Logic is perfect

[SpheresOfBalance]

Nice to see that someone here has an understanding of Formal Logic.

Which you've proven time and time again is the only thing you really care about, just a 'slightly' more mellow chaz. Your education, is your weapon, to 'needlessly' smite, when it could better serve you otherwise. Surely it serves no high moral standing.

Like I said Logic can't be used to prove anything that our senses are incapable of sensing. So it has limitations, with means it's not perfect. And that which you cling to, "to be and/or not to be," (Was Shakespeare keen with logic?) is quite elementary, and not very profound really. Sorry but no gods would ever be subservient to such simplicity, at least in my book.

So you really believe you're in a running program, huh? And you claim you're an atheist?

Like I said, with respect to all those definitions, Logic is 100% only that which deals with the human perspective, it is definitely not necessarily inter-universal, quite possibly not even inter-solar, let alone inter-galactic.

Compliments Wikipedia:
"Existence has been variously defined by sources.[citation needed] In common usage, it is the world one is aware or conscious of, and that persists independent of one's absence. Other definitions describe it as everything that 'is', or more simply, everything. Some define it to be everything that most people believe in."

Compliments Dictionary.com:
agnostic [ag-nos-tik]
noun
1. a person who holds that the existence of the ultimate cause, as God, and the essential nature of things are unknown and unknowable,
or that human knowledge is limited to experience.

Like I and the dictionary states, I'm currently Agnostic, which means that 'experience' may change that.

[Arising_uk]

Which you've proven time and time again is the only thing you really care about, just a 'slightly' more mellow chaz. Your education, is your weapon, to 'needlessly' smite, when it could better serve you otherwise. Surely it serves no high moral standing.

What an insecure bunny you are. In case it's skipped your notice this section is about Logic and Philosophy of Mathematics and all I was doing was passing another member a compliment upon their knowledge as it's reasonably rare upon this site to chat with someone who has an opinion upon something they've actually studied.

Like I said Logic can't be used to prove anything that our senses are incapable of sensing. So it has limitations, with means it's not perfect. And that which you cling to, "to be and/or not to be," (Was Shakespeare keen with logic?) is quite elementary, and not very profound really. Sorry but no gods would ever be subservient to such simplicity, at least in my book.

Unfortunately that book appears not to contain any Logic or much knowledge of Shakespeare. You keep confusing the empirical with the logical, they are not the same. Symbolic Logic is perfect for two reasons, one(as wyman pointed out to me) because it is defined that way and two, because it arises due to there being things and states of affairs, its the logic of existence and if 'God's' exist then they are subject to it. I'm still waiting for you to tell me how a 'God' can exist and not exist?

So you really believe you're in a running program, huh? And you claim you're an atheist?

No, I am an atheist as the thought of a 'God or God's' never enters my mind as a cause or an explanation unless in discussion with theists or philosophers. I did not say I believe in the ideas of Zuze, Fredkin, et al, I said that if I was to bother to hold a metaphysic then I'd choose a culturally up-to-date one and what they punt can't get more with the times.

Like I said, with respect to all those definitions, Logic is 100% only that which deals with the human perspective, it is definitely not necessarily inter-universal, quite possibly not even inter-solar, let alone inter-galactic.

It's universal, that you can't grasp this is because you've got a weird epistemology that tells you that 'I know nothing' which completely ignores the fact that this statement is a logical contradiction.

Compliments Wikipedia:
"Existence has been variously defined by sources.[citation needed] In common usage, it is the world one is aware or conscious of, and that persists independent of one's absence. ...

If it is the world one is aware or conscious of then how does one know it persists in one's absence?

Other definitions describe it as everything that 'is', or more simply, everything. Some define it to be everything that most people believe in."

Compliments Dictionary.com:
agnostic [ag-nos-tik]
noun
1. a person who holds that the existence of the ultimate cause, as God, and the essential nature of things are unknown and unknowable,
or that human knowledge is limited to experience.

Like I and the dictionary states, I'm currently Agnostic, which means that 'experience' may change that.

If the essential nature of things, i.e. 'God's' are unknown and unknowable what experience do you think would make the unknowable knowable?

[Arising_uk]

Pure nonsense!

I doubt you even understood what I said.

Logic can do preliminary investigation in crime cases. Ie if a lot of murders has been going on, profilers can run some diagnostics via computers that will find suspects based on probability.

Profiling is psychology, anything else is just a database search(which is logic, relational algebra to be precise) but in the end the murderers they find will already be in prison. All they can do is see if they can match other open-cases.

Many stock market investors uses algorithms to buy stocks these days, as humans are very slow and can't process thousands of data/sec.

Most lose money if they can't afford the hardware or access to the right data-streams, pretty much the only algorithm users who make money this way are the HFT and they do it by front-running, i.e. gaming the system, not by stock analysis.

[SpheresOfBalance]

Which you've proven time and time again is the only thing you really care about, just a 'slightly' more mellow chaz. Your education, is your weapon, to 'needlessly' smite, when it could better serve you otherwise. Surely it serves no high moral standing.

