What are the achievements of logic?

What is the basis for reason? And mathematics?

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A_Seagull
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Re: What are the achievements of logic?

Post by A_Seagull »

Arising_uk wrote:
A_Seagull wrote:...
Perhaps there is confusion, when I used the word 'logic' in the OP I was not referring to logical and clear thinking; I was referring to syllogisms, so called laws of logic and formal logic. ...
But these are examples of logical thinking?

Why do you think the laws of logic are so-called?
Because it sounds better than the Possibilities of logic?
And yes I think that those instances of philosophy fail Hume's fork.
Except his fork was about theology and metaphysics and Logic does discuss appear to discuss fact and existence as it marks the boundaries of what is impossible, necessary and contingent.
Not the way Hume wrote it, it wasn't.
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A_Seagull
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Re: What are the achievements of logic?

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Arising_uk wrote:
A_Seagull wrote:It seems to me that logic is decidedly useless in philosophy. It would seem to have achieved nothing. ...
Grounded and helped clarify the foundations of Mathematics and produced the study of Formal Axiomatic Systems.
If logic is the foundations of mathematics then what are the foundations of logic?

Historically it has been one of the legs of Philosophy.
And what has that achieved?
Scott Mayers
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Re: What are the achievements of logic?

Post by Scott Mayers »

A_Seagull wrote:
Arising_uk wrote:Grounded and helped clarify the foundations of Mathematics and produced the study of Formal Axiomatic Systems.
If logic is the foundations of mathematics then what are the foundations of logic?

Historically it has been one of the legs of Philosophy.
And what has that achieved?
Math is the logic that uses Numbers as input premises.

Think of logic as what and how the electronics are designed in your smart phone. It allows inputs of varying types and outputs in kind. The machine acts universally upon any inputs and doesn't concern whether the inputs is are 'true' by some nature. While 2 + 2 will certainly generate 4, it doesn't care that a '2' exists for the conclusion of '4'. All that matters is that for ANY input, as long as the machine is not confused about the kind of input*, it will have a VALID answer appropriately designed by that machine. ( *like you can't try to put a cup of water as an input)
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A_Seagull
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Re: What are the achievements of logic?

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Scott Mayers wrote:
A_Seagull wrote:
If logic is the foundations of mathematics then what are the foundations of logic?

Historically it has been one of the legs of Philosophy.
And what has that achieved?
Math is the logic that uses Numbers as input premises.

Think of logic as what and how the electronics are designed in your smart phone. It allows inputs of varying types and outputs in kind. The machine acts universally upon any inputs and doesn't concern whether the inputs is are 'true' by some nature. While 2 + 2 will certainly generate 4, it doesn't care that a '2' exists for the conclusion of '4'. All that matters is that for ANY input, as long as the machine is not confused about the kind of input*, it will have a VALID answer appropriately designed by that machine. ( *like you can't try to put a cup of water as an input)
I entirely agree with you here. But just as you can't input a cup of water, neither can you input the string 'a cup of water' and expect the machine to treat it as anything more than a string of symbols. The machine would have no concept of what 'a cup of water' actually meant in the way that a sentient beings who speak English can understand what 'a cup of water' means.
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Re: What are the achievements of logic?

Post by Scott Mayers »

A_Seagull wrote:
Scott Mayers wrote: Math is the logic that uses Numbers as input premises.

Think of logic as what and how the electronics are designed in your smart phone. It allows inputs of varying types and outputs in kind. The machine acts universally upon any inputs and doesn't concern whether the inputs is are 'true' by some nature. While 2 + 2 will certainly generate 4, it doesn't care that a '2' exists for the conclusion of '4'. All that matters is that for ANY input, as long as the machine is not confused about the kind of input*, it will have a VALID answer appropriately designed by that machine. ( *like you can't try to put a cup of water as an input)
I entirely agree with you here. But just as you can't input a cup of water, neither can you input the string 'a cup of water' and expect the machine to treat it as anything more than a string of symbols. The machine would have no concept of what 'a cup of water' actually meant in the way that a sentient beings who speak English can understand what 'a cup of water' means.
Sure, but we too are just an extension based upon an extensive complex logic. You CAN technically recreate a machine that 'thinks' its real. The brain uses a logic based on not simply changing 'currents' of electrons but 'growth/shrinking', 'thresholds logic', among many that make up the complexity of the laws of physics, chemistry, biology, etc. .
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Arising_uk
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Re: What are the achievements of logic?

