Chapter 8 Inference and the Extension of Knowledge
This page is part of my self study project into philosophy. What is written are my own personal notes taken as a means of formalizing what I've read and/or learned. The information may not be accurate, as I may have took away the wrong points. Also the information could be basic or partial - as learning requires taking on small parts before getting deeper. The content may be a tad scatterbrain as well. Either way, it should be an interesting read and maybe you'll learn something with me.
Take the following example to start:
I hear knocking. I wonder if someone is at the door. I then hear extended and very rapid knocking. It now occurs to me that this is a pecking sound, and I conclude there is a woodpecker nearby.
We can see that the way of coming to believe something differs from the way I came to believe there was knocking in the first place. The belief was perceptual - coming from hearing knocking. The belief there there is a woodpecker nearby is not perceptual. It arises, not perceptually (as in seeing the bird), but from further belief: that the rapid knocking sound - it's character - and came to believe that it sounds like a woodpecker.
An inference (which is like a kind of reasoning) proceed by way of something general (or specific) to something specific (or general).
- 1 The Process, Content and Structure
- 2 Reasoned Belief and Belief for a Reason
- 3 Two Ways Beliefs may be Inferential
- 4 Direct and Indirect Belief
- 5 The Development of Belief, Justification and Knowledge
- 6 Source Conditions & Transmission Conditions for Inferential Knowledge and Justification
- 6.1 Deductive and Inductive Inference
- 6.2 Subsumptive and Analogical Inference
- 6.3 Inferential Transmission of Justification & Knowledge
- 6.4 Inductive Transmission & Probabilistic Inference
- 6.5 Some Inferential Transmission Principles
- 6.6 Deductive Transmission of Justification & Knowledge
- 6.7 Degrees and Kinds of Deductive Transmission
- 7 Memorial Preservation of Inferential Justification and Knowledge
The Process, Content and Structure
Basically with the woodpecker example, one is saying on the basis of my belief, the knocking sound like that of a woodpecker's pecking, I conclude that there is a woodpecker nearby. One is inferring that there is one nearby from what is believed about the knocking.
What is concluded, in some sense derive from something else I believe. The concluding and the beliefs are mental, but neither what I conclude, nor what I believe from which I conclude it, is mental: these things are contents of my beliefs, as they might be of yours. They are not properties of anyone's mind, as in some sense beliefs themselves are. Such contents of beliefs are commonly thought to be propositions (or statements, hypothesis, etc). This can be considered objects of beliefs.
There are two senses of inference:
- Inferential process: is concluding it on the basis of one or more of my beliefs or assumptions. It is a mental episode of reasoning.
Example: I conclude Albert was bitten by a deer tick on the basis of my belief (just acquired) that he has Lyme disease and my back ground belief that this is caused by deer tick bites.
- Inferential Content: is abstract and not a process. Drawing a conclusion is the set of two or more propositions, which are my conclusions and my ground for it.
Inferential content indicates what is inferred from what - a conclusion from one or more premises. Inferential process is getting to the conclusion from one or more premises.
Reasoned Belief and Belief for a Reason
So inferring is a type of reasoning, but it is not necessarily self conscious. Sometimes we have to reason (infer) to a conclusion, but in other ways, we just conclude that a woodpecker is nearby without a process.
A reasoned belief is one reasoned and based on that reasoning.
Example: I wonder what I hear. It sounds like pecking. I infer a woodpecker is nearby.
A belief for a reason is more of an automatic or non-inferential belief. It's held for a reason, but at the time of the belief it's not reasoned.
Example: Taking the woodpecker example. Let's suppose that overtime you've experienced this knocking. Eventually you're eating supper, hear the knocking, and without any distraction form eating, you believe a woodpecker is nearby. This view is automatic, and it's not reasoned, but the belief is held for a reason as being quite familiar with the woodpecker sound.
The idea here is that you can have a reasoned belief retained by memory. After time you may forget the premises of the reasoning are forgotten. Even if the premises of the reasoning is forgotten. Even if the premises are not forgotten, one no longer reasons upon learning the pecking sound, they just have the non-inferential belief (belief for a reason).
