come back. Everything is forgiven.

Just make sure next time you use the proper vocabulary.
EB

 

[Speakpigeon]

in pure mathematics, we only find knowledge of logical truths. In order that such a knowledge be possible, it is necessary that there should be self-evident logical truths, that is to say, truths which are known without demonstration. These are the truths which are the premises of pure mathematics as well as of the deductive elements in every demonstration on any subject whatever.

Good point, Bertrand! That's very perspicacious and quite literally obviously true.

However, how could one admit that self-evident logical truths are indeed necessary to any logical reasoning whatever, including the one necessary for mathematics and science to exist at all, and nonetheless deny that human beings have an intrinsic logical capability; or deny that this logical capability is the only reference we have; or deny that therefore any formal logic has to be at least consistent with it?
EB

 

[Speakpigeon]

Frege believed that the truths of arithmetic and of all mathematics are derived from self-evident logical truths.

Joan, thanks for that!

Yeah, even Frege believed that... Whoa. He died bitter and in isolation. He would feel even worse if he could come back.
EB

 

[fast]

Gosh, the more I learn, the less it’s true I know what I thought I did. If I keep this up, I’m gonna run around thinking I know nothing. Better stop while still properly disillusioned.

 

[fast]

...

 

[Speakpigeon]

...

Hey, man, we could infer anything from that, and validly, you know?!
EB