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What does it mean to "deduce reality"?

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RSalar
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If someone says, "I think you might be deducing reality," what is meant? Does it mean that he thinks you are "creating" a reality through the process of deductive logic? Where does one get the information to use in the deduction? Don't all rational people use their senses to obtain the raw data of the world and then use logic to deduce how it all works? I would think that is would be good to deduce reality. Even when the moon is on the other side of the earth and not visible to us, we still know it is there. How do we know it is there, if not for deduction? Or is that "induction?" (I have always had trouble with the difference between deduction and induction.) If that is the case; is it better to induce reality or deduce reality?

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If someone says, "I think you might be deducing reality," what is meant? Does it mean that he thinks you are "creating" a reality through the process of deductive logic?
I've never heard or seen anyone say that, but my naive guess is that that's right. But more specifically, I think it might mean "you're assuming something way beyond what you have warrant to assume, and then using tricky words to arrive at unsupported conclusions".
Don't all rational people use their senses to obtain the raw data of the world and then use logic to deduce how it all works?
No, all people, rational and irrational, use their senses to obtain data, and then rational people use that to induce general principles. Faith-based people may decide -- in a leap of faith -- to accept a particular statement and then pretend that certain conclusions derive "logically" from the arbitrary conclusions.
I would think that is would be good to deduce reality.
Why?
Even when the moon is on the other side of the earth and not visible to us, we still know it is there. How do we know it is there, if not for deduction? Or is that "induction?"
If you're asking a historical question, I don't know and I'll even bet that nobody here knows (please, someone, prove me wrong). If you mean now, it's a simple observational statement.
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#1)QUOTE: "I would think that is would be good to deduce reality."

Why?

#2)QUOTE: "Even when the moon is on the other side of the earth and not visible to us, we still know it is there. How do we know it is there, if not for deduction? Or is that 'induction?'"

If you're asking a historical question, I don't know and I'll even bet that nobody here knows (please, someone, prove me wrong). If you mean now, it's a simple observational statement.

#1) Because by "deducing" I am coming to a conclusion based on reasoning--I am determining what reality is by making logical connections and coming to a conclusion. In other words I am thinking. Can I know reality any other way?

A.R.(VOS_p22): "The process of concept-formation does not consist merely of grasping a few simple abstractions, such as "chair," "table," "hot," "cold," and of learning to speak. It consists of a method of using one's consciousness, best designated by the term "conceptualizing." It is not a passive state of registering random impressions. It is an actively sustained process of identifying one's impressions in conceptual terms, of integrating every event and every observation into a conceptual context, of grasping relationships, differences, similarities in one's perceptual material and of abstracting them into new concepts, of drawing inferences, of making deductions, of reaching conclusions, of asking new questions and discovering new answers and expanding one's knowledge into an ever-growing sum. The faculty that directs this process, the faculty that works by means of concepts, is: reason. The process is thinking." (Bold added by RSalar.)

#2) No, I am not speaking about history; I am referring to things in nature that we observe in the present. I sit out side on a clear night and I see the moon. I watch it transit the meridian and finally set. Where did it go? Is it gone for good ... or will it rise again? I deduce the reality that the earth has rotated so that I can no longer see the moon (it is below the horizon but it still exists). If I know something exists, that I cannot see nor touch nor use any of my senses to detect, I must know it exists through the process of reasoning. Since deducing is act of concluding through reasoning it could be said that I am deducing reality when I conclude that the moon exists even when it cannot be seen.

Based on this reasoning I would say that "deducing reality" must be a good thing. In the context that it was said, however, I got the sense that he was implying that it wasn't a good thing. Anyway I did a search on the internet and could not find the meaning of the phrase so I posted my question here.