Two Ways Beliefs may be Inferential
Episodically Inferential: Take the example of the reasoned belief that there is a woodpecker nearby (considered at the time I formed it). At the time it arises from a process or episode of inferring - explicitly drawing a conclusion from something one believes.
Structurally Inferential: The example where one knows it is a woodpecker by an automatic belief. A belief for a reason. It's not episodically inferential, it is nonetheless based on another belief in the way one belief is based on a sound.
Thank of the first as I do something and the second just happens in me. An episodically inferential belief at the time it is formed will become structurally inferential when it is retained.
Direct and Indirect Belief
You can see how a belief can be inferentially based without being episodically inferential, in such a case where are believes something first perceptually. Suppose you think you saw Aaron at the mall. You didn't get the best look, but nonetheless believe you see him. Suppose you later get testimony from a friend that they met Aaron's wife at the mall. Now you believe you saw Aaron on the basis of this testimony and what you saw. This is like a structural inference because the testimony isn't reasoned, but merely evidence or structural holding up the belief.
The two kinds of inferential belief are indirect. We believe on thing on the basis of believing another. Direct belief wouldn't be a belief based off another belief. Different people could hold the same belief; one through indirect and the other direct.
The Development of Belief, Justification and Knowledge
Confirmatory vs Generative Inferences
Inference is typically a source of new beliefs, but it need not be. Confirmatory inference is as it sounds. It adds to the belief system by confirmation of what is already believed. Generative inference is one that creates a new belief.
Inference as a Dependent Source of Justification & Knowledge
My inference justifies me in believing my conclusion only if I'm justified in believing the premise(s). Since one could be justified in believing a premise, that could be false, inference isn't a basic source of knowledge.
It is rather that it transmits and thereby extends them from one or more premises to the conclusion inferred from them. There are two kinds of inferential enhancement of knowledge and justification.
- (1) Inferential Extension: Yields an increase in the content of what we know or are justified in believing.
- (2) Inferential Strengthening: Yields an increase in the quantity of our justification regarding the same content - or in the strength of our grounds for knowledge regarding the same content.
Source Conditions & Transmission Conditions for Inferential Knowledge and Justification
If inference is not a basic source of justification and knowledge, but transmits it, it must meet two kinds of conditions. One concerns the premise(s) of the inference - its foundations. The second concerns the relation of the premise(s) to the conclusion - how well the evidential pillars support what is built on them - ie: whether they express strong evidence for believing it.
First there are source conditions, as one needs justification or knowledge in the first place. So if you're of the belief that the knocking sound means a person at the door and you're completely unaware of a pecking sound. One has started with knowledge, but it didn't transmit to the belief of the conclusion.
This means there are transmission conditions as well a source conditions, that an inference must meet in order to yield knowledge of its conclusion. The first 7 chapters dealt with the source conditions - like perception - so that focus will be on transmission conditions.
Deductive and Inductive Inference
Take the following: I reasoned from the premises that (1) the noise represented a backfire and (2) if it did represent that, then there was a vehicle backfire, to the conclusion that (3) there was a vehicle backfire.
This argument (like inferring) is from the premise of the argument to its conclusion is (deductively) valid - since it's impossible for premise (1) and (2) to be true and (3) false. The premises of a deductive (valid) arguments can be false, but it's absolutely impossible for the premises to be true and the conclusion false. The term valid is only applied to deductive arguments.
Take the following: (1) the noise sounds like that of a backfire; (2) the likeliest explanation of the noise is that of a vehicle backfire; probably then (3) a vehicle backfired.
The word "probably" indicates this isn't valid or deductive. Even based on the premises, without the word probably, it wouldn't be deductive. This type of probabilistic reasoning is "inductively valid" meaning (roughly) that relative to it's premise there is a high probability that its conclusion is true. Could also be referred to as inductively good or inductively strong.