What an insecure bunny you are. In case it's skipped your notice this section is about Logic and Philosophy of Mathematics and all I was doing was passing another member a compliment upon their knowledge as it's reasonably rare upon this site to chat with someone who has an opinion upon something they've actually studied.
Fact: I'm no bunny, and you've proven otherwise on more than one occasion, case in point. Well at least one more for the list. I'm not saying I don't do it. But I'm pretty sure I don't usually start it, at least I'm sure I'd rather not.

Like I said Logic can't be used to prove anything that our senses are incapable of sensing. So it has limitations, with means it's not perfect. And that which you cling to, "to be and/or not to be," (Was Shakespeare keen with logic?) is quite elementary, and not very profound really. Sorry but no gods would ever be subservient to such simplicity, at least in my book.

Unfortunately that book appears not to contain any Logic or much knowledge of Shakespeare. You keep confusing the empirical with the logical, they are not the same. Symbolic Logic is perfect for two reasons, one(as wyman pointed out to me) because it is defined that way and two, because it arises due to there being things and states of affairs, its the logic of existence and if 'God's' exist then they are subject to it. I'm still waiting for you to tell me how a 'God' can exist and not exist?
You assume that they have to "exist or not exist" by your definition of existence, as if it's definitely the only one there is, which you cannot know for sure. Do you know how ridiculous is sounds to use such an argument as, "Because it's defined that way?" OK, I'll define something. Rain: the manifestation of gods tears. So it must be true because it was defined that way, absurd!

Like I said a few messages ago, as to the definitions of logic: validity, reasoning, principles, correctness, reliability, inference, proper, reasonable, a particular way, formal processes, and thinking, are all ambiguous, they are not necessarily quantifiable, such that they are defined as the particular human case warrants, by those humans steering the case.

Things and states of affairs simply speaks of existence, and as I've already stated, humans don't necessarily know what that is in all cases, as logic in those cases, falls flat on it's face.

So you really believe you're in a running program, huh? And you claim you're an atheist?

No, I am an atheist as the thought of a 'God or God's' never enters my mind as a cause or an explanation unless in discussion with theists or philosophers. I did not say I believe in the ideas of Zuze, Fredkin, et al, I said that if I was to bother to hold a metaphysic then I'd choose a culturally up-to-date one and what they punt can't get more with the times.
Actually that's, not how you originally phrased it, I'll have to find the original.

Like I said, with respect to all those definitions, Logic is 100% only that which deals with the human perspective, it is definitely not necessarily inter-universal, quite possibly not even inter-solar, let alone inter-galactic.

It's universal, that you can't grasp this is because you've got a weird epistemology that tells you that 'I know nothing' which completely ignores the fact that this statement is a logical contradiction.
You seem to not pay attention, as I've said in the past, it's not to be taken literally in 100% of all the possible cases, that it's to ground oneself, that it should be the fundamental starting place, and should always be considered to stave off the possibly of jumping to conclusions. And no, the human perspective of measurement, judgement, is surely not universal. That you can't grasp it is surely reflected in that personally type of yours that you've mentioned.

Compliments Wikipedia:
"Existence has been variously defined by sources.[citation needed] In common usage, it is the world one is aware or conscious of, and that persists independent of one's absence. ...

If it is the world one is aware or conscious of then how does one know it persists in one's absence?
Silly question, have you only been everywhere only once?

Other definitions describe it as everything that 'is', or more simply, everything. Some define it to be everything that most people believe in."

Compliments Dictionary.com:
agnostic [ag-nos-tik]
noun
1. a person who holds that the existence of the ultimate cause, as God, and the essential nature of things are unknown and unknowable,
or that human knowledge is limited to experience.

Like I and the dictionary states, I'm currently Agnostic, which means that 'experience' may change that.

If the essential nature of things, i.e. 'God's' are unknown and unknowable what experience do you think would make the unknowable knowable?
Another silly assertion, as obviously such a statement can only be spoken in the present tense, unless you believe yourself clairvoyant? How do we make any progress then? Easy the creator finally, instantaneously speaks to each and every animal alive, with the exact same message, "see me, I exist as you exist." I mean, at least that's one possibility. I can think of others even more far fetched, relative to the animal of the day, that is.

[Arising_uk]

I am using the term 'induction' as the same as 'non-deductive' , ie 'the conclusions, while indicated by the premises, do not follow deductively from the premises."

Perception is inductive, because the conclusion: eg 'that there is a table in front of me' does not follow deductively from the 'premisses' (ie the sense data that enters my eyes.). ...

Hmm... and yet we could consider the CNS as a parallel neural net which 'deduces' that there is a table in front of me from the sense-data entering it?

In a combined argument of induction plus deduction the conclusion must be inductive as there will remain that element of uncertainty.

You can arrive at a set of theories from induction, as in science, but the creation of axioms is quite a different matter. Axioms are the basis for abstract systems (such as pure mathematics and pure geometry), but any application of them to the real world (ie that which we know from sense-data) requires a mapping from one to the other.

I take your point.