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A_Seagull wrote:If logic is the foundations of mathematics then what are the foundations of logic?
That there are things and states of affairs.
And what has that achieved?
An understanding of the boundaries of Reason with respect to certain things and states of affairs and the ability to tell someone they are completely wrong and why.
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Re: What are the achievements of logic?

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Etymologically it's from the Greek "logos", not "log" in the sense of a "record," which etymologically stems from "log" in the sense of "piece of wood."

Logos is defined as "word, speech, statement, discourse," also "computation, account," also "reason."

Some of those terms seem like they'd connect logos to "log" in the "record" sense, but here are the roots of the "record" sense of "log" rather: "loriginally 'record of a ship's progress,' 1842, sailor's shortening of log-book (1670s), the daily record of a ship's speed, progress, etc., which is from log (n.1) "piece of wood. The book so called because it recorded the speed measurements made by means of a weighted chip of a tree log on the end of a reeled log line (typically 150 to 200 fathoms). The log lay dead in the water, and sailors counted the time it took the line to play out. The line was marked by different numbers of knots, or colored rags, tied at regular intervals; hence the nautical measurement sense of knot (n.)."
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Re: What are the achievements of logic?

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Re logic as foundational for mathematics, there's actually a name for that view--logicism.

Logicism is typically considered to have been falsified, so that logic can't (at least not completely) serve as the basis for mathematics, by work in the late 1800s and first half of the 1900s by Frege, Russell & Whitehead, Goedel, Skolem and others. Russell & Whitehead's infamous Principia Mathematica was essentially a work of logicism, where Russell & Whitehead attempted to systematically, formally establish logic as the foundation of mathematics. Instead, they came to the conclusion while writing it that such an attempt couldn't work, for formal reasons.

Some people have later argued that logicism could be rescued via various tactics, though that's controversial, or at least it's not at all the received view yet.
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Arising_uk
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Re: What are the achievements of logic?

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A_Seagull wrote:Not the way Hume wrote it, it wasn't.
"If we take in our hand any volume; of divinity or school metaphysics, for instance; ..."?
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Re: What are the achievements of logic?

Post by Scott Mayers »

Terrapin Station wrote:Etymologically it's from the Greek "logos", not "log" in the sense of a "record," which etymologically stems from "log" in the sense of "piece of wood."

Logos is defined as "word, speech, statement, discourse," also "computation, account," also "reason."

Some of those terms seem like they'd connect logos to "log" in the "record" sense, but here are the roots of the "record" sense of "log" rather: "loriginally 'record of a ship's progress,' 1842, sailor's shortening of log-book (1670s), the daily record of a ship's speed, progress, etc., which is from log (n.1) "piece of wood. The book so called because it recorded the speed measurements made by means of a weighted chip of a tree log on the end of a reeled log line (typically 150 to 200 fathoms). The log lay dead in the water, and sailors counted the time it took the line to play out. The line was marked by different numbers of knots, or colored rags, tied at regular intervals; hence the nautical measurement sense of knot (n.)."
I like etymology. But do NOT take any one source as sufficient to certify the actual story because there is a tendency for different cultures to attempt to both connect and disconnect from certain associations based on culture and, especially, religion. What is important however for 'light' use (as opposed to requiring legal or accurate and precise sources for archeology, etc) is to allow flexible interpretations if only to AID in associating contemporary use. I wouldn't use it if it didn't serve to help understand intentions of definitions etc.

On the word "logic", though, I was correct and the wood factor relates. A "log" was as much an adjectival or colloquial way in the past to refer to both the tree log AND to scrolls. A big one is representative of often "anal" (annual, not ones ass) works and records. The word "logarithm" is the similar associated term which specifically was a "look up" list of mathematical entries actually used to do quicker multiplication using the the law of exponents/(or logarithms). Thus a "log" was a way of describing scrolls that were very intense and as big as "logs". I'm not sure if "look" came to English as a secondary word for "see" or the other way around. But "to look", rather than 'see' is used more specifically for what used to be recorded, where "science" from, "to see", relates to the DIRECT action of using ones eyes rather than the more specific record of WHAT we see.

This is how "science" can be understood to differentiate from "logic". They both relate when we analyze reality. The act of observing and then recording it, including using a mechanical means to manipulate symbols (algorithms) are why science and logic are required to work together. So all the above DO relate and act exactly as biological evolution.
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Re: What are the achievements of logic?