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#1) Because by "deducing" I am coming to a conclusion based on reasoning--I am determining what reality is by making logical connections and coming to a conclusion. In other words I am thinking. Can I know reality any other way?
Okay, but then I don't see why you would want to limit this to deduction, i.e. only a rather restricted method of reasoning. The answer to the "any other way?" question is "by observation". Deduction is really a very poor way to create knowledge, and it is really only good tor making explicit the consequences of some statement that you have reason to hold true. Once you grasp that consequence, you have to make observations to determine if the consequence is actually true. The mistake that many people make is that since deduction is a part of the art of logic, it is logic, and that since much knowledge that we have in inferential, then all knowledge is inferential.
#2) No, I am not speaking about history; I am referring to things in nature that we observe in the present.
There are a number of ways that the moon's existence can be verified. One is by simultaneous observations across the globe, for example you could set up listening posts in Norway, Sri Lanka, Japan and Hawaii, so that your colleagues could call you and tell you "I see the moon". Also, guys in outer space have a les-obstructed view of the moon.
I deduce the reality that the earth has rotated so that I can no longer see the moon (it is below the horizon but it still exists).
What principle did you deduce that from? I can see it as an induction, but for the life of me I don't know how to deduce that, unless maybe you start with a religious axiom, but even then, I suspect that all religions which have anything to say about this hold that the Earth doesn't move and the heavens do move. So I'm puzzled about the basis for your deduction.
If I know something exists, that I cannot see nor touch nor use any of my senses to detect, I must know it exists through the process of reasoning.
Huh? Are you starting with the premise that you know that a particular thing exists? Like "If I know something exists, then I know it exists (through reasoning)"? Here's a paraphrase -- you tell me if it says what you really mean: "All knowledge must arise from using reasoning". How do you get observation in there? Are you claiming that observation has no place in the acquisition of knowledge? Surely not!
Since deducing is act of concluding through reasoning
No, deducing is the act of deriving a conclusion that is contained in the premises. For example, from the premises "All men are mortals" and "Socrates is a man", we can derive the conclusion "Socrates is a mortal", i.e. that conclusion is implicit in the premises. Or, if you assume that "Snow is white and rice is white", then you can conclude that "Snow is white", since again that conclusion is contained in the premises.

Induction, OTOH, is the process of building from specific instances to general statements, i.e. deriving universally quantified propositions through inductive generalization. From such a proposition, you can deductively conclude specific cases through universal instantiation: the case that you deduce in that manner might not have been directly observed (e.g. "The moon is visible in Sri Lanka now").

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No, deducing is the act of deriving a conclusion that is contained in the premises.

Deduce:

1.To reach (a conclusion) by reasoning.

2.To infer from a general principle; reason deductively.

3.To trace the origin or derivation of.

[Middle English deducen, from Latin deducere, to lead away or down : de-, de- + ducere, to lead.]

Excerpted from The American Heritage Dictionary of the English Language, Third Edition Copyright © 1992 by Houghton Mifflin Company. Electronic version licensed from Lernout & Hauspie Speech Products N.V., further reproduction and distribution restricted in accordance with the Copyright Law of the United States. All rights reserved.

Let's remember the original question: What does it mean to "deduce reality?" All the side issues only serve to push us away from what we set out to accomplish.

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I'm pretty familiar with the etymology of "deduce", also "induce". I'm saying that you should not use the word "deduce" to mean "reason". Instead, say "reason", because "deduce" has a particular meaning -- definition 2 in what you gave -- which is in fact the technical definition of the term as used in philosophy, and since Objectivism is the philosophy of Ayn Rand, it's unwise to use a word on an Objectivist discussion board with an inappropriate meaning in mind.

Let's remember the original question: What does it mean to "deduce reality?" All the side issues only serve to push us away from what we set out to accomplish.
As I said, you have to ask someone who actually says such a thing what they mean when they say it. My opinion is that it's a silly thing to say, or else insulting, and I would not want to be accused of "deducing reality". I suppose that a Kantian would consider it to be a complement. The only thing I can imagine it meaning is "making up reality a priori, with no reference to existence".
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Deduction is really a very poor way to create knowledge, and it is really only good tor making explicit the consequences of some statement that you have reason to hold true.
Why do you claim that deduction is a poor way to create knowledge? I don't claim that the opposite is true, I'm just curious.

Do you mean that deduction is a way to create knowledge but compared to induction it is an inferior way? Let's take the example you gave. Suppose someone has reached the principle that all men are mortal through generalization from observations (i.e. induction). Then a couple of days later he recognizes that Socrates is a man. I can see why the conclusion (i.e. Socrates is mortal) is logically contained in the premises but the thinker has to make a new mental integration between the general principle and the concrete observation. Would you say that the new integration constitutes new knowledge?

Or do you mean that the deduction would not have been possible without the prior induction (with which I fully agree)?