This mapping is often presumed to be perfect in a 'naïve' perspective of the world, eg when physicists hold that the matter of the universe 'obeys' the 'laws of physics'.

Hmm... I think the physicists, at least the QMers, have long accepted that there is no absolute truth to the matter.

But philosophers need to be mindful that a mapping between an axiomatic abstract system and the 'real world' is not perfect and that , for example, the motions of matter in the real world is only approximately described by the 'laws of physics'.

Which is why they talk in probabilities now, and you gotta admit a probability to eleven or more decimal places is pretty probable, about 99.99999999999% certain.

[Arising_uk]

Fact: I'm no bunny, and you've proven otherwise on more than one occasion, case in point. Well at least one more for the list. I'm not saying I don't do it. But I'm pretty sure I don't usually start it, at least I'm sure I'd rather not.

Total bunny, as you find offence in a compliment to others and your insecurity is shown in the faux-intellectual speech forms you use. Add to that that you rush to the defense of others when it's neither requested nor required.

You assume that they have to "exist or not exist" by your definition of existence, as if it's definitely the only one there is, which you cannot know for sure.

Go ahead, tell me of an existence that exists and does not exist?

you know how ridiculous is sounds to use such an argument as, "Because it's defined that way?" OK, I'll define something. Rain: the manifestation of gods tears. So it must be true because it was defined that way, absurd!

I didn't say it was true, I said it was perfect, i.e. it's perfectly designed to fulfil it's function and that function is to deduce valid and true conclusions from true premises. The other thing it is is the symbolic expression of the facts of existence, but you go ahead and tell me something that can exist and not exist in this or any universe. You've still not told me how these 'God's' can exist and not exist? How they can make something reflect a wavelength of 495–570 nm and not reflect a wavelength of 495–570 nm.

Like I said a few messages ago, as to the definitions of logic: validity, reasoning, principles, correctness, reliability, inference, proper, reasonable, a particular way, formal processes, and thinking, are all ambiguous, they are not necessarily quantifiable, such that they are defined as the particular human case warrants, by those humans steering the case.

No, they are absolutely definable, pick-up a book on Logic before you talk more about what you haven't read.

and states of affairs simply speaks of existence, and as I've already stated, humans don't necessarily know what that is in all cases, as logic in those cases, falls flat on it's face.

See how your lack of understanding of Logic makes you say meaningless and contradictory things? You are talking about things you say we cannot necessarily know, i.e. those cases that you say we don't know and then making an assertion about them, i.e. that logic fails in them, if what you say is true how can you do this!!? Things and states of affairs ARE existence! No things or states of affairs no existence.

Actually that's, not how you originally phrased it, I'll have to find the original.

Feel free, as I know what I say and think about things philosophical.

You seem to not pay attention, as I've said in the past, it's not to be taken literally in 100% of all the possible cases, that it's to ground oneself, that it should be the fundamental starting place, and should always be considered to stave off the possibly of jumping to conclusions. And no, the human perspective of measurement, judgement, is surely not universal. That you can't grasp it is surely reflected in that personally type of yours that you've mentioned.

The fundamental starting place in Philosophy is Logic dosed with a healthy scepticism but once you have a truth then you can deduce valid and true conclusions.

Silly question, have you only been everywhere only once?

If the world is only what one is conscious or aware of how can you tell it remains there when you are not there?

Another silly assertion, as obviously such a statement can only be spoken in the present tense, unless you believe yourself clairvoyant?

No, I believe there is a difference between unknown and unknowable, you apparently don't?

How do we make any progress then? Easy the creator finally, instantaneously speaks to each and every animal alive, with the exact same message, "see me, I exist as you exist." I mean, at least that's one possibility. I can think of others even more far fetched, relative to the animal of the day, that is.

Then this 'creator' is not unknowable is it, it's just been unknown. Do you think you think it'll make much sense if it said, 'See me, I exist and I don't exist'. Still waiting for you to tell me of an experience that would make the unknowable known?

[SpheresOfBalance]

Fact: I'm no bunny, and you've proven otherwise on more than one occasion, case in point. Well at least one more for the list. I'm not saying I don't do it. But I'm pretty sure I don't usually start it, at least I'm sure I'd rather not.

Total bunny, as you find offence in a compliment to others and your insecurity is shown in the faux-intellectual speech forms you use. Add to that that you rush to the defense of others when it's neither requested nor required.

You assume that they have to "exist or not exist" by your definition of existence, as if it's definitely the only one there is, which you cannot know for sure.

Go ahead, tell me of an existence that exists and does not exist?

you know how ridiculous is sounds to use such an argument as, "Because it's defined that way?" OK, I'll define something. Rain: the manifestation of gods tears. So it must be true because it was defined that way, absurd!

I didn't say it was true, I said it was perfect, i.e. it's perfectly designed to fulfil it's function and that function is to deduce valid and true conclusions from true premises. The other thing it is is the symbolic expression of the facts of existence, but you go ahead and tell me something that can exist and not exist in this or any universe. You've still not told me how these 'God's' can exist and not exist? How they can make something reflect a wavelength of 495–570 nm and not reflect a wavelength of 495–570 nm.