Subsumptive and Analogical Inference
Subsumptive Reasoning (or instantial reasoning) is to draw a conclusion about something or someone by subsuming the thing or person under a generalization about similar entities, say people. Since Socrates is a person. All people are mortal. Therefore Socrates is mortal. This is deductive reasoning.
Inductive reasoning - as reasoning that aims at providing good grounds for its conclusion, but not validity. Secondly is best evaluated in terms of degree of probability of its conclusion relative to its premises.
Analogous is concluding that a plant probably has a property, has roots, because it is much like (analogous to) another plant that has that property.
Abduction would be inferring b as an explanation about a.
Inferential Transmission of Justification & Knowledge
The natural thing to say initially is that justification and knowledge are transmitted in deductive inferences only if the underlying argument is valid and, inductive inference, only if the underlying argument is (inductively) good. These principles are correct, but needs clarification: bad reasoning doesn't lead to transmission.
Take the example that Chris produces the argument (1) all opera lovers appreciate The Magic Flute and (2) Will appreciates it The Magic Flute (3) Will is an opera lover. This is invalid deductive reasoning and even with true premises that premises that Chris is justified in believing - it would not transmit either justification or knowledge from his beliefs of them (premises) to his belief of its conclusion. IE: Bad reasoning.
Inductive Transmission & Probabilistic Inference
Inductive reasoning is more complicated. Good inductive reasoning is a bit vague. If probability is what is more likely to be true, but what does that mean? A probability over 0.5 (above 50-50). But if we're talking about a probability of 0.5+ (the cusp of crossing the 50-50) is literally as likely to be wrong as it is right. One wouldn't want to describe reasoning as good at the 0.5+ point.
There is also the aspect of additional premises and information that can change the probability. Let's say you have "X" cancer and the probability of death is 0.6. This would be a fair conclusion - you will die from cancer. But suppose there are more pieces of information. Being young, athletic and receiving new treatment options the probability of death is 0.08. The point being is that you can reach a conclusion above 0.6, but without considering relevant evidence.
One may assume that good inductive reasoning has reasoning has premises taking account of all relevant evidence. The problem here is that one probably can't get all relevant evidence, but also does one need all relevant evidence to make a conclusion. This is promising for a single chain of premises. What about inferences that lead to premises in other inferences.
Take for example that inference (1) has a probability of 0.75 and the next inference in the chain is 0.6. Simple math shows that the probabilities together are 0.45. So is one justified? It would fail to transmit justification from its premises to the conclusion.
Some Inferential Transmission Principles
To understand transmission of justification and knowledge we must consider two sorts of conditions: necessary conditions for transmission of knowledge and justification, conditions such that transmission occurs only if they are met by an inference; and sufficient conditions, those such that if they are met by an inference, then transmission occurs.
Sufficient conditions are much harder to specify then necessary ones - since sufficient conditions must cover all necessary ones: if it does not imply that each of them holds, it leaves out something necessary, and so is not sufficient.
Consider the inductive transmission principle: if by good inductive reasoning, one infers something from premises which take account of all the relevant evidence, then if one is justified in believing those premises, one is justified in believing the conclusion.
Deductive Transmission of Justification & Knowledge
The simple deductive transmission principle for knowledge: that if (at a given time) you validly infer a proposition from an inferential ground you know (and believe it on the ground), then you know this proposition.
Degrees and Kinds of Deductive Transmission
A qualified deductive transmission principle for justification holds; typically, valid reasoning from justified beliefs transmits justification to its conclusion belief.
A qualified deductive transmission principle for knowledge holds; typically valid reasoning from known premises transmits knowledge to its conclusion (where the conclusion belief is based on the premise belief(s) as would be normal).
Memorial Preservation of Inferential Justification and Knowledge
There are cases where you can remember the premises and conclusion, but not the grounds - as in how to work a theorem or the book information came from. Your memory can retain beliefs as knowledge and as justified beliefs. The difference is that it no longer retains the inferential grounds and as such does not necessarily retain the beliefs as inferential. The point being is that an inferential belief at one time may be non-inferential at another.