Once you grasp that consequence, you have to make observations to determine if the consequence is actually true.
Very interesting. Do you care to elaborate this point?
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Do you mean that deduction is a way to create knowledge but compared to induction it is an inferior way? Let's take the example you gave. Suppose someone has reached the principle that all men are mortal through generalization from observations (i.e. induction). Then a couple of days later he recognizes that Socrates is a man. I can see why the conclusion (i.e. Socrates is mortal) is logically contained in the premises but the thinker has to make a new mental integration between the general principle and the concrete observation. Would you say that the new integration constitutes new knowledge?

Or do you mean that the deduction would not have been possible without the prior induction (with which I fully agree)?

I have to say that I find the classic Socrates example to be really funny. Can you imagine someone suddenly realizing, a couple days after meeting Socrates, "Oh my gosh! Socrates is a man!". And then 2 minutes later exclaiming "But wait! I can integrate that fact with the inductively reached conclusion that all men are mortals; and what that tells me is something that I did not know before -- Socrates is a mortal!". I would say that deduction is inferior, as a tool for creating knowledge, to observation and induction. Let me add that since emotion or religious faith are not tools for knowledge creation at all, I have nothing to say about their role. Deduction is the weakest (thus worst) of the three tools for creating knowledge. In some cases, deduction can play an active role in making explicit the consequences of premises, but this does not happen so often (and thus deduction is less useful).

As for the issue of validating a deductively-derived conclusion, this basically affirms the primacy of existence over consciousness, so that even if you have a really iron-clad argument that all swans are white and therefore a particular swan in Alice Springs (one not yet observed) must be white, that deductive conclusion can't override the fact of the swan's blackness. The existence of the planet Neptune was deduced from certain principles of physics, yet observation was required to validate that prediction; and similarly the existence of the planet Vulcan was deduced, and observation was required to invalidate that conclusion (and thus the underlying physical principles). Deduction alone would not distinguish the case of Neptune from that of Vulcan.

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A.R.(VOS_p22): "The process of concept-formation does not consist merely of grasping a few simple abstractions, such as "chair," "table," "hot," "cold," and of learning to speak. It consists of a method of using one's consciousness, best designated by the term "conceptualizing." It is not a passive state of registering random impressions. It is an actively sustained process of identifying one's impressions in conceptual terms, of integrating every event and every observation into a conceptual context, of grasping relationships, differences, similarities in one's perceptual material and of abstracting them into new concepts, of drawing inferences, of making deductions, of reaching conclusions, of asking new questions and discovering new answers and expanding one's knowledge into an ever-growing sum. The faculty that directs this process, the faculty that works by means of concepts, is: reason. The process is thinking." (Bold added by RSalar.)

Yes, she says deduction, but right before that she says "drawing inferences," which is induction. Both are essential aspects of reasoning. Also, consider that she is not enumerating strictly separate methods, but poetically stating and restating different aspects to reasoning. (For instance, "reaching conclusions" can be either deduction or induction based on whether you are reaching a wider generalized conclusion or a narrower one about a particular concrete.) Then she summarizes all this by naming it "reasoning" (or "thinking," which is synonymous in this context).

The error about "deducing reality," at least as used in an Objectivist context, refers to the error of starting with the axioms and deducing every other piece of knowledge. On this premise of rationalism, you could deduce that man has rights knowing nothing more than that A is A. (This is a very common approach among math-oriented people.) Now it is true that you must rely on the truth that A is A to properly arrive at any conclusion, but that does not mean that that is all you need. You need to look at the facts of any given context to induce conclusions about those contexts. This means in the case of "man has rights," for instance, you need to consider all the relevant facts about man, none of which is implied in "existence exists."

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The existence of the planet Neptune was deduced from certain principles of physics, yet observation was required to validate that prediction; and similarly the existence of the planet Vulcan was deduced, and observation was required to invalidate that conclusion (and thus the underlying physical principles). Deduction alone would not distinguish the case of Neptune from that of Vulcan.

Astronomers are discovering many more extrasolar planetary systems every day! No one yet has actually observed a single one. They concluded that they exist by the way the light waves from their distant suns shift indicating a gravitationally induced wobble that could only be cause by (a) planet(s). No observation ... yet conclusive evidence has yielded new knowledge. As far as induction goes … how many times must we observe something before we can conclude with certainty that it will act the same way again? Deductive logic is 100% certain! I'd rather be called a deducer than an inducer any day!?! :-)

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As far as induction goes … how many times must we observe something before we can conclude with certainty that it will act the same way again?