Like I said a few messages ago, as to the definitions of logic: validity, reasoning, principles, correctness, reliability, inference, proper, reasonable, a particular way, formal processes, and thinking, are all ambiguous, they are not necessarily quantifiable, such that they are defined as the particular human case warrants, by those humans steering the case.

No, they are absolutely definable, pick-up a book on Logic before you talk more about what you haven't read.

and states of affairs simply speaks of existence, and as I've already stated, humans don't necessarily know what that is in all cases, as logic in those cases, falls flat on it's face.

See how your lack of understanding of Logic makes you say meaningless and contradictory things? You are talking about things you say we cannot necessarily know, i.e. those cases that you say we don't know and then making an assertion about them, i.e. that logic fails in them, if what you say is true how can you do this!!? Things and states of affairs ARE existence! No things or states of affairs no existence.

Actually that's, not how you originally phrased it, I'll have to find the original.

Feel free, as I know what I say and think about things philosophical.

You seem to not pay attention, as I've said in the past, it's not to be taken literally in 100% of all the possible cases, that it's to ground oneself, that it should be the fundamental starting place, and should always be considered to stave off the possibly of jumping to conclusions. And no, the human perspective of measurement, judgement, is surely not universal. That you can't grasp it is surely reflected in that personally type of yours that you've mentioned.

The fundamental starting place in Philosophy is Logic dosed with a healthy scepticism but once you have a truth then you can deduce valid and true conclusions.

Silly question, have you only been everywhere only once?

If the world is only what one is conscious or aware of how can you tell it remains there when you are not there?

Another silly assertion, as obviously such a statement can only be spoken in the present tense, unless you believe yourself clairvoyant?

No, I believe there is a difference between unknown and unknowable, you apparently don't?

How do we make any progress then? Easy the creator finally, instantaneously speaks to each and every animal alive, with the exact same message, "see me, I exist as you exist." I mean, at least that's one possibility. I can think of others even more far fetched, relative to the animal of the day, that is.

Then this 'creator' is not unknowable is it, it's just been unknown. Do you think you think it'll make much sense if it said, 'See me, I exist and I don't exist'. Still waiting for you to tell me of an experience that would make the unknowable known?

A place holder until I get back, so you can't edit without it being known, as my thought on rebuttal has to do with what I have just read.

[Arising_uk]

Apparently it's above your head. My meaning that is. ...

Apparently so but from my perspective you are not making much sense.

Like I've said before, your mind is so full of everyone elses beliefs, that you have no room to consider mine. ...

You mistake me, I consider your beliefs but find them unconvincing.

Neither of us know of gods, so neither of us can speak for them. You have your take on what a god is and I have mine. The main difference between us is that you believe that your education is the pinnacle of understanding, allowing you to define gods, and I know that's not the case. I know that no matter how much education anyone has, in fact they can only know that they know nothing.

Which is a logical contradiction in terms and given this is philosophy forum that makes them false all the time.

And I know that you'll only be able to see my words above from only your perspective, and to be honest I don't really have the time nor the inclination to break it down for you. Your ignoring what I say, while supplying your incorrect version wears thin on me, but you already know that. And I believe that's your ploy! I don't think you're very honest.

In this format I'm pretty much honest to a fault. I find your problem to be that everything has to have a psychological justification and in the main one that involves the assumption of dishonesty.

I can't keep up with your typing speed, my keyboard being much of the problem, like I've told you before.

I type with two fingers, I think you mean you can't keep up with my thinking speed but that is not surprising as my training has been in such situations. Please do not feel you need to reply straight away, take as much time as you need to reply, I'm in no hurry in this format and will and have been around for a long=time and would prefer responses to be well thought-out.

So until you stop putting words in my mouth, I'll have to move along. If you took actually communicating 'with' others more seriously than attempting to talk down 'at' them, then there would be no problem.

Apologises if I appear brusque, my trainign has given me a thick skin when it comes to having ones thoughts challenged and I forget that it can be a bit raw upon others.

This bit from wikipedia:
"Intentionality is a philosophical concept defined by the Stanford Encyclopedia of Philosophy as "the power of minds to be about, to represent, or to stand for, things, properties and states of affairs""

proves my point that it's all about the human perspective. As to minds, we can only speak of human minds. AND THAT'S IT!

Not quite, as there has to be things, properties and states of affairs for us to have intentions about and if there are then other minds will have intentions about them as well.

Here, I found a way to show you what I meant unless you're disingenuous in your response.
I found this on wikipedia:

"In philosophy, a state of affairs, also known as a situation, is a way the actual world must be in order to make some given proposition about the actual world true; in other words, a state of affairs (situation) is a truth-maker, whereas a proposition is a truth-bearer. Whereas states of affairs (situations) either obtain or fail-to-obtain, propositions are either true or false.[1] In a sense of "state of affairs" favored by Ernest Sosa, states of affairs are situational conditions. In fact, in the Cambridge Dictionary of Philosophy,[2] Sosa defines a condition to be a state of affairs, "way things are" or situation—most commonly referred to by a nominalization of a sentence. The expression "Snow's being white", which refers to the condition snow's being white, is a nominalization of the sentence "Snow is white".[2] "The truth of the proposition that snow is white" is a nominalization of the sentence "the proposition that snow is white is true". Snow's being white is a necessary and sufficient condition for the truth of the proposition that snow is white. Conditions in this sense may be called situational."

