Is it correct to say that inferences are subjective at all times because they are always made by individual minds and depend on a range of factors influencing those particular minds?
Or can inferences be somehow objective?
The originating context of this question is the making of inferences of fact based on circumstantial evidence by legal triers of fact (e.g. a jury or a judge in the absence of a jury). But the question is not aimed to be tied to that context.
Part of the issue here is terminological. Inferences, at least in the ordinary sense of the term, are things that happen in the minds of rational agents. An agent believes some A, or maybe some A, B, C, ..., and considers that this provides a ground, reason, or justification for accepting Z, and so can be said to infer Z from the given premises. So, inferences are made by individuals and as such are subjective.
One rational agent may attach more weight to some premise than another agent, or may believe that some premise is too unlikely to be plausible, or may judge that it is more likely that the conclusion is false than that all the premises are true. In the context of a jury, some jurors may be more swayed by a convincing testimony than others, while others might give more weight to physical evidence. Some might disregard forensic evidence if they don't understand it. Some might choose to ignore a witness if they believe the witness lacks credibility. Even if the jurors agree on the evidence, they may differ in whether it justifies a verdict beyond reasonable doubt.
However, the term inference is often used within logic to refer to a formal deduction. Logicians use the term rule of inference to refer to the rules of a formal system that allow one proposition to be deduced from others. Such rules are not subjective in nature: the rules of a logic apply without exception. This terminology is unfortunate and several logicians, such as Gilbert Harman, have long argued that we should drop the term rule of inference and replace it with rule of implication. Logicians learned over a hundred years ago to separate logic from psychology, but the use of inference in this way is a hangover.
So, if by inference you mean the activity of rational agent in coming to believe something on the grounds of other beliefs, then inferences are typically subjective. Even if you use formal logic to deduce B from A, the logic itself will not tell you whether it is more plausible to believe both or to believe neither. This is sometimes expressed by the phrase: one person's modus ponens is another person's modus tollens.
On the other hand, if you follow the convention of using inference to mean a logical deduction, then there are agreed standards for such things. However, deduction is not the only kind of inference. There is abductive and inductive reasoning, there is reasoning by analogy, statisitical inference, etc. The kind of reasoning that occurs in a courtroom is often of the abductive kind. A criminal case might be concerned with establishing whether the guilt of the defendant provides the best explanation of the evidence.
Is it correct to say that inferences are subjective at all times (...)?
The inference you make is irremediably subjective, but it may become an objective fact that a number of other individuals agree with your inference. If so, your inference remains subjective but it is at the same time an objective fact that other people at least seem to agree with it.
This applies to everything we think. It is an objective fact that many people at least claim to believe in God, and this even though each of them only has a subjective belief that God exists (since there is no objective proof that it does).
Here is the relevant dictionary definition of "objective":
Objective b. Based on observable phenomena; empirical: objective facts.
When reasoning about non-formal things like the material world, an inference can be called "objective given commonly agreed upon facts and thinking methods" if there is such a set of agreed upon facts and methods, and if those facts and methods only allow a single conclusion. This is also bound to the people involved (those who agree on those facts and methods).
When an inference requires additional facts that are not agreed upon (or the exclusion of such facts), then it is known to not be objective based on the commonly agreed upon facts.
This definition of "objectivity" allows to usefully distinguish between subjective and objective definitions in the real life. This also changes an inference from "objective" to "subjective" when new facts arise, or even from subjective to objective when previously agreed upon facts are not agreed upon anymore.
However it would seem that no inference could ever be made objectively when increasing the number of people that have to agree about facts. With enough humans included, there is bound to always be individuals and small groups which will disagree about facts for one reason or another. So for sufficiently big groups of humans (hundreds, thousands or millions) and sufficiently complex topics, it is more useful to define objectivity not based on the agreement of all people about a matter, but of a (sufficiently large and diverse) subgroup of "unbiased, qualified people".
Something similar happens in a jury selection process where from an initial large set of people, defendants and prosecution will eliminate the most biased (or unqualified) people until a smaller set of sufficiently many individuals is left to make a legal decision.
Or it happens in cosmology when leaving the inference about the history of the universe to experts in the field drawn from diverse nations and institutions.
If the selection process is deemed sufficiently fair, inferences can still be called "objective" given the subgroup of people who agreed upon facts, even if there will be other people left who disagree about the facts used for the inference. But that is a weaker definition of objectivity than one which includes all people involved.
Logical inference ought to be OBJECTIVELY TRUE. By objective I mean ideas that reflect the real world that are independently true of human beings. By that I mean a proposition is not simply TRUE because I say so or some one with prestige says so. That is, we are not looking for a human being with authority over other humans like a drill sergeant is an authority over recruits. We are not seeking a politician with several graduate degree to know if something is true or not. We are not looking for superiors at the workplace to find out if something is true or false. Triangles would have three sides even if the authorities were to disappear. We do not need someone pulling rank over us to order us around. The Sun is a STAR is a true proposition independently of any human being; triangles have exactly three sides is true independently of what human beings believe, All women are human beings is true independently and so on.
Logical inferences were developed to be truth preserving. If the inference is true in all cases there should be no instance of the inference yielding a false conclusion. All cases means 100 percent of the time and nothing less. An inference that is true 88 percent is not reliable. How would you know if this percent is one of the correct answers or not? For instance, Demorgan's Law is 100 percent accurate. Each time we use it, we know the formula we get must be correct OR we applied the rule incorrectly with human error. The main idea is if we have true premises and use the inference rules correctly we cannot derive a false conclusion because the rules are objective.
Subjective on the other hand opens the window of errors to occur. Subjective means there are no 100 percent answers by definition. All answers must be less than 100 percent or they would be absolutes (aka objective). Subjective indicates a lower percentage than 100 --that is 99 percent all the way down to 1 percent. Zero is an absolute also and not subjective. For instance, No odd numbers are divisible by 2 indicates there are zero odd numbers being divisible by the number 2. No dogs are cats also indicates zero dogs are cats. So we can conclude the absolutes are 100 percent and zero. Subjective is the rest of the probabilities left over.
Subjective also carries the connotation that emotions are part of the answer too. For instance, Butter pecan ice cream from Hagen Dazs is the best ice cream on Earth is subjective. Surely it is not 100 percent accurate right? Blue is the best color is also not 100 percent accurate. If our inference rules were subjective how would we know if this is a true instance of it or are you making a human error? Your conclusion , if true, would be by accident. Some people are blessed in that they get the correct conclusion but have no clue how they obtained it. When we use majority voting or surveys to decide results we also indicate there are percentages involved and different people with emotion and experiences who will differ in response. This is not as reliable as absolutes. With absolutes there are no doubts. By absolute I mean the truth value does not change and cannot change ever. A formal system has the beauty of checks and balances. If I show a formal proof to an educated and informed audience, there will hopefully be feedback. So if I do err, someone will be able to show exactly where the error is in the proof: what line number, why the inference is wrong, what would fix the error, etc. We want checks and balances instead of a dictator like Hitler to tell us what is Valid from Invalid, True from False, What is Good and Bad and so on. We want objectivity. This is more reliable than emotion or feeling and beliefs.