This is a mistaken notion of induction. Have you read all the threads on induction on this forum? (You can search for threads whose titles contain "induction" with the search feature.) I highly suggest those if you are interested in understanding the error in your question. In particular, the argument that induction is method of causality (not counting) has been made several times. If there any specific parts of the argument that you don't understand or disagree with, I'd be happy to elaborate further.

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I have to say that I find the classic Socrates example to be really funny. Can you imagine someone suddenly realizing, a couple days after meeting Socrates, "Oh my gosh! Socrates is a man!". And then 2 minutes later exclaiming "But wait! I can integrate that fact with the inductively reached conclusion that all men are mortals; and what that tells me is something that I did not know before -- Socrates is a mortal!".
Absolutely. Admittedly, this is a simple example and you made it look ridiculous by making the thinker's thought processes explicit and overly long. But in general I don't see why deductively reached conclusions do not qualify as knowledge. Just in case: I'm not trying to defend rationalism or dimish the role of inductions.

I would say that deduction is inferior, as a tool for creating knowledge, to observation and induction. Let me add that since emotion or religious faith are not tools for knowledge creation at all, I have nothing to say about their role. Deduction is the weakest (thus worst) of the three tools for creating knowledge. In some cases, deduction can play an active role in making explicit the consequences of premises, but this does not happen so often (and thus deduction is less useful).
So you are saying that deduction is inferior to induction (and observation) because it is used less frequently. How did you arrive at that conclusion? Used less frequently by whom? For what (e.g. in science, in research, in everyday life)? And why would the worth of a form of reasoning be dependent on the frequency of its use?

As for the issue of validating a deductively-derived conclusion, this basically affirms the primacy of existence over consciousness, so that even if you have a really iron-clad argument that all swans are white and therefore a particular swan in Alice Springs (one not yet observed) must be white, that deductive conclusion can't override the fact of the swan's blackness.
So a person could inductively arrive at a principle that is true in his context of knowledge and then apply this principle deductively to a fact that is outside of his original context of knowledge and discover that the principle does not apply and thus recognize that he has reached a false conclusion. Very good point! Thank you.
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Astronomers are discovering many more extrasolar planetary systems every day! No one yet has actually observed a single one. They concluded that they exist by the way the light waves from their distant suns shift indicating a gravitationally induced wobble that could only be cause by (a) planet(s). No observation ... yet conclusive evidence has yielded new knowledge. As far as induction goes … how many times must we observe something before we can conclude with certainty that it will act the same way again? Deductive logic is 100% certain! I'd rather be called a deducer than an inducer any day!?! :-)
Why could it only be caused by planets? Why couldn't it be caused by some phenomenon not yet known? Because if there was another phenomenon causing it then the entire deduction would crumble. Deduction is not 100% certain regardless of the context.
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Why do you claim that deduction is a poor way to create knowledge? I don't claim that the opposite is true, I'm just curious.

Do you mean that deduction is a way to create knowledge but compared to induction it is an inferior way? Let's take the example you gave. Suppose someone has reached the principle that all men are mortal through generalization from observations (i.e. induction). Then a couple of days later he recognizes that Socrates is a man. I can see why the conclusion (i.e. Socrates is mortal) is logically contained in the premises but the thinker has to make a new mental integration between the general principle and the concrete observation. Would you say that the new integration constitutes new knowledge?

If I may add my two cents worth: The deduced conclusion is "new knowledge" to the deducer, but not necessarily to anyone else. And since the deductive conclusion is implicit in the premises, nothing new has been added by the deduction. In contrast, a valid induction, especially in one of the specialized fields of study like physics, may identify a new causal relationship previously unknown to anyone.

However, I would not say that deduction is inferior to induction, for that might imply that deductive conclusions are somehow less certain than inductive conclusions, which is certainly not the case. I would say that induction is more important, since all the crucial principles of philosophy are reached inductively.

Why could it only be caused by planets? Why couldn't it be caused by some phenomenon not yet known? Because if there was another phenomenon causing it then the entire deduction would crumble. Deduction is not 100% certain regardless of the context.
You seem to have deduced, with certainty, that deduction is not 100% certain. If that were the case, would it not also apply to the deduction you just made? Would that not be an example of a self-exclusionary statement?
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So you are saying that deduction is inferior to induction (and observation) because it is used less frequently. How did you arrive at that conclusion?
By observation, naturally!
Used less frequently by whom? For what (e.g. in science, in research, in everyday life)? And why would the worth of a form of reasoning be dependent on the frequency of its use?
By almost anyone, for almost any purpose. Mathematicians tend to eschew observation and induction (except for "mathematical induction" which is really a type of deductive inference), so they would be exceptions.