The proposition: "snow is white" is conditional on the snow actually being white. However the actual state of affairs is that snow is probably only white because all humans can see is white light. If they could see other frequencies of EME then the snow may look totally different. Here your logic clearly fails if it was coined prior to humans understanding this fact. ...

No it doesn't, as my logic says that whatever frequency is seem it cannot be the case that it is that frequency and not that frequency, you are too tied up in the empirical.

And I'm sure the gods are not bowing in subserviency at that bit of logic.

Yes they are.

Crap you yourself said you believe all existence is simply a running program, or something similar, obviously that shits your states of affairs out the window, as far as any logic a human could coin if in fact it were true. ...

Nope, I said that there is a metaphysic out there that says that this existence may be sim or calculation running upon some calculating engine but like a brain-in-a-vat or an idea in a 'god or god's' mind Logic will still have to hold.

And that's my point. Don't pretend you don't understand me and say some BS, It'll just prove you a liar. And not really worth anyone's time. If I lost you because my language is inept, then simply ask for clarification, instead of attempting to insult me.

You underestimate yourself as I thought your language comprehensible and was just challenging what I see as the errors and contradcitions in your thoughts.

[SpheresOfBalance]

Apparently it's above your head. My meaning that is. ...

Apparently so but from my perspective you are not making much sense.

Like I've said before, your mind is so full of everyone elses beliefs, that you have no room to consider mine. ...

You mistake me, I consider your beliefs but find them unconvincing.

Neither of us know of gods, so neither of us can speak for them. You have your take on what a god is and I have mine. The main difference between us is that you believe that your education is the pinnacle of understanding, allowing you to define gods, and I know that's not the case. I know that no matter how much education anyone has, in fact they can only know that they know nothing.

Which is a logical contradiction in terms and given this is philosophy forum that makes them false all the time.

And I know that you'll only be able to see my words above from only your perspective, and to be honest I don't really have the time nor the inclination to break it down for you. Your ignoring what I say, while supplying your incorrect version wears thin on me, but you already know that. And I believe that's your ploy! I don't think you're very honest.

In this format I'm pretty much honest to a fault. I find your problem to be that everything has to have a psychological justification and in the main one that involves the assumption of dishonesty.

I can't keep up with your typing speed, my keyboard being much of the problem, like I've told you before.

I type with two fingers, I think you mean you can't keep up with my thinking speed but that is not surprising as my training has been in such situations. Please do not feel you need to reply straight away, take as much time as you need to reply, I'm in no hurry in this format and will and have been around for a long=time and would prefer responses to be well thought-out.

So until you stop putting words in my mouth, I'll have to move along. If you took actually communicating 'with' others more seriously than attempting to talk down 'at' them, then there would be no problem.

Apologises if I appear brusque, my trainign has given me a thick skin when it comes to having ones thoughts challenged and I forget that it can be a bit raw upon others.

This bit from wikipedia:
"Intentionality is a philosophical concept defined by the Stanford Encyclopedia of Philosophy as "the power of minds to be about, to represent, or to stand for, things, properties and states of affairs""

proves my point that it's all about the human perspective. As to minds, we can only speak of human minds. AND THAT'S IT!

Not quite, as there has to be things, properties and states of affairs for us to have intentions about and if there are then other minds will have intentions about them as well.

Here, I found a way to show you what I meant unless you're disingenuous in your response.
I found this on wikipedia:

"In philosophy, a state of affairs, also known as a situation, is a way the actual world must be in order to make some given proposition about the actual world true; in other words, a state of affairs (situation) is a truth-maker, whereas a proposition is a truth-bearer. Whereas states of affairs (situations) either obtain or fail-to-obtain, propositions are either true or false.[1] In a sense of "state of affairs" favored by Ernest Sosa, states of affairs are situational conditions. In fact, in the Cambridge Dictionary of Philosophy,[2] Sosa defines a condition to be a state of affairs, "way things are" or situation—most commonly referred to by a nominalization of a sentence. The expression "Snow's being white", which refers to the condition snow's being white, is a nominalization of the sentence "Snow is white".[2] "The truth of the proposition that snow is white" is a nominalization of the sentence "the proposition that snow is white is true". Snow's being white is a necessary and sufficient condition for the truth of the proposition that snow is white. Conditions in this sense may be called situational."

The proposition: "snow is white" is conditional on the snow actually being white. However the actual state of affairs is that snow is probably only white because all humans can see is white light. If they could see other frequencies of EME then the snow may look totally different. Here your logic clearly fails if it was coined prior to humans understanding this fact. ...

No it doesn't, as my logic says that whatever frequency is seem it cannot be the case that it is that frequency and not that frequency, you are too tied up in the empirical.