Post by Scott Mayers »

WARNING: this is a digression of the OP in that it may be going too deep by many. So only if you understand the philosophical definitions involved and some background will this be useful.
Terrapin Station wrote:Re logic as foundational for mathematics, there's actually a name for that view--logicism.

Logicism is typically considered to have been falsified, so that logic can't (at least not completely) serve as the basis for mathematics, by work in the late 1800s and first half of the 1900s by Frege, Russell & Whitehead, Goedel, Skolem and others. Russell & Whitehead's infamous Principia Mathematica was essentially a work of logicism, where Russell & Whitehead attempted to systematically, formally establish logic as the foundation of mathematics. Instead, they came to the conclusion while writing it that such an attempt couldn't work, for formal reasons.

Some people have later argued that logicism could be rescued via various tactics, though that's controversial, or at least it's not at all the received view yet.
I responded from your previous post to relate to this interpretation of yours in this one. "Logicism" is more of a derogatory term, like "scientism" by outsiders only. But by your understood meaning, Godel's Incompleteness theorem dealt with trying to show how Russel's Paradox that was circumvented by Russel and Whitehead (by definition on Types), proved Incompleteness BASED ON ASSUMING (1) Consistency, (2) Non-Contradiction, and (3) Exclusive Middle, and are WHAT is 'falsified' only! The falsification is in itself based on the very same logical minimum. As such, even the second part of Godel's theorem PROVED in the logic he was using that you cannot prove a system of logic BY that same system, contradicts his own theory if you trust it. But it does PROVE that reality assures nature and reasoning itself is based upon a different approach:

Laws based initially on NO LAWS. This makes sense considering a law itself requires some means to assure these laws are not broken (obeyed.) This implies a 'God' like essence which just pushes back the question of its own 'reason'. So logicism by your interpretation is NOT false. You can actually tie science directly to logic where logic can derive all reality which we experience. The problem is that this is potentially INFINITE, and what makes science useful only as a "hint" to what is true about reality as a whole. So science requires logic and logic requires science FOR US HUMANS ONLY because we are trapped to a contingent world of many.

You are false about the math as not being founded on logic or to your apparent interpretation. Russel and Whitehead DID do this. It was only to the question of whether logic based on the three laws above that are most useful for maths that LIMIT the capacity of logic to prove all mathematical truths. But the math that gets left out CAN be proven with Logic without those biased laws beginning with none!
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Re: What are the achievements of logic?

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A_Seagull wrote:
If logic is the foundations of mathematics then what are the foundations of logic?
It can be argued that logic is intuitive, in the sense that it is the necessary foundation for all thought. That doesn't make it true, it is simply necessary for us to think in the way we do. We literally cannot think of it being false.

But another idea is that they are deduced from experience. That just as science forms general conclusions from experience, by looking at those general conclusions we discover even simpler, and thus even more general conclusions, and ultimately these are represented in the axioms of logic.
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Re: What are the achievements of logic?

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Scott Mayers wrote:I responded from your previous post to relate to this interpretation of yours in this one.
It's not an interpretation (of mine). It's the received view. Logicism failed.
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Re: What are the achievements of logic?

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Scott Mayers wrote:I like etymology. But do NOT take any one source as sufficient . . .
Your additional source is apparently "stuff I make up."
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Re: What are the achievements of logic?

Post by Scott Mayers »

Londoner wrote:
A_Seagull wrote:
If logic is the foundations of mathematics then what are the foundations of logic?
It can be argued that logic is intuitive, in the sense that it is the necessary foundation for all thought. That doesn't make it true, it is simply necessary for us to think in the way we do. We literally cannot think of it being false.

But another idea is that they are deduced from experience. That just as science forms general conclusions from experience, by looking at those general conclusions we discover even simpler, and thus even more general conclusions, and ultimately these are represented in the axioms of logic.
Science is about the senses to which we have no other way to even know of the world without. So we are doomed to initially INDUCE (guess by repeated common patterns inexperience) our reality which INCLUDES logic. But you are also right that it is intuitive because the hardwired brain needs to do this. We just don't think of what we intuit this way as 'logic' proven, just the 'sense' of thinking, just as to our regular senses. But this is the same.

Once you begin observing life by sensing though, the very first things you MUST do is to learn the patterns of patterns. We don't use words at that stage but the lessons we learn become so necessary that the brain removes the 'training wheels' of our initial learning such that we forget how we initially learned to reason about reasoning. This makes environmental learning also become "intuition" later on.
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