When you hierarchically evaluate a set of tools, you're asking what is, generally speaking, better for a given purpose across contexts. So a bucket with no hole is going to be better than a bucket with a hole, because more often -- faced with reality -- you can use the bucket with no hole in order to reach a goal, than you can use the bucket with a hole. Of course the context might arise when you need a bucket with a hole and nothing will substitute. The question is, how often does the context arise when you need a bucket with a hole? So what I'm saying is that the context where you need deduction to actual acquire knowledge is not as common.

Frequency of use directly addresses the need for a tool. The obvious counter would be the possibility of having a tool that is called on less often, but is significantly more powerful in terms of what it does for you. But that's not the case here, which is why day-to-day utility is the decisive consideration.

BTW, looking ahead (seconds before hitting "post") I want to emphasise in connection with AisA's point that utility is not to be confused with validity. Deduction is not invalid, it is simply less useful. So it is inferior, in the sense that in a hierarchy where you evaluate the goodness of tools for a purpose, deduction would be in third place, at the bottom of the list. Somebody has to be in third place if there are three things and you have a hierarchy.

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Astronomers are discovering many more extrasolar planetary systems every day! No one yet has actually observed a single one.

That isn't true. The Hubble Heritage project collects photographic images of distant bodies in the universe. Planets are among these (there's one really beautiful blue gaseous planet). It's beside the point, but inaccurate.

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Astronomers are discovering many more extrasolar planetary systems every day! No one yet has actually observed a single one.
Is this an observation? See also this. Even if it were true, I don't see how it would be relevant. Are you saying that their deductions (and photographs) are bogus (given Vulcan) or valid (given Neptune)? Actually, you're wrong about the observations, because the inferences are based on observations (of the stars). These hypothesized planets are conjectured as the explanation for the observations, just as Vulcan was conjectured. I think it's a very reasonable conclusion, but it is not certain. If Stephen were here, he might be willing to make substantive observations about what kinds of facts other than planets might imaginably explain what has been observed.
Deductive logic is 100% certain! I'd rather be called a deducer than an inducer any day!?! :-)
When did that happen? What is it certain of? Or, certain to be?

And, as Doug said, induction is not about counting cases.

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You seem to have deduced, with certainty, that deduction is not 100% certain.
I thought about David's swan example in which someone inductively and properly arrives at the principle that all swans are white and then tries to apply that principle deductively to another swan not yet observed (which could be black). As Doug pointed out, induction is not achieved by enumeration but by causal identification so the swan example could be a little misleading unless the person has identified the cause of the color. But even then, the cause of the color could be absent in a yet unknown swan. Or there could be an additional cause superseding the cause for white.

The other example was RSalar's astronomy example. From those two examples I induced that deduction is not 100% certain (regardless of context) because principles are created in a given context of knowledge but do not necessarily have to apply to facts that are only known in a bigger context of knowledge.

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By almost anyone, for almost any purpose. Mathematicians tend to eschew observation and induction (except for "mathematical induction" which is really a type of deductive inference), so they would be exceptions.

When you hierarchically evaluate a set of tools, you're asking what is, generally speaking, better for a given purpose across contexts. So a bucket with no hole is going to be better than a bucket with a hole, because more often -- faced with reality -- you can use the bucket with no hole in order to reach a goal, than you can use the bucket with a hole. Of course the context might arise when you need a bucket with a hole and nothing will substitute. The question is, how often does the context arise when you need a bucket with a hole? So what I'm saying is that the context where you need deduction to actual acquire knowledge is not as common.

Frequency of use directly addresses the need for a tool. The obvious counter would be the possibility of having a tool that is called on less often, but is significantly more powerful in terms of what it does for you. But that's not the case here, which is why day-to-day utility is the decisive consideration.