And I'm sure the gods are not bowing in subserviency at that bit of logic.

Yes they are.

Crap you yourself said you believe all existence is simply a running program, or something similar, obviously that shits your states of affairs out the window, as far as any logic a human could coin if in fact it were true. ...

Nope, I said that there is a metaphysic out there that says that this existence may be sim or calculation running upon some calculating engine but like a brain-in-a-vat or an idea in a 'god or god's' mind Logic will still have to hold.

And that's my point. Don't pretend you don't understand me and say some BS, It'll just prove you a liar. And not really worth anyone's time. If I lost you because my language is inept, then simply ask for clarification, instead of attempting to insult me.

You underestimate yourself as I thought your language comprehensible and was just challenging what I see as the errors and contradcitions in your thoughts.

This ploy is laughable! I shall get back to you on the previous message as I mentioned.

[Wyman]

Thank you for the reminder, A_Seagull - and by the way, Arising owes me a response on this thread also.

I am using the term 'induction' as the same as 'non-deductive' , ie 'the conclusions, while indicated by the premises, do not follow deductively from the premises."

Perception is inductive, because the conclusion: eg 'that there is a table in front of me' does not follow deductively from the 'premisses' (ie the sense data that enters my eyes.).

In a combined argument of induction plus deduction the conclusion must be inductive as there will remain that element of uncertainty.

You can arrive at a set of theories from induction, as in science, but the creation of axioms is quite a different matter. Axioms are the basis for abstract systems (such as pure mathematics and pure geometry), but any application of them to the real world (ie that which we know from sense-data) requires a mapping from one to the other.

This mapping is often presumed to be perfect in a 'naïve' perspective of the world, eg when physicists hold that the matter of the universe 'obeys' the 'laws of physics'.

But philosophers need to be mindful that a mapping between an axiomatic abstract system and the 'real world' is not perfect and that , for example, the motions of matter in the real world is only approximately described by the 'laws of physics'.

I don't think our terminology is on the same page re: induction as negatively defined as anything that is not deductive. And maybe the two ideas are not as distinct as we often use them - i.e. maybe there are areas where they overlap.

I think a great mystery in physics is in the fact that mathematical systems do model aspects of the world so well. Here are a couple quotes to illustrate the point:

Archimedes to Hawking : Laws of Science and the Great Minds Behind Them (Clifford Pickover)
- Highlight Loc. 578-80 | Added on Tuesday, March 29, 2011, 11:45 PM
Heisenberg once made the following remark to Einstein: “If nature leads us to mathematical forms of great simplicity and beauty … that no one has previously encountered, we cannot help thinking that they are ‘true,’ that they reveal a genuine feature of nature.”

Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas. I am convinced that we can discover by purely mathematical constructions the concepts and the laws connecting [mathematics and physical reality] with each other, which furnish the key to the understanding of natural phenomena. … In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed. —Albert Einstein, “On the Methods of Theoretical Physics,” 1933
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However, it is a difficult subject, even for Einstein(perhaps he changed his mind over the intervening 12 years):

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. —Albert Einstein, “Geometry and Experience,” Address to the Prussian Academy of Sciences, 1921

I think the interplay between axioms, their interpretation, and scientific observation - i.e. how and to what extent the world can be modeled mathematically is a fascinating, but extremely difficult subject. For instance, in mathematical logic, an interpretation of an axiom system (assignment of elements of a model to each primitive term in the axioms) is called a 'model' of the axiom system if the interpretation is 'true' for the axiom system. Given such a model, it follows that the model must hold for any subsequent theorem of the same system. So, for instance, if a theorem is proposed, one way to disprove it (or prove one via reductio ad absurdum - assume its opposite and disprove it) is to show that it is false for a model of the system. This is called a disproof by counter example.

This is difficult to explain, but an example is in geometry (where your standard high school interpretation involving points and lines is a valid model) would be 'all triangles have at least one right angle.' You could disprove this by constructing a counter example within the standard model.

I always thought this sounded a lot like an analogue to the verification theory in science, where any observation which contradicts a theory(or theorem) is deemed to refute the theory(or theorem). But doesn't this only hold true if we are treating the theory as a consistent set of axioms and reality as a model of those axioms?

Think of Einstein's prediction of a change in the observed position of stars as their light passed close to the sun on their way to Earth. He deduced that 'theorem' from his theory of relativity and claimed that if his prediction (deduction) was wrong, then his theory crumbled. Why should reality be subject to, or abide by, such deductions? It is easier to understand how we can come up with inductive hypotheses to describe observed patterns in reality (i.e. light travels at a constant speed and is influenced by gravity, etc). But why do theorems logically deduced from these hypotheses hold true? There seems to be no apparent necessity that reality abide by logic, is there?

[Arising_uk]

This ploy is laughable!

Then the joke is on you as I have no idea what you are babbling about? That I sometimes(rarely) answer posts out of sequence can be due to various factors, I was too tired to continue and then forgot, I needed time to think, I just couldn't be arsed at the time, etc. When I answer posts I address the content of the words, no ploy involved.

What an insecure and suspicious world you live in.

I shall get back to you on the previous message as I mentioned.

Whatever.

[Arising_uk]

Right, you understood what I was saying - take 'E' as a backwards epsilon and (x) as the universal quantifier. I do understand your position better now, as before I did not.

Ah! Should have used the reverse epsilon

I happened to have just read Tarski's 'Introduction to Logic' to brush up on my logic. It is short, well written and it's always interesting to read a master in a subject matter explaining introductory ideas - like Einstein's books on Relativity for laypersons.

Someone else who has read this! Although it was still fairly tough I thought.

Thanks for the ref, I've found a pdf of it and most interesting it is as my training didn't cover the variables and constants using number so I'm enjoying the different take.

Anyway, I see predicate logic as, at least in part, an attempt to formalize what a 'proposition' is in the sentence calculus. I think that was what Russell, Frege, Wittgenstein were doing in the early days. I.e. they were asking 'what is a proposition,' or 'a truth bearing variable' in the sentence calculus.

Maybe, sounds right as propositional logic can't unpack a proposition whereas with the split of the predicate and subject one can in predicate logic. One can also talk about sets of objects with predicate logic.

So, they went 'up' a level, so to speak, from sentence calculus and created a formal system (predicate logic) to axiomatize and define the elements of a proposition (as well as to create a language that would be more useful than sentence calculus). That went something like:

The most basic form of a proposition is (x)Fx - , i.e.'for all x, x is F.' The negation of the predicate - (x)notFx - says 'for all x, x is not F.' And finally, the negation of the whole proposition - not(x)Fx - says that 'it is not the case that all x's are F.' This last is equivalent to E(x)Fx - 'there exists at least one x, such that x is F.'

So, the existential quantifier, E(x) can be defined in terms of the universal quantifier as it's negation. I think you could also start with the existential quantifier and define the universal quantifier in its terms if you chose.

I thought it more, ~(Vx)P(x) ≡ (Ex)~P(x) and vice versa ~(Ex)P(x) ≡ (Vx)~P(x).

I think Wittgenstein, in the Tractactus, said something like that - the basic form of a proposition is (x)Fx.

Maybe, I'd have to re-read.

Getting back to your claim, I think you are doing something similar to the above but without being as explicit. If you say, in sentence calculus, that 'F cannot both exist and not exist' is true, you are going outside of the sentence calculus, stating something about how we are to treat 'existence' in formal logic, but without following it through to it's logical end, which would be a formalization of 'propositions' in terms of quantification and predication.

Well I can see that I could say (Vx)~(P(x) ^ ~P(x)) and I do understand that in this I'd be using the P as a predicate for 'exists' which I thought is problematic? But ~(P ^ ~P) is a tautology in PL and I can't see why the P can't stand for the proposition 'God exists' or any other proposition.

The content of 'p' in sentence calculus is just T or F - filling in a 'p' with other content is going 'up' a level from sentence calculus and stating things about the world, or else stating something about the nature of 'propositions.'

Hmm...disagree, the variables in PL stand for propositions, that they can also be T or F is true but T or F is manily used to construct the truth tables that make explict all the possible cases for the truth-functions and the states of affairs, or some such.

[Wyman]

I thought it more, ~(Vx)P(x) ≡ (Ex)~P(x) and vice versa ~(Ex)P(x) ≡ (Vx)~P(x).

Oh yes, you are exactly right, I got tangled up in my ordinary language translation - if it is not the case that all x's are P, then there is at least one x which is not P.

Well I can see that I could say (Vx)~(P(x) ^ ~P(x)) and I do understand that in this I'd be using the P as a predicate for 'exists' which I thought is problematic?

Right, it is problematic (the subsequent quote you refer to from my post basically says something similar, I just wasn't clear). That was the question I was asking you to address.

I was saying that E(x) says 'there exists an x such that.' The idea of 'existence' is written into the axiom system of predicate logic but is never divorced from the 'such that.' To use it again as a predicate is redundant, or a rejection of predicate logic. But I am far from sure on this.

It was perhaps the slipperiness of the concept of 'x exists,' without the 'such that' that led to (or helped shape) the formation of the predicate logic. Like 'Pegasus does not exist.' However, I can say 'Pegasus is white.' How can I talk about something that does not exist? (seems to violate your tautology, saying that Pegasus is and is not at the same time) Russell's definite description theory resolves the paradox with predicate logic.

[A_Seagull]

I don't think our terminology is on the same page re: induction as negatively defined as anything that is not deductive. And maybe the two ideas are not as distinct as we often use them - i.e. maybe there are areas where they overlap.

I think a great mystery in physics is in the fact that mathematical systems do model aspects of the world so well. Here are a couple quotes to illustrate the point:

However, it is a difficult subject, even for Einstein(perhaps he changed his mind over the intervening 12 years):

I think the interplay between axioms, their interpretation, and scientific observation - i.e. how and to what extent the world can be modeled mathematically is a fascinating, but extremely difficult subject. For instance, in mathematical logic, an interpretation of an axiom system (assignment of elements of a model to each primitive term in the axioms) is called a 'model' of the axiom system if the interpretation is 'true' for the axiom system. Given such a model, it follows that the model must hold for any subsequent theorem of the same system. So, for instance, if a theorem is proposed, one way to disprove it (or prove one via reductio ad absurdum - assume its opposite and disprove it) is to show that it is false for a model of the system. This is called a disproof by counter example.

This is difficult to explain, but an example is in geometry (where your standard high school interpretation involving points and lines is a valid model) would be 'all triangles have at least one right angle.' You could disprove this by constructing a counter example within the standard model.

I always thought this sounded a lot like an analogue to the verification theory in science, where any observation which contradicts a theory(or theorem) is deemed to refute the theory(or theorem). But doesn't this only hold true if we are treating the theory as a consistent set of axioms and reality as a model of those axioms?

Think of Einstein's prediction of a change in the observed position of stars as their light passed close to the sun on their way to Earth. He deduced that 'theorem' from his theory of relativity and claimed that if his prediction (deduction) was wrong, then his theory crumbled. Why should reality be subject to, or abide by, such deductions? It is easier to understand how we can come up with inductive hypotheses to describe observed patterns in reality (i.e. light travels at a constant speed and is influenced by gravity, etc). But why do theorems logically deduced from these hypotheses hold true? There seems to be no apparent necessity that reality abide by logic, is there?

I agree that our terminology seems to be different.

There is a logical non-sequitor that is akin to 'faith' in claiming that a model of the real world actually describes the way the world actually is. There is no justification for such a naïve presumption other than pragmatic considerations - i.e. "this seems to work well enough so we shall claim it as 'true'.".

On the other hand, axioms are indubitable only within the particular system for which they are axioms. E.g The rules of chess are axiomatic for the game of chess.
Also the axioms of mathematics are only indubitable within the system of mathematics. (Though there is a difficulty here as most of the axioms are implicit rather than explicit.) Then all the 'true' theorems of the system can be derived from those axioms. Your example regarding triangles and right angles would then become: The theorem "all triangles have right angles" would not be generated in a self-consistent system of mathematics/geometry as it can generate the theorem (or its equivalent) "some triangles do not have right angles".

With regard to Einstein, light and gravity: It is quite possible that a theory which has been generated using data from a particular domain may not be applicable for a range outside of that domain. But this does not mean that the theory is 'true' nor that it reflects the ontology of the physical world. All it demonstrates is that the theory constitutes a useful model.

As someone once said: " The world is not only stranger than we suppose, it is stranger than we can suppose."

[Wyman]

I agree that our terminology seems to be different.

There is a logical non-sequitor that is akin to 'faith' in claiming that a model of the real world actually describes the way the world actually is. There is no justification for such a naïve presumption other than pragmatic considerations - i.e. "this seems to work well enough so we shall claim it as 'true'.".

On the other hand, axioms are indubitable only within the particular system for which they are axioms. E.g The rules of chess are axiomatic for the game of chess.
Also the axioms of mathematics are only indubitable within the system of mathematics. (Though there is a difficulty here as most of the axioms are implicit rather than explicit.) Then all the 'true' theorems of the system can be derived from those axioms. Your example regarding triangles and right angles would then become: The theorem "all triangles have right angles" would not be generated in a self-consistent system of mathematics/geometry as it can generate the theorem (or its equivalent) "some triangles do not have right angles".

With regard to Einstein, light and gravity: It is quite possible that a theory which has been generated using data from a particular domain may not be applicable for a range outside of that domain. But this does not mean that the theory is 'true' nor that it reflects the ontology of the physical world. All it demonstrates is that the theory constitutes a useful model.

As someone once said: " The world is not only stranger than we suppose, it is stranger than we can suppose."

I agree with your idea of a 'true' description - with a capital 'T' - being dubious. But start with that realization, step back, and look at the situation again. Then you may see the very fact that models predict so well as being a mysterious, incredible 'fact.' I think that is the perspective from which the above quoted physicists are coming.

Let me approach it this way. It is an observed 'fact' that humans produce mathematical models which predict future events with great accuracy. Physicists do not analyze this 'fact' scientifically - they do not explain it from within the model they use to explain other 'facts.' They are too busy creating the very models in question to get outside that model and explain this 'fact' and they cannot explain such 'macro' problems from within these theories as they are too complex. They can only speculate in wonder and amazement like the rest of us.

So, after we agree on your assertion of "belief that models truly describe reality is a non sequitur' - what then? Why do some models make such incredibly accurate predictions (such as quantum theory)? If it is not the case that the model is describing reality, what is your alternative explanation?

As for my example of a proof by counter example - I was not clear and perhaps it is too broad a subject to get into. Such proofs are fundamentally different than normal deductive proofs from axioms. Although you certainly can disprove my example theorem via the normal method, proof by counter example is different and involves the relation between models and deductive systems, which is a subject that fascinates me. It involves metalogical considerations, which is a topic explored in model theory. It came to mind with your comments on 'mapping.'