I have to admit that I am not exceptionally good at introspection when it comes to methods of reasoning. But I still find it hard to believe that induction is used more often than deduction. One of the typical everyday-life situation that I thought of is driving a car: one knows a set of principles (obey the traffic rules, don't collide with other objects, etc.) and applies them to a given situation. Or consider language: one knows - implicitly or explicitly - a set of rules for properly forming sentences and then just applies them.
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Is this an observation? See also this. Even if it were true, I don't see how it would be relevant. Are you saying that their deductions (and photographs) are bogus (given Vulcan) or valid (given Neptune)? Actually, you're wrong about the observations, because the inferences are based on observations (of the stars). These hypothesized planets are conjectured as the explanation for the observations, just as Vulcan was conjectured. I think it's a very reasonable conclusion, but it is not certain. If Stephen were here, he might be willing to make substantive observations about what kinds of facts other than planets might imaginably explain what has been observed.

Back to "deduced reality" for a moment … it was hypothesized that by deducing realty I may somehow be conjuring reality up out of thin air. How is it possible to make a deductive conclusion about anything if you do not start with an observation? The only source if information about the outside world is through our senses. Take a newborn baby and clip the connections from all of its sensory organs so that its brain can pick up nothing from its body or the outside world -- how much deducting will this human being ever be able to do? Zippo!

The astronomers that I mentioned who are discovering new planets in other solar systems do not directly observe these planets; instead they conclude (based on both inductive and deductive logic) that they MUST be there. There is no other explanation for the observed phenomenon.

Without deductive reasoning there would be no mathematics, and without mathematics all the sciences that depend on mathematics would be reduced to only that which can be directly observed—a mere tiny fraction of what these sciences are today.

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The astronomers that I mentioned who are discovering new planets in other solar systems do not directly observe these planets; instead they conclude (based on both inductive and deductive logic) that they MUST be there. There is no other explanation for the observed phenomenon.
Suppose someone was murdered and you want to find out who the murderer is. You have three suspects: the victim's wife, the victim's son and the neighbor. After interrogating the suspects you have found out that two of them have an aliby. Thus you conclude that the third suspect is the murderer.

Can you see anything wrong with this type of reasoning? If so, what?

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How is it possible to make a deductive conclusion about anything if you do not start with an observation?
Yes, this is exactly right. Every deduction is based on observation and induction (of a principle). That's what puts deduction in third place.
Without deductive reasoning there would be no mathematics, and without mathematics all the sciences that depend on mathematics would be reduced to only that which can be directly observed—a mere tiny fraction of what these sciences are today.
This is often claimed, but I don't see any way to check the claim. It is certainly a fact that deduction is central to mathematical proofs as they are done now. But you aren't just making a historical observation, you making a universal claim: that the essential methods of mathematics that are the foundation of science could not be arrived at any other way, for example, that experimental mathematics is an absolute impossibility. I have no idea how you could ever prove such a claim.
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This is often claimed, but I don't see any way to check the claim. It is certainly a fact that deduction is central to mathematical proofs as they are done now. But you aren't just making a historical observation, you making a universal claim: that the essential methods of mathematics that are the foundation of science could not be arrived at any other way, for example, that experimental mathematics is an absolute impossibility. I have no idea how you could ever prove such a claim.

All mathematics is is a language of symbols used to identify relationships between units that exist in reality. Reality is what reality is. The language we use to identify it does not change what reality is. If another intelligent life form has evolved in another part of the universe they might symbolize the number 1 with #, and the number 2 with %, instead of using + to represent addition they might symbolize it with >, and instead of = they might use @. The symbols would not change the fact that # > # @ %. The relationship is not affected by the symbols used to represent it. If this were not universally true then reality would not be real.

Can you see anything wrong with this type of reasoning? If so, what?

The problem with that type of reasoning is that it misses the point.

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All mathematics is is a language of symbols used to identify relationships between units that exist in reality. Reality is what reality is. The language we use to identify it does not change what reality is.
I don't see how that constitutes an argument that mathematical methods can only be discovered by deductive inference.
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I don't see how that constitutes an argument that mathematical methods can only be discovered by deductive inference.

I tried to find where someone said that, "mathematical methods can only be discovered by deductive inference," but was unable to. I said (post #20): "Without deductive reasoning there would be no mathematics..." By that I mean that math is deductive. Are you saying that because it may be possible to discover another method, other than deductive inference, to describe the relationship between integers, that my statement is not universally true? Based on that principle no statement is universally true, because in all cases there exists the possibility that there might be an exception discovered someday (even though we have no way to show that there might be an exception